Topic: Ozan's 159-edo-based tuning
4 scales
| File | Description | Notes | Period (¢) |
|---|---|---|---|
| guiron77 | Guiron[77] (118&159 temperament) in 159-et | 77 | 1200.0 |
| octoid72 | Octoid[72] in 224-et tuning | 72 | 1200.0 |
| octoid80 | Octoid[80] in 224-et tuning | 80 | 1200.0 |
| ozan80 | Ozan[80] (80&159 temperament) in 159-et | 80 | 1200.0 |
Thread (207 messages)
From: monz (2006-02-16) Subject: Ozan's 159-edo-based tuning Hi Oz, Please post either the details of your subset-of-159-edo tuning, or links to previous posts containing them. Thanks. I want to make some Tonescape files of it. -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-02-16) Subject: Re: [tuning] Ozan's 159-edo-based tuning Dear monz, my tuning scheme involves 33 equal divisions of the pure fourth. 1. [log (4/3) * 1200]/(log 2) divided by 33 = 15.092272701048866128954947492807 cents. 2. Carry the comma to the 79th step and you reach 1192.2895433828604241874408519317 cents. 3. Complete the octave to 1200 cents and move the 22.802729318188441941514095561079 cent comma between steps 45-46. You do this by key transposing the tuning to the -46th step. Voila! You now have a circulating temperament which is practically a subset of 159-tET. There are three sizes of fifths by which one can formulate diatonical scales: 0: 1/1 C RAST 1: 15.092 cents C/ 2: 30.185 cents C// 3: 45.277 cents C^ Db( 4: 60.369 cents C) Dbv 5: 75.461 cents C#\ Db\\ 6: 90.554 cents C# Db\ 7: 105.646 cents C#/ Db 8: 120.738 cents C#// Db/ 9: 135.830 cents C#^ D( 10: 150.923 cents C#) Dv 11: 166.015 cents D\\ 12: 181.107 cents D\ 13: 196.200 cents D DUGAH 14: 211.292 cents D/ Dugah again 15: 226.384 cents D// 16: 241.476 cents D^ Eb( 17: 256.569 cents D) Ebv 18: 271.661 cents D#\ Eb\\ 19: 286.753 cents D# Eb\ 20: 301.845 cents D#/ Eb 21: 316.938 cents D#// Eb/ 22: 332.030 cents D#^ E( 23: 347.122 cents D#) Ev 24: 362.215 cents E\\ 25: 377.307 cents E\ lower segah 26: 392.399 cents E SEGAH 27: 407.491 cents E/ Fb Buselik 28: 422.584 cents E// Fb/ Nishabur 29: 437.676 cents E^ F( 30: 452.768 cents E) Fv 31: 467.860 cents E#\ F\\ 32: 482.953 cents E# F\ 33: 498.045 cents F CHARGAH 34: 513.137 cents F/ 35: 528.230 cents F// 36: 543.322 cents F^ Gb( 37: 558.414 cents F) Gbv 38: 573.506 cents F#\ Gb\\ 39: 588.599 cents F# Gb\ 40: 603.691 cents F#/ Gb 41: 618.783 cents F#// Gb/ 42: 633.875 cents F#^ G( 43: 648.968 cents F#) Gv 44: 664.060 cents G\\ 45: 679.152 cents G\ 46: 701.955 cents G NEVA 47: 717.047 cents G/ 48: 732.140 cents G// 49: 747.232 cents G^ Ab( 50: 762.324 cents G) Abv 51: 777.416 cents G#\ Ab\\ 52: 792.509 cents G# Ab\ 53: 807.601 cents G#/ Ab 54: 822.693 cents G#// Ab/ 55: 837.785 cents G#^ A( 56: 852.878 cents G#) Av 57: 867.970 cents A\\ 58: 883.062 cents A\ Hisar 59: 898.155 cents A HUSEYNI/Hisarek 60: 913.247 cents A/ Huseyni again 61: 928.339 cents A// 62: 943.431 cents A^ Bb( 63: 958.524 cents A) Bbv 64: 973.616 cents A#\ Bb\\ 65: 988.708 cents A# Bb\ 66: 1003.800 cents A#/ Bb 67: 1018.893 cents A#// Bb/ 68: 1033.985 cents A#^ B( 69: 1049.077 cents A#) Bv 70: 1064.170 cents B\\ 71: 1079.262 cents B\ 72: 1094.354 cents B EVDJ 73: 1109.446 cents B/ Cb Mahur 74: 1124.539 cents B// Cb/ Mahurek (my proposal) 75: 1139.631 cents B^ C( 76: 1154.723 cents B) Cv 77: 1169.815 cents B#\ C\\ 78: 1184.908 cents B# C\ 79: 1200.000 cents C GERDANIYE Some degrees yield excellent 11 limit results, while others produce adorable 5 limit and sufficiently close 7 limit intervals. I had implemented this tuning on my special Qanun, and also installed Wittner fine-tuners to the strings for accuracy of pitch. Although my hands are still numb from all that tuning, I am very pleased, and so are Qanun performers who were "unfortunate" enough to have met me. Cordially Oz. ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 16 \ufffdubat 2006 Per\ufffdembe 11:19 Subject: [tuning] Ozan's 159-edo-based tuning > Hi Oz, > > > Please post either the details of your subset-of-159-edo tuning, > or links to previous posts containing them. Thanks. > > I want to make some Tonescape files of it. > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > >
From: monz (2006-02-16) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, Thanks for posting those details. I still have some questions: --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Dear monz, my tuning scheme involves 33 equal divisions > of the pure fourth. > > 1. [log (4/3) * 1200]/(log 2) divided by 33 = > 15.092272701048866128954947492807 cents. > > 2. Carry the comma to the 79th step and you reach > 1192.2895433828604241874408519317 cents. > > 3. Complete the octave to 1200 cents and move the > 22.802729318188441941514095561079 cent comma between > steps 45-46. This isn't clear to me. I see that the final step, between ~1192 cents and the octave, is ~7.710456617 cents, and that that plus one step of ~15.0922727 cents is the ~22.8027293-cent "comma". But doesn't "completing the octave" eliminate that and leave you only with the smaller ~7.7-cent step? > You do this by key transposing the tuning to the -46th step. You started from zero and went upwards to the 79th step. So what's the "-46th step"? I tried constructing steps of ~15.092 cents backwards into the negative numbers, then transposed, but i didn't get the same results you did. There's no ~3/2 ratio in mine. -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-02-16) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning monz, ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 16 \ufffdubat 2006 Per\ufffdembe 19:56 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Hi Oz, > > > Thanks for posting those details. > I still have some questions: > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Dear monz, my tuning scheme involves 33 equal divisions > > of the pure fourth. > > > > 1. [log (4/3) * 1200]/(log 2) divided by 33 = > > 15.092272701048866128954947492807 cents. > > > > 2. Carry the comma to the 79th step and you reach > > 1192.2895433828604241874408519317 cents. > > > > 3. Complete the octave to 1200 cents and move the > > 22.802729318188441941514095561079 cent comma between > > steps 45-46. > > > This isn't clear to me. I see that the final step, > between ~1192 cents and the octave, is ~7.710456617 cents, > and that that plus one step of ~15.0922727 cents is the > ~22.8027293-cent "comma". But doesn't "completing the octave" > eliminate that and leave you only with the smaller ~7.7-cent > step? > Aie. What I meant is that you replace 1192 cents with 1200 cents. You know, move it up a notch so that the octave is pure. > > You do this by key transposing the tuning to the -46th step. > > > You started from zero and went upwards to the 79th step. > So what's the "-46th step"? > Given the octave equivalance of 0 cents = 1200 cents, key transposing the scale over to the -46th step is equivalent to transposing it to the 33rd step. You are, in effect moving the larger `comma` between the 45.-46. steps. > I tried constructing steps of ~15.092 cents backwards > into the negative numbers, then transposed, but i didn't > get the same results you did. There's no ~3/2 ratio in mine. > > > If you are using scala do this: 1. File>New>Equal temperament, division 33, formal octave 4/3, number of tones 79. 2. Edit the 79th degree pitch and type 1200.0 from the Edit Window 3. Modify>Key>To degree 33, or else, -46. 2. Set nota E79 Voila! > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > > Oz.
From: Carl Lumma (2006-02-16) Subject: Re: Ozan's 159-edo-based tuning Ozan, Have you ever tried recording your Qanun? It sounds like a marvelous instrument! -Carl > Dear monz, my tuning scheme involves 33 equal divisions of the > pure fourth. > > 1. [log (4/3) * 1200]/(log 2) divided by 33 = > 15.092272701048866128954947492807 cents. > > 2. Carry the comma to the 79th step and you reach > 1192.2895433828604241874408519317 cents. > > 3. Complete the octave to 1200 cents and move the > 22.802729318188441941514095561079 cent comma between steps 45-46. > You do this by key transposing the tuning to the -46th step. > > Voila! You now have a circulating temperament which is practically > a subset of 159-tET. There are three sizes of fifths by which one > can formulate diatonical scales: > > 0: 1/1 C RAST > 1: 15.092 cents C/ > 2: 30.185 cents C// > 3: 45.277 cents C^ Db( > 4: 60.369 cents C) Dbv > 5: 75.461 cents C#\ Db\\ > 6: 90.554 cents C# Db\ > 7: 105.646 cents C#/ Db > 8: 120.738 cents C#// Db/ > 9: 135.830 cents C#^ D( > 10: 150.923 cents C#) Dv > 11: 166.015 cents D\\ > 12: 181.107 cents D\ > 13: 196.200 cents D DUGAH > 14: 211.292 cents D/ Dugah again > 15: 226.384 cents D// > 16: 241.476 cents D^ Eb( > 17: 256.569 cents D) Ebv > 18: 271.661 cents D#\ Eb\\ > 19: 286.753 cents D# Eb\ > 20: 301.845 cents D#/ Eb > 21: 316.938 cents D#// Eb/ > 22: 332.030 cents D#^ E( > 23: 347.122 cents D#) Ev > 24: 362.215 cents E\\ > 25: 377.307 cents E\ lower segah > 26: 392.399 cents E SEGAH > 27: 407.491 cents E/ Fb Buselik > 28: 422.584 cents E// Fb/ Nishabur > 29: 437.676 cents E^ F( > 30: 452.768 cents E) Fv > 31: 467.860 cents E#\ F\\ > 32: 482.953 cents E# F\ > 33: 498.045 cents F CHARGAH > 34: 513.137 cents F/ > 35: 528.230 cents F// > 36: 543.322 cents F^ Gb( > 37: 558.414 cents F) Gbv > 38: 573.506 cents F#\ Gb\\ > 39: 588.599 cents F# Gb\ > 40: 603.691 cents F#/ Gb > 41: 618.783 cents F#// Gb/ > 42: 633.875 cents F#^ G( > 43: 648.968 cents F#) Gv > 44: 664.060 cents G\\ > 45: 679.152 cents G\ > 46: 701.955 cents G NEVA > 47: 717.047 cents G/ > 48: 732.140 cents G// > 49: 747.232 cents G^ Ab( > 50: 762.324 cents G) Abv > 51: 777.416 cents G#\ Ab\\ > 52: 792.509 cents G# Ab\ > 53: 807.601 cents G#/ Ab > 54: 822.693 cents G#// Ab/ > 55: 837.785 cents G#^ A( > 56: 852.878 cents G#) Av > 57: 867.970 cents A\\ > 58: 883.062 cents A\ Hisar > 59: 898.155 cents A HUSEYNI/Hisarek > 60: 913.247 cents A/ Huseyni again > 61: 928.339 cents A// > 62: 943.431 cents A^ Bb( > 63: 958.524 cents A) Bbv > 64: 973.616 cents A#\ Bb\\ > 65: 988.708 cents A# Bb\ > 66: 1003.800 cents A#/ Bb > 67: 1018.893 cents A#// Bb/ > 68: 1033.985 cents A#^ B( > 69: 1049.077 cents A#) Bv > 70: 1064.170 cents B\\ > 71: 1079.262 cents B\ > 72: 1094.354 cents B EVDJ > 73: 1109.446 cents B/ Cb Mahur > 74: 1124.539 cents B// Cb/ Mahurek (my proposal) > 75: 1139.631 cents B^ C( > 76: 1154.723 cents B) Cv > 77: 1169.815 cents B#\ C\\ > 78: 1184.908 cents B# C\ > 79: 1200.000 cents C GERDANIYE > > Some degrees yield excellent 11 limit results, while others > produce adorable 5 limit and sufficiently close 7 limit > intervals. I had implemented this tuning on my special Qanun, > and also installed Wittner fine-tuners to the strings for > accuracy of pitch. Although my hands are still numb from all > that tuning, I am very pleased, and so are Qanun performers > who were "unfortunate" enough to have met me. > > Cordially > Oz.
From: Joe (2006-02-16) Subject: Re: Ozan's 159-edo-based tuning I would like to hear it as well, oh Ambassador of the Qanun. --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > Ozan, > > Have you ever tried recording your Qanun? It sounds like a > marvelous instrument! > > -Carl > > > Dear monz, my tuning scheme involves 33 equal divisions of the > > pure fourth. > > > > 1. [log (4/3) * 1200]/(log 2) divided by 33 = > > 15.092272701048866128954947492807 cents. > > > > 2. Carry the comma to the 79th step and you reach > > 1192.2895433828604241874408519317 cents. > > > > 3. Complete the octave to 1200 cents and move the > > 22.802729318188441941514095561079 cent comma between steps 45-46. > > You do this by key transposing the tuning to the -46th step. > > > > Voila! You now have a circulating temperament which is practically > > a subset of 159-tET. There are three sizes of fifths by which one > > can formulate diatonical scales: > > > > 0: 1/1 C RAST > > 1: 15.092 cents C/ > > 2: 30.185 cents C// > > 3: 45.277 cents C^ Db( > > 4: 60.369 cents C) Dbv > > 5: 75.461 cents C#\ Db\\ > > 6: 90.554 cents C# Db\ > > 7: 105.646 cents C#/ Db > > 8: 120.738 cents C#// Db/ > > 9: 135.830 cents C#^ D( > > 10: 150.923 cents C#) Dv > > 11: 166.015 cents D\\ > > 12: 181.107 cents D\ > > 13: 196.200 cents D DUGAH > > 14: 211.292 cents D/ Dugah again > > 15: 226.384 cents D// > > 16: 241.476 cents D^ Eb( > > 17: 256.569 cents D) Ebv > > 18: 271.661 cents D#\ Eb\\ > > 19: 286.753 cents D# Eb\ > > 20: 301.845 cents D#/ Eb > > 21: 316.938 cents D#// Eb/ > > 22: 332.030 cents D#^ E( > > 23: 347.122 cents D#) Ev > > 24: 362.215 cents E\\ > > 25: 377.307 cents E\ lower segah > > 26: 392.399 cents E SEGAH > > 27: 407.491 cents E/ Fb Buselik > > 28: 422.584 cents E// Fb/ Nishabur > > 29: 437.676 cents E^ F( > > 30: 452.768 cents E) Fv > > 31: 467.860 cents E#\ F\\ > > 32: 482.953 cents E# F\ > > 33: 498.045 cents F CHARGAH > > 34: 513.137 cents F/ > > 35: 528.230 cents F// > > 36: 543.322 cents F^ Gb( > > 37: 558.414 cents F) Gbv > > 38: 573.506 cents F#\ Gb\\ > > 39: 588.599 cents F# Gb\ > > 40: 603.691 cents F#/ Gb > > 41: 618.783 cents F#// Gb/ > > 42: 633.875 cents F#^ G( > > 43: 648.968 cents F#) Gv > > 44: 664.060 cents G\\ > > 45: 679.152 cents G\ > > 46: 701.955 cents G NEVA > > 47: 717.047 cents G/ > > 48: 732.140 cents G// > > 49: 747.232 cents G^ Ab( > > 50: 762.324 cents G) Abv > > 51: 777.416 cents G#\ Ab\\ > > 52: 792.509 cents G# Ab\ > > 53: 807.601 cents G#/ Ab > > 54: 822.693 cents G#// Ab/ > > 55: 837.785 cents G#^ A( > > 56: 852.878 cents G#) Av > > 57: 867.970 cents A\\ > > 58: 883.062 cents A\ Hisar > > 59: 898.155 cents A HUSEYNI/Hisarek > > 60: 913.247 cents A/ Huseyni again > > 61: 928.339 cents A// > > 62: 943.431 cents A^ Bb( > > 63: 958.524 cents A) Bbv > > 64: 973.616 cents A#\ Bb\\ > > 65: 988.708 cents A# Bb\ > > 66: 1003.800 cents A#/ Bb > > 67: 1018.893 cents A#// Bb/ > > 68: 1033.985 cents A#^ B( > > 69: 1049.077 cents A#) Bv > > 70: 1064.170 cents B\\ > > 71: 1079.262 cents B\ > > 72: 1094.354 cents B EVDJ > > 73: 1109.446 cents B/ Cb Mahur > > 74: 1124.539 cents B// Cb/ Mahurek (my proposal) > > 75: 1139.631 cents B^ C( > > 76: 1154.723 cents B) Cv > > 77: 1169.815 cents B#\ C\\ > > 78: 1184.908 cents B# C\ > > 79: 1200.000 cents C GERDANIYE > > > > Some degrees yield excellent 11 limit results, while others > > produce adorable 5 limit and sufficiently close 7 limit > > intervals. I had implemented this tuning on my special Qanun, > > and also installed Wittner fine-tuners to the strings for > > accuracy of pitch. Although my hands are still numb from all > > that tuning, I am very pleased, and so are Qanun performers > > who were "unfortunate" enough to have met me. > > > > Cordially > > Oz. >
From: Ozan Yarman (2006-02-17) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hello Carl and Joe, Well, since you insist, I made an amateurish recording here: http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 (This is not for the faint of heart!) Fumbling as I am, I tried to show some basic modulations that are desirable through the Seyir of a Taqsim. This pitiable attempt of mine makes use of Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some Nikriz flavours even higher up. Cordially, Oz. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 16 \ufffdubat 2006 Per\ufffdembe 22:30 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Ozan, > > Have you ever tried recording your Qanun? It sounds like a > marvelous instrument! > > -Carl > ----------- I would like to hear it as well, oh Ambassador of the Qanun.
From: Keenan Pepper (2006-02-17) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning On 2/16/06, Ozan Yarman <ozanyarman@ozanyarman.com> wrote: > Hello Carl and Joe, > > Well, since you insist, I made an amateurish recording here: > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > (This is not for the faint of heart!) > > Fumbling as I am, I tried to show some basic modulations that are desirable > through the Seyir of a Taqsim. This pitiable attempt of mine makes use of > Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some > Nikriz flavours even higher up. > > Cordially, > Oz. I thought it sounded awesome! Is the qanun similar to Harry Partch's Harmonic Canon? Same root word? Keenan
From: Ozan Yarman (2006-02-17) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Thank you Keenan! Qanun is surely synonymous with the Latin word Canon. It may further be associated with Canaan, which reminds me, your name seems to be derived from a similar root. We could be talking about biblical history here. As for Harry Partch's harmonic canon, I do believe he was trying to invent something else. Cordially, Ozan ----- Original Message ----- From: "Keenan Pepper" <keenanpepper@gmail.com> To: <tuning@yahoogroups.com> Sent: 17 \ufffdubat 2006 Cuma 4:35 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > On 2/16/06, Ozan Yarman <ozanyarman@ozanyarman.com> wrote: > > Hello Carl and Joe, > > > > Well, since you insist, I made an amateurish recording here: > > > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > > (This is not for the faint of heart!) > > > > Fumbling as I am, I tried to show some basic modulations that are desirable > > through the Seyir of a Taqsim. This pitiable attempt of mine makes use of > > Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some > > Nikriz flavours even higher up. > > > > Cordially, > > Oz. > > I thought it sounded awesome! Is the qanun similar to Harry Partch's > Harmonic Canon? Same root word? > > Keenan >
From: Carl Lumma (2006-02-17) Subject: Re: Ozan's 159-edo-based tuning Ozan, that's simply wonderful! Wow! You must take it upon yourself to refine your techniques until you are satisfied with them. Then share more! -Carl > Hello Carl and Joe, > > Well, since you insist, I made an amateurish recording here: > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > (This is not for the faint of heart!) > > Fumbling as I am, I tried to show some basic modulations that > are desirable through the Seyir of a Taqsim. This pitiable > attempt of mine makes use of Maqam Buselik with a Hijaz > tetrachord attached to the dominant tone and some Nikriz > flavours even higher up. > > Cordially, > Oz. > > ----- Original Message ----- > From: "Carl Lumma" <clumma@...> > To: <tuning@yahoogroups.com> > Sent: 16 Þubat 2006 Perþembe 22:30 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > Ozan, > > > > Have you ever tried recording your Qanun? It sounds like a > > marvelous instrument! > > > > -Carl
From: Ozan Yarman (2006-02-17) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Thank you for the encouragement Carl! I'll see what I can do. Cordially, Ozan ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 17 \ufffdubat 2006 Cuma 15:49 Subject: [tuning] Re: Ozan's 159-edo-based tuning Ozan, that's simply wonderful! Wow! You must take it upon yourself to refine your techniques until you are satisfied with them. Then share more! -Carl
From: Dave Seidel (2006-02-17) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I agree with Carl: very nice, Ozan! - Dave Ozan Yarman wrote: > Thank you for the encouragement Carl! I'll see what I can do. > > Cordially, > Ozan > > ----- Original Message ----- > From: "Carl Lumma" <clumma@yahoo.com> > To: <tuning@yahoogroups.com> > Sent: 17 \ufffdubat 2006 Cuma 15:49 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > Ozan, that's simply wonderful! Wow! > You must take it upon yourself to refine your techniques until > you are satisfied with them. Then share more! > > -Carl > > > > You can configure your subscription by sending an empty email to one > of these addresses (from the address at which you receive the list): > tuning-subscribe@yahoogroups.com - join the tuning group. > tuning-unsubscribe@yahoogroups.com - leave the group. > tuning-nomail@yahoogroups.com - turn off mail from the group. > tuning-digest@yahoogroups.com - set group to send daily digests. > tuning-normal@yahoogroups.com - set group to send individual emails. > tuning-help@yahoogroups.com - receive general help information. > > Yahoo! Groups Links > > > > > > >
From: Can Akkoc (2006-02-17) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Ben de _ me too. Can Akkoc Dave Seidel <dave@superluminal.com> wrote: I agree with Carl: very nice, Ozan! - Dave Ozan Yarman wrote: > Thank you for the encouragement Carl! I'll see what I can do. > > Cordially, > Ozan > > ----- Original Message ----- > From: "Carl Lumma" > To: > Sent: 17 \ufffdubat 2006 Cuma 15:49 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > Ozan, that's simply wonderful! Wow! > You must take it upon yourself to refine your techniques until > you are satisfied with them. Then share more! > > -Carl > > > > You can configure your subscription by sending an empty email to one > of these addresses (from the address at which you receive the list): > tuning-subscribe@yahoogroups.com - join the tuning group. > tuning-unsubscribe@yahoogroups.com - leave the group. > tuning-nomail@yahoogroups.com - turn off mail from the group. > tuning-digest@yahoogroups.com - set group to send daily digests. > tuning-normal@yahoogroups.com - set group to send individual emails. > tuning-help@yahoogroups.com - receive general help information. > > Yahoo! Groups Links > > > > > > > You can configure your subscription by sending an empty email to one of these addresses (from the address at which you receive the list): tuning-subscribe@yahoogroups.com - join the tuning group. tuning-unsubscribe@yahoogroups.com - leave the group. tuning-nomail@yahoogroups.com - turn off mail from the group. tuning-digest@yahoogroups.com - set group to send daily digests. tuning-normal@yahoogroups.com - set group to send individual emails. tuning-help@yahoogroups.com - receive general help information. Yahoo! Groups Links
From: monz (2006-02-17) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, I agree with the others: this sounds great! Can you post any photos of your Qanun? How about a score of what you played on this mp3? (Doesn't have to be in regular notation, any format is fine, even ASCII. I'd love to make a Tonescape file of it.) BTW, thanks for clarifying how you constructed the tuning. Now i've got it. -monz http://tonalsoft.com Tonescape microtonal music software --- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote: > > I agree with Carl: very nice, Ozan! > > - Dave > > Ozan Yarman wrote: > > Thank you for the encouragement Carl! I'll see what I can do. > > > > Cordially, > > Ozan > > > > ----- Original Message ----- > > From: "Carl Lumma" <clumma@...> > > To: <tuning@yahoogroups.com> > > Sent: 17 Þubat 2006 Cuma 15:49 > > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > > > Ozan, that's simply wonderful! Wow! > > You must take it upon yourself to refine your techniques until > > you are satisfied with them. Then share more! > > > > -Carl
From: monz (2006-02-17) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Some degrees yield excellent 11 limit results, while > others produce adorable 5 limit and sufficiently close > 7 limit intervals. Other than the one perfect 3/2 ratio, do you consider this tuning to represent 3 as a prime-factor? Can you please post a table showing how you associate these prime-factors with their respective scale degrees? It would help me put together a Tonescape Tonespace of your tuning. Has Gene or anyone else investigated any possible unison-vectors, or whether this tuning represents a TM-reduced-basis, etc.? My point is that to create a Tonespace of it, i need to know what to use as generators. There are already several possibilities: * a chain created by (4/3)^(1/33) * a chain created by 2^(1/159), with ~half the notes missing * a 4-dimensional "block" created by tempered approximations of prime-factors 2, 5, 7, 11 -monz http://tonalsoft.com Tonescape microtonal music software
From: Magnus Jonsson (2006-02-18) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I definitely agree with Carl. On Fri, 17 Feb 2006, Carl Lumma wrote: > Ozan, that's simply wonderful! Wow! > You must take it upon yourself to refine your techniques until > you are satisfied with them. Then share more! > > -Carl > >> Hello Carl and Joe, >> >> Well, since you insist, I made an amateurish recording here: >> >> http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 >> (This is not for the faint of heart!) >> >> Fumbling as I am, I tried to show some basic modulations that >> are desirable through the Seyir of a Taqsim. This pitiable >> attempt of mine makes use of Maqam Buselik with a Hijaz >> tetrachord attached to the dominant tone and some Nikriz >> flavours even higher up. >> >> Cordially, >> Oz. >> >> ----- Original Message ----- >> From: "Carl Lumma" <clumma@...> >> To: <tuning@yahoogroups.com> >> Sent: 16 Þubat 2006 Perþembe 22:30 >> Subject: [tuning] Re: Ozan's 159-edo-based tuning >> >>> Ozan, >>> >>> Have you ever tried recording your Qanun? It sounds like a >>> marvelous instrument! >>> >>> -Carl > > > > > > > > You can configure your subscription by sending an empty email to one > of these addresses (from the address at which you receive the list): > tuning-subscribe@yahoogroups.com - join the tuning group. > tuning-unsubscribe@yahoogroups.com - leave the group. > tuning-nomail@yahoogroups.com - turn off mail from the group. > tuning-digest@yahoogroups.com - set group to send daily digests. > tuning-normal@yahoogroups.com - set group to send individual emails. > tuning-help@yahoogroups.com - receive general help information. > > Yahoo! Groups Links > > > > > > >
From: Yahya Abdal-Aziz (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning Ozan, On Fri, 17 Feb 2006, Ozan Yarman wrote: > > Hello Carl and Joe, > > Well, since you insist, I made an amateurish recording here: > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > (This is not for the faint of heart!) > > Fumbling as I am, I tried to show some basic modulations that are desirable > through the Seyir of a Taqsim. This pitiable attempt of mine makes use of > Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some > Nikriz flavours even higher up. Very enjoyable! Thank you. Could you point out the times at which you use the Hijaz tetrachord, and also the Nikriz? Regards, Yahya -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.375 / Virus Database: 267.15.11/264 - Release Date: 17/2/06
From: wallyesterpaulrus (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Oz, > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > Some degrees yield excellent 11 limit results, while > > others produce adorable 5 limit and sufficiently close > > 7 limit intervals. > > > Other than the one perfect 3/2 ratio, do you consider > this tuning to represent 3 as a prime-factor? > > Can you please post a table showing how you associate these > prime-factors with their respective scale degrees? It would > help me put together a Tonescape Tonespace of your tuning. > > Has Gene or anyone else investigated any possible > unison-vectors, We have been trying very hard to do so, since so many useful MOS (and, more generally, DE) scales arise so naturally from delimiting the lattice by a set of unison vectors, all but one of which is tempered out. So far, though, Ozan's answers to our queries have been inconsistent, seemingly, both with one another and with such an approach. I'm reserving any judgment until there's a lot more clarity in our mutual understanding. > or whether this tuning represents a > TM-reduced-basis, etc.? What would that mean, exactly? You can TM-reduce the set of unison vectors that are tempered out, but of course this has no effect on the resulting tuning system. Meanwhile, a tuning representing or having a basis of vanishing unison vectors would seem to consist of only one note, so I'm not sure what use that would be. > > > My point is that to create a Tonespace of it, i need to > know what to use as generators. There are already several > possibilities: > > * a chain created by (4/3)^(1/33) > > * a chain created by 2^(1/159), with ~half the notes missing > > * a 4-dimensional "block" created by tempered approximations > of prime-factors 2, 5, 7, 11 Why isn't prime 3 in there too?
From: Gene Ward Smith (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote: > > I agree with Carl: very nice, Ozan! Some striking modulations. Is that what the system is for?
From: Gene Ward Smith (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > Has Gene or anyone else investigated any possible > unison-vectors, or whether this tuning represents a > TM-reduced-basis, etc.? It's a MOS, 79 steps per octave with generator 2 steps of 159. Correspondng linear temperaments do not seem distinguished. In the 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the 5-limit comma |3 -18 11> > > My point is that to create a Tonespace of it, i need to > know what to use as generators. There are already several > possibilities: I'd recommend a chain created by 2^(2/159), which is very little different than (4/3)^(1/33); it has pure octaves rather than pure fourths.
From: Gene Ward Smith (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > Has Gene or anyone else investigated any possible > > unison-vectors, or whether this tuning represents a > > TM-reduced-basis, etc.? > > It's a MOS, 79 steps per octave with generator 2 steps of 159. > Correspondng linear temperaments do not seem distinguished. In the > 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the > 5-limit comma |3 -18 11> I should note, however, that 159 is interesting as a high or very high limit system, and the 80&159 temperament looks better in higher limits. Of course in something like the 29 limit you may as well just use all 159 notes, and I really don't see why Ozan doesn't do that always, and simply adopt 159edo as a way of notating maqam music. Anyway, 159 is consistent through the 17 limit, but the patent (ie "standard") val is strong up to 29 at least. Aside from being nice for higher limits, it has a nearly pure fifth, inherited from 53, a flat meantone fifth in the vicinity of 19 equal, and a 709.4 cent fifth of the kind Paul has been pointing out can be useful. With its best tuning, it tempers out 15625/15552 and 32805/32768 (inherited from 53) as well as 1029/1024 and 10976/10935, which are not 53-et commas. Tempering out both 1029/1024 and 32805/32768, leading to "guiron", gives a generator of 31 steps of 159, which is an example of the sort of thing one might do by way of an alternative to the 79-note MOS (a 77-note MOS, perhaps).
From: Carl Lumma (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning > I should note, however, that 159 is interesting as a high or very > high limit system, and the 80&159 temperament looks better in > higher limits. Of course in something like the 29 limit you may > as well just use all 159 notes, and I really don't see why Ozan > doesn't do that always, He's answered that. 'Too many notes.' -Carl
From: monz (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote: > > > Ozan, > > On Fri, 17 Feb 2006, Ozan Yarman wrote: > > > > Hello Carl and Joe, > > > > Well, since you insist, I made an amateurish recording here: > > > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > > (This is not for the faint of heart!) > > > > Fumbling as I am, I tried to show some basic modulations > > that are desirable through the Seyir of a Taqsim. This > > pitiable attempt of mine makes use of Maqam Buselik with > > a Hijaz tetrachord attached to the dominant tone and > > some Nikriz flavours even higher up. > > > Very enjoyable! Thank you. > > Could you point out the times at which you use > the Hijaz tetrachord, and also the Nikriz? And also, could you provide ratios and cents values to illustrate these Turkish terms? I've followed very little of the discussion of Turkish music that's been going on here for about the last year, but am very interested in it. At some future point, when i have the time to learn about it, i'd like to explore its historical connections -- i'd guess that part of it follows a line like: Sumerian -> Babylonian -> Persian -> Greek -> (Roman) -> Turkish. I've made a Tonescape file of your 79-MOS as a subset of 159-edo in (2,)5,7,11-space, with 2 as the identity interval, and using TM-basis for the 159-edo periodicity-block. I'll post the 79-MOS-degree_to_ratio correspondence as soon as i get a chance. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning Hi Gene, --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@> > wrote: > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > Has Gene or anyone else investigated any possible > > > unison-vectors, or whether this tuning represents a > > > TM-reduced-basis, etc.? > > > > It's a MOS, 79 steps per octave with generator 2 steps > > of 159. Correspondng linear temperaments do not seem > > distinguished. In the 7-limit we have <<33 55 95 9 58 69||, > > with commas 10976/10935 and the 5-limit comma |3 -18 11> > > I should note, however, that 159 is interesting as a high > or very high limit system, and the 80&159 temperament looks > better in higher limits. Of course in something like the > 29 limit you may as well just use all 159 notes, and I > really don't see why Ozan doesn't do that always, and > simply adopt 159edo as a way of notating maqam music. Yes, that makes a lot of sense to me too. > Anyway, 159 is consistent through the 17 limit, but the > patent (ie "standard") val is strong up to 29 at least. > > Aside from being nice for higher limits, it has a nearly > pure fifth, inherited from 53, a flat meantone fifth in > the vicinity of 19 equal, and a 709.4 cent fifth of the > kind Paul has been pointing out can be useful. With its > best tuning, it tempers out 15625/15552 and 32805/32768 > (inherited from 53) as well as 1029/1024 and 10976/10935, > which are not 53-et commas. Tempering out both 1029/1024 > and 32805/32768, leading to "guiron", gives a generator > of 31 steps of 159, which is an example of the sort of > thing one might do by way of an alternative to the 79-note > MOS (a 77-note MOS, perhaps). Gene, since you have a working copy of Tonescape, could you make some Tuning files representing Ozan's tuning? I'd appreciate that. I've just attempted to upload my Tonescape file of it to our website, but am having a server problem. Should be up there later today. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning Hi Ozan, Yahya, et al, --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > I've made a Tonescape file of your 79-MOS as a subset > of 159-edo in (2,)5,7,11-space, with 2 as the identity > interval, and using TM-basis for the 159-edo periodicity-block. > I'll post the 79-MOS-degree_to_ratio correspondence as soon > as i get a chance. And here it is ... Ozan, see how well it agrees/disagrees with your perceptions. Ozan Yarman's Qanun tuning as 79-MOS out of 159-edo, in 5-7-11-space identity interval = 2/1 ratio degree ... ~cents .. ------ monzo ------- ....... ratio ...................... 2 .. 5 .. 7 .. 11 ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1 ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175 ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55 ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125 ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025 ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875 ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929 ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272 ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256 ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112 .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32 .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10 .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44 .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25 .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605 .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375 .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401 .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539 .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343 .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847 .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539 .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64 .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100 .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40 .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125 .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275 .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625 .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464 .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98 .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343 .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77 .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49 .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121 .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385 .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400 .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625 .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250 .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976 .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448 .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196 .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88 .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7 .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121 .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11 .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175 .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605 .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331 .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80 .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32 .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50 .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625 .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125 .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125 .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392 .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343 .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77 .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49 .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121 .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77 .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331 .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500 .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200 .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625 .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792 .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784 .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343 .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14 .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49 .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11 .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35 .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121 .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275 .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655 .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125 .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584 .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568 .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64 .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28 .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88 (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1) -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Ozan, Yahya, et al, > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > I've made a Tonescape file of your 79-MOS as a subset > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > interval, and using TM-basis for the 159-edo periodicity-block. > > I'll post the 79-MOS-degree_to_ratio correspondence as soon > > as i get a chance. > > > And here it is ... Ozan, see how well it agrees/disagrees > with your perceptions. And here's an alternate version of my table, for those who want the monzo without the interpolated spacer periods: Ozan Yarman's Qanun tuning as 79-MOS out of 159-edo, in 5-7-11-space identity interval = 2/1 ratio degree ... ~cents .. 2,5,7,11-monzo ...... ratio ... 0 ..... 0.000 .. [ 0 0 0 0 > ......... 1 / 1 ... 1 .... 15.094 .. [ 4 -2 -1 1 > ..... 176 / 175 ... 2 .... 30.189 .. [ 3 -1 1 -1 > ...... 56 / 55 ... 3 .... 45.283 .. [ 7 -3 0 0 > ...... 128 / 125 ... 4 .... 60.377 .. [ 6 -2 2 -2 > .... 3136 / 3025 ... 5 .... 75.472 .. [10 -4 1 -1 > .... 7168 / 6875 ... 6 .... 90.566 .. [ 1 5 -2 -2 > .... 6250 / 5929 ... 7 ... 105.660 .. [-7 1 -2 3 > ..... 6655 / 6272 ... 8 ... 120.755 .. [-8 2 0 1 > ....... 275 / 256 ... 9 ... 135.849 .. [-4 0 -1 2 > ...... 121 / 112 .. 10 ... 150.943 .. [-5 1 1 0 > ........ 35 / 32 .. 11 ... 166.038 .. [-1 -1 0 1 > ....... 11 / 10 .. 12 ... 181.132 .. [-2 0 2 -1 > ....... 49 / 44 .. 13 ... 196.226 .. [ 2 -2 1 0 > ....... 28 / 25 .. 14 ... 211.321 .. [ 1 -1 3 -2 > ..... 686 / 605 .. 15 ... 226.415 .. [ 5 -3 2 -1 > .... 1568 / 1375 .. 16 ... 241.509 .. [ 1 3 -4 1 > ..... 2750 / 2401 .. 17 ... 256.604 .. [ 0 4 -2 -1 > ..... 625 / 539 .. 18 ... 271.698 .. [ 4 2 -3 0 > ...... 400 / 343 .. 19 ... 286.792 .. [ 3 3 -1 -2 > .... 1000 / 847 .. 20 ... 301.887 .. [ 7 1 -2 -1 > ..... 640 / 539 .. 21 ... 316.981 .. [-6 0 1 1 > ........ 77 / 64 .. 22 ... 332.075 .. [-2 -2 0 2 > ...... 121 / 100 .. 23 ... 347.170 .. [-3 -1 2 0 > ....... 49 / 40 .. 24 ... 362.264 .. [ 1 -3 1 1 > ...... 154 / 125 .. 25 ... 377.358 .. [ 0 -2 3 -1 > ..... 343 / 275 .. 26 ... 392.453 .. [ 4 -4 2 0 > ...... 784 / 625 .. 27 ... 407.547 .. [-5 5 -1 -1 > .... 3125 / 2464 .. 28 ... 422.642 .. [-1 3 -2 0 > ...... 125 / 98 .. 29 ... 437.736 .. [ 3 1 -3 1 > ...... 440 / 343 .. 30 ... 452.830 .. [ 2 2 -1 -1 > ..... 100 / 77 .. 31 ... 467.925 .. [ 6 0 -2 0 > ....... 64 / 49 .. 32 ... 483.019 .. [ 5 1 0 -2 > ...... 160 / 121 .. 33 ... 498.113 .. [ 9 -1 -1 -1 > .... 512 / 385 .. 34 ... 513.208 .. [-4 -2 2 1 > ...... 539 / 400 .. 35 ... 528.302 .. [ 0 -4 1 2 > ...... 847 / 625 .. 36 ... 543.396 .. [-1 -3 3 0 > ...... 343 / 250 .. 37 ... 558.491 .. [-5 3 -3 2 > .... 15125 / 10976 .. 38 ... 573.585 .. [-6 4 -1 0 > ...... 625 / 448 .. 39 ... 588.679 .. [-2 2 -2 1 > ...... 275 / 196 .. 40 ... 603.774 .. [-3 3 0 -1 > ...... 125 / 88 .. 41 ... 618.868 .. [ 1 1 -1 0 > ....... 10 / 7 .. 42 ... 633.962 .. [ 0 2 1 -2 > ...... 175 / 121 .. 43 ... 649.057 .. [ 4 0 0 -1 > ....... 16 / 11 .. 44 ... 664.151 .. [ 8 -2 -1 0 > ..... 256 / 175 .. 45 ... 679.245 .. [ 7 -1 1 -2 > ..... 896 / 605 .. 46 ... 701.887 .. [ 4 3 0 -3 > ..... 2000 / 1331 .. 47 ... 716.981 .. [-4 -1 0 2 > ...... 121 / 80 .. 48 ... 732.075 .. [-5 0 2 0 > ........ 49 / 32 .. 49 ... 747.170 .. [-1 -2 1 1 > ....... 77 / 50 .. 50 ... 762.264 .. [ 3 -4 0 2 > ...... 968 / 625 .. 51 ... 777.358 .. [ 2 -3 2 0 > ...... 196 / 125 .. 52 ... 792.453 .. [ 6 -5 1 1 > ..... 4928 / 3125 .. 53 ... 807.547 .. [-3 4 -2 0 > ...... 625 / 392 .. 54 ... 822.642 .. [ 1 2 -3 1 > ...... 550 / 343 .. 55 ... 837.736 .. [ 0 3 -1 -1 > ..... 125 / 77 .. 56 ... 852.830 .. [ 4 1 -2 0 > ....... 80 / 49 .. 57 ... 867.925 .. [ 3 2 0 -2 > ...... 200 / 121 .. 58 ... 883.019 .. [ 7 0 -1 -1 > ..... 128 / 77 .. 59 ... 898.113 .. [ 6 1 1 -3 > ..... 2240 / 1331 .. 60 ... 913.208 .. [-2 -3 1 2 > ...... 847 / 500 .. 61 ... 928.302 .. [-3 -2 3 0 > ...... 343 / 200 .. 62 ... 943.396 .. [ 1 -4 2 1 > ..... 1078 / 625 .. 63 ... 958.491 .. [-8 5 -1 0 > ..... 3125 / 1792 .. 64 ... 973.585 .. [-4 3 -2 1 > ..... 1375 / 784 .. 65 ... 988.679 .. [ 0 1 -3 2 > ...... 605 / 343 .. 66 .. 1003.774 .. [-1 2 -1 0 > ....... 25 / 14 .. 67 .. 1018.868 .. [ 3 0 -2 1 > ....... 88 / 49 .. 68 .. 1033.962 .. [ 2 1 0 -1 > ....... 20 / 11 .. 69 .. 1049.057 .. [ 6 -1 -1 0 > ...... 64 / 35 .. 70 .. 1064.151 .. [ 5 0 1 -2 > ...... 224 / 121 .. 71 .. 1079.245 .. [ 9 -2 0 -1 > ..... 512 / 275 .. 72 .. 1094.340 .. [ 8 -1 2 -3 > ... 12544 / 6655 .. 73 .. 1109.434 .. [ 0 -5 2 2 > ..... 5929 / 3125 .. 74 .. 1124.528 .. [-9 4 -1 1 > ..... 6875 / 3584 .. 75 .. 1139.623 .. [-5 2 -2 2 > ..... 3025 / 1568 .. 76 .. 1154.717 .. [-6 3 0 0 > ....... 125 / 64 .. 77 .. 1169.811 .. [-2 1 -1 1 > ....... 55 / 28 .. 78 .. 1184.906 .. [-3 2 1 -1 > ...... 175 / 88 (. 79 .. 1200.000 .. [ 1 0 0 0 > ......... 2 / 1) -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-18) Subject: Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > Hi Ozan, Yahya, et al, > > > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > I've made a Tonescape file of your 79-MOS as a subset > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > > interval, and using TM-basis for the 159-edo periodicity-block. > > > I'll post the 79-MOS-degree_to_ratio correspondence as soon > > > as i get a chance. > > > > > > And here it is ... Ozan, see how well it agrees/disagrees > > with your perceptions. I've uploaded a screenshot of a Tonescape Lattice of Ozan's tuning to the tuning_files group: http://launch.groups.yahoo.com/group/tuning_files/files/monz/ozan_79-mos_159-edo_5-7-11-space_lattice.gif The Lattice points are labeled with the degree numbers. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-19) Subject: Re: Ozan's 159-edo-based tuning Hi Gene, --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > Gene, since you have a working copy of Tonescape, could > you make some Tuning files representing Ozan's tuning? > I'd appreciate that. > > I've just attempted to upload my Tonescape file of it > to our website, but am having a server problem. Should > be up there later today. I emailed it to you as an attachment, to two different addresses i have for you. The svpal one bounced back. The other was your gmail. -monz http://tonalsoft.com Tonescape microtonal music software
From: Gene Ward Smith (2006-02-19) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > I emailed it to you as an attachment, to two different > addresses i have for you. The svpal one bounced back. > The other was your gmail. OK, but I'm unclear what you want done; I had thought you'd taken care of the problem judging by your recent posts.
From: Can Akkoc (2006-02-19) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Joe, You might have to join the *notayaz* group in cyberspace if you are truly interested in getting to the bottom of some *mysterious* structures embedded in Turkish makam music. That means you have to start learning Turkish soon. Can Akkoc monz <monz@tonalsoft.com> wrote: --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote: > > > Ozan, > > On Fri, 17 Feb 2006, Ozan Yarman wrote: > > > > Hello Carl and Joe, > > > > Well, since you insist, I made an amateurish recording here: > > > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > > (This is not for the faint of heart!) > > > > Fumbling as I am, I tried to show some basic modulations that are desirable through the Seyir of a Taqsim. This pitiable attempt of mine makes use of Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and some Nikriz flavours even higher up. > Very enjoyable! Thank you. > > Could you point out the times at which you use > the Hijaz tetrachord, and also the Nikriz? And also, could you provide ratios and cents values to illustrate these Turkish terms? I've followed very little of the discussion of Turkish music that's been going on here for about the last year, but am very interested in it. At some future point, when i have the time to learn about it, i'd like to explore its historical connections -- i'd guess that part of it follows a line like: Sumerian -> Babylonian -> Persian -> Greek -> (Roman) -> Turkish. I've made a Tonescape file of your 79-MOS as a subset of 159-edo in (2,)5,7,11-space, with 2 as the identity interval, and using TM-basis for the 159-edo periodicity-block. I'll post the 79-MOS-degree_to_ratio correspondence as soon as i get a chance. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-19) Subject: Re: Ozan's 159-edo-based tuning Hi Gene, --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > I emailed it to you as an attachment, to two different > > addresses i have for you. The svpal one bounced back. > > The other was your gmail. > > OK, but I'm unclear what you want done; I had thought > you'd taken care of the problem judging by your recent posts. It wasn't really that i saw a problem ... just many different ways of modeling Ozan's Qanun tuning, and i was interested to see what you might come up with. The "solution" i used here doesn't totally satisfy me, because it's a subset of 159-edo which only has ~half of the notes of 159-edo: thus, there are holes all over the Lattice. I'd prefer: 1) to use the actual tuning which Ozan apparently prefers, (4/3)^(1/33), which is very close to but not exactly the same as 159-edo; 2) to set it up in a 5,7,11-space rather than just as a "linear" chain of generators; 3) to use consecutive powers of the generators, so that it doesn't have all the "holes". Besides, i just would like to see you playing around with Tonescape again ... it's been a long time since you showed me anything you did with it. Note that (for the handful of testers we're working with) the "Mustang" version is available from our website now, when you login. You should download and install that, so that you have the latest version running. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-19) Subject: Re: Ozan's 159-edo-based tuning Hi Can, --- In tuning@yahoogroups.com, Can Akkoc <can193849@...> wrote: > > Joe, > > You might have to join the *notayaz* group in cyberspace > if you are truly interested in getting to the bottom of > some *mysterious* structures embedded in Turkish makam music. > > That means you have to start learning Turkish soon. Yes, i'm already aware of notayaz from Ozan. I've avoided it so far precisely because i don't have time right now to learn any more Turkish than the miniscule amount i already know. I've been planning (more like wishing for) a trip to Istanbul for a couple of decades now ... someday ... -monz http://tonalsoft.com Tonescape microtonal music software
From: Gene Ward Smith (2006-02-20) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > Besides, i just would like to see you playing around > with Tonescape again ... it's been a long time since > you showed me anything you did with it. I've been waiting for a new version to come out to see if I could use it for composing.
From: wallyesterpaulrus (2006-02-20) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@> > wrote: > > > > > I should note, however, that 159 is interesting as a high or very high > limit system, and the 80&159 temperament looks better in higher > limits. So this implies an 80-note MOS rather than a 79-note one should be interesting? Tempering out both 1029/1024 and > 32805/32768, leading to "guiron", gives a generator of 31 steps of > 159, which is an example of the sort of thing one might do by way of > an alternative to the 79-note MOS (a 77-note MOS, perhaps). > Fascinating.
From: wallyesterpaulrus (2006-02-20) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > I should note, however, that 159 is interesting as a high or very > > high limit system, and the 80&159 temperament looks better in > > higher limits. Of course in something like the 29 limit you may > > as well just use all 159 notes, and I really don't see why Ozan > > doesn't do that always, > > He's answered that. 'Too many notes.' > > -Carl But one would think that if one chooses a subset, it would be one where the consonant intervals can be transposed once or twice by the usual intervals of modulation (fourths and fifths), wouldn't one?
From: wallyesterpaulrus (2006-02-20) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Ozan, Yahya, et al, > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > I've made a Tonescape file of your 79-MOS as a subset > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > interval, and using TM-basis for the 159-edo periodicity-block. Can you state this with more precision and detail, please, for those of us attempting to follow along? > > I'll post the 79-MOS-degree_to_ratio correspondence as soon > > as i get a chance. > > > And here it is ... Ozan, see how well it agrees/disagrees > with your perceptions. > > > > Ozan Yarman's Qanun tuning > as 79-MOS out of 159-edo, in 5-7-11-space > identity interval = 2/1 ratio > > > degree ... ~cents .. ------ monzo ------- ....... ratio > ...................... 2 .. 5 .. 7 .. 11 > > ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1 > ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175 > ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55 > ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125 > ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025 > ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875 > ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929 > ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272 > ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256 > ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112 > .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32 > .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10 > .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44 > .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25 > .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605 > .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375 > .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401 > .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539 > .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343 > .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847 > .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539 > .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64 > .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100 > .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40 > .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125 > .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275 > .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625 > .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464 > .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98 > .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343 > .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77 > .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49 > .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121 > .. 33 ... 498.113 .. [ 9 ..-1 ..-17 ..-1 > ..... 512 / 385 I find it pretty humorous that you didn't even get 4/3 for 33 steps, one of the few clues Ozan has explicitly given us . . . > .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400 > .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625 > .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250 > .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976 > .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448 > .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196 > .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88 > .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7 > .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121 > .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11 > .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175 > .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605 > .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331 > .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80 > .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32 > .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50 > .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625 > .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125 > .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125 > .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392 > .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343 > .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77 > .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49 > .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121 > .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77 > .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331 > .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500 > .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200 > .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625 > .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792 > .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784 > .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343 > .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14 > .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49 > .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11 > .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35 > .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121 > .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275 > .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655 > .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125 > .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584 > .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568 > .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64 > .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28 > .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88 > (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1) > > > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Gene, ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 18 \ufffdubat 2006 Cumartesi 8:43 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> > wrote: > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > Has Gene or anyone else investigated any possible > > > unison-vectors, or whether this tuning represents a > > > TM-reduced-basis, etc.? > > > > It's a MOS, 79 steps per octave with generator 2 steps of 159. > > Correspondng linear temperaments do not seem distinguished. In the > > 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the > > 5-limit comma |3 -18 11> > > I should note, however, that 159 is interesting as a high or very high > limit system, and the 80&159 temperament looks better in higher > limits. Of course in something like the 29 limit you may as well just > use all 159 notes, and I really don't see why Ozan doesn't do that > always, and simply adopt 159edo as a way of notating maqam music. > Anyway, 159 is consistent through the 17 limit, but the patent (ie > "standard") val is strong up to 29 at least. > Can you give the step numbers for 80? I cannot use all the 159 notes, because there is no space on the Qanun to fix that many mandals! > Aside from being nice for higher limits, it has a nearly pure fifth, > inherited from 53, a flat meantone fifth in the vicinity of 19 equal, > and a 709.4 cent fifth of the kind Paul has been pointing out can be > useful. With its best tuning, it tempers out 15625/15552 and > 32805/32768 (inherited from 53) as well as 1029/1024 and 10976/10935, > which are not 53-et commas. Tempering out both 1029/1024 and > 32805/32768, leading to "guiron", gives a generator of 31 steps of > 159, which is an example of the sort of thing one might do by way of > an alternative to the 79-note MOS (a 77-note MOS, perhaps). > > Can you also give the step numbers for 77?
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning To be precise, `too many notes for any instrument of Maqam Music`. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 18 \ufffdubat 2006 Cumartesi 9:05 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > I should note, however, that 159 is interesting as a high or very > > high limit system, and the 80&159 temperament looks better in > > higher limits. Of course in something like the 29 limit you may > > as well just use all 159 notes, and I really don't see why Ozan > > doesn't do that always, > > He's answered that. 'Too many notes.' > > -Carl > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Is this lattice based on 159-eq? Or my 33 equal division of 4/3? ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 19 \ufffdubat 2006 Pazar 0:13 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > Hi Ozan, Yahya, et al, > > > > > > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > > I've made a Tonescape file of your 79-MOS as a subset > > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > > > interval, and using TM-basis for the 159-edo periodicity-block. > > > > I'll post the 79-MOS-degree_to_ratio correspondence as soon > > > > as i get a chance. > > > > > > > > > And here it is ... Ozan, see how well it agrees/disagrees > > > with your perceptions. > > > > I've uploaded a screenshot of a Tonescape Lattice of Ozan's > tuning to the tuning_files group: > > http://launch.groups.yahoo.com/group/tuning_files/files/monz/ozan_79-mos_159 -edo_5-7-11-space_lattice.gif > > > The Lattice points are labeled with the degree numbers. > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning monz, ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 18 \ufffdubat 2006 Cumartesi 22:42 Subject: [tuning] Re: Ozan's 159-edo-based tuning SNIP > > > > Could you point out the times at which you use > > the Hijaz tetrachord, and also the Nikriz? > > > > And also, could you provide ratios and cents values > to illustrate these Turkish terms? Ok. The scales are these according to SCALA E79 with step numbers: D Fb F G A B( C# D 13 27 33 46 59 68 85 92 (Buselik principal scale) D E( F# G A B( C# D 13 22 39 46 59 68 85 92 (Zirguleli Hijaz, meaning Hijaz using perde zirgule at C#, effectively doubling the Hijaz tetrachord over the dominant tone.) A B( C# D Fb F-F# G A -20 -11 6 13 27 33-39 46 59 (Hijaz principal scale) 3/4 away from its designated tonic G A B( C# D E( F# G 46 59 68 85 92 101 118 125 (Nikriz principal scale - supplementary uses E and F) 3/2 away from its designated tonic Compressed to one octave, the cent values are these: 0: 1/1 D 1: 135.830 cents Eb 2: 211.292 cents E 3: 301.845 cents F 4: 392.399 cents F# 5: 505.755 cents G 6: 701.955 cents A 7: 837.785 cents Bb 8: 1094.354 cents C# 9: 1200.000 cents D > > I've followed very little of the discussion of Turkish > music that's been going on here for about the last year, > but am very interested in it. Glad to hear it. At some future point, > when i have the time to learn about it, i'd like to > explore its historical connections -- i'd guess that > part of it follows a line like: Sumerian -> Babylonian -> > Persian -> Greek -> (Roman) -> Turkish. > That would be much anticipated. > > I've made a Tonescape file of your 79-MOS as a subset > of 159-edo in (2,)5,7,11-space, with 2 as the identity > interval, and using TM-basis for the 159-edo periodicity-block. > I'll post the 79-MOS-degree_to_ratio correspondence as soon > as i get a chance. > > I'll look into it. > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > > Oz.
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning monz, ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 18 \ufffdubat 2006 Cumartesi 23:43 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan, Yahya, et al, > > > --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > > I've made a Tonescape file of your 79-MOS as a subset > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > interval, and using TM-basis for the 159-edo periodicity-block. > > I'll post the 79-MOS-degree_to_ratio correspondence as soon > > as i get a chance. > > > And here it is ... Ozan, see how well it agrees/disagrees > with your perceptions. > Let me see. > > > Ozan Yarman's Qanun tuning > as 79-MOS out of 159-edo, in 5-7-11-space > identity interval = 2/1 ratio > > > degree ... ~cents .. ------ monzo ------- ....... ratio > ...................... 2 .. 5 .. 7 .. 11 > > ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1 > ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175 > ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55 > ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125 > ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025 > ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875 > ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929 > ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272 > ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256 > ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112 > .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32 > .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10 > .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44 > .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25 > .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605 > .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375 > .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401 > .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539 > .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343 > .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847 > .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539 > .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64 > .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100 > .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40 > .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125 > .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275 > .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625 > .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464 > .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98 > .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343 > .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77 > .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49 > .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121 > .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385 This is the reason why I prefer a pure fourth to the 53-edo fourth, although they differ by 0.068 cents. > .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400 > .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625 > .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250 > .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976 > .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448 > .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196 > .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88 > .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7 > .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121 > .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11 > .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175 > .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605 > .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331 The fifth should have been 3/2. The complication arises from your preference of 159 equal divisions of the octave, which is a very close approximation to my proposal. > .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80 > .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32 > .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50 > .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625 > .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125 > .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125 > .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392 > .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343 > .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77 > .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49 > .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121 > .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77 > .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331 > .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500 > .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200 > .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625 > .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792 > .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784 > .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343 > .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14 > .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49 > .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11 > .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35 > .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121 > .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275 > .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655 > .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125 > .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584 > .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568 > .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64 > .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28 > .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88 > (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1) > > Some famous intervals made their way in, but would you not prefer my version instead? > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Dear monz, Thanks very much for the praises. I have uploaded to pictures of my Qanun to: http://www.ozanyarman.com/anonymous/ Sorry for the bad quality. My webcam can do no better and the Qanun just won't fit in my flatbed scanner! A score is very easy to prepare with a frequency analyzer program. Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and could not transcribe the piece. The unalterated notes used are these according to SCALA e79: A B( C# D Fb F G A B( C# D E( F# G A B( C# D Fb equates to E buselik, not E segah, hence the characteristic of the Buselik Maqam, whose tonic is lower D. However, I finished on lower A Ashiran with a Hijaz flavor. Cordially, Oz. ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 18 Şubat 2006 Cumartesi 1:23 Subject: [tuning] Re: Ozan's 159-edo-based tuning Hi Oz, I agree with the others: this sounds great! Can you post any photos of your Qanun? How about a score of what you played on this mp3? (Doesn't have to be in regular notation, any format is fine, even ASCII. I'd love to make a Tonescape file of it.) BTW, thanks for clarifying how you constructed the tuning. Now i've got it. -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi monz, ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 18 Şubat 2006 Cumartesi 1:38 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Hi Oz, > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > Some degrees yield excellent 11 limit results, while > > others produce adorable 5 limit and sufficiently close > > 7 limit intervals. > > > Other than the one perfect 3/2 ratio, do you consider > this tuning to represent 3 as a prime-factor? > Surely, one may look at it that way also. > Can you please post a table showing how you associate these > prime-factors with their respective scale degrees? It would > help me put together a Tonescape Tonespace of your tuning. > I can give you the whole-tone zone right here: 0: 1/1 C 1: 15.092 cents C/ comma 2: 30.185 cents C// minor diesis 3: 45.277 cents C^ Db( quarter-tone 4: 60.369 cents C) Dbv 1/3 tone/major diesis 5: 75.461 cents C#\ Db\\ minor chroma 6: 90.554 cents C# Db\ limma 3 & 5-limit 7: 105.646 cents C#/ Db apotome 3-limit 8: 120.738 cents C#// Db/ apotome 5-limit 9: 135.830 cents C#^ D( tridecimal 2/3 tone 10: 150.923 cents C#) Dv unidecimal neutral second 11: 166.015 cents D\\ Ptolemy's second 12: 181.107 cents D\ minor whole tone 13: 196.200 cents D major whole tone 1 14: 211.292 cents D/ major whole tone 2 (super-Pyth.) SNIP Oz.
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning To a great extent, yes. I have not even begun to scratch the surface of all the possibilities. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 18 Şubat 2006 Cumartesi 6:52 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, Dave Seidel <dave@...> wrote: > > > > I agree with Carl: very nice, Ozan! > > Some striking modulations. Is that what the system is for? > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Paul, you are not helping in the least. I am not a tuning expert nor do I claim to possess superior knowledge in matters of consonances. For gosh sakes, I'm still new here and English is not my mother tongue. I have pointed out to the best of my ability all the criteria that Maqam Music requires and am very much satisfied with the results of my proposal at this moment. But since you are hard to please, oblige me... what inconsistencies have you discovered that I and the others are unaware of? ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 18 Şubat 2006 Cumartesi 6:47 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > > > Hi Oz, > > > > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > > Some degrees yield excellent 11 limit results, while > > > others produce adorable 5 limit and sufficiently close > > > 7 limit intervals. > > > > > > Other than the one perfect 3/2 ratio, do you consider > > this tuning to represent 3 as a prime-factor? > > > > Can you please post a table showing how you associate these > > prime-factors with their respective scale degrees? It would > > help me put together a Tonescape Tonespace of your tuning. > > > > Has Gene or anyone else investigated any possible > > unison-vectors, > > We have been trying very hard to do so, since so many useful MOS > (and, more generally, DE) scales arise so naturally from delimiting > the lattice by a set of unison vectors, all but one of which is > tempered out. So far, though, Ozan's answers to our queries have been > inconsistent, seemingly, both with one another and with such an > approach. I'm reserving any judgment until there's a lot more clarity > in our mutual understanding. > > > or whether this tuning represents a > > TM-reduced-basis, etc.? > > What would that mean, exactly? You can TM-reduce the set of unison > vectors that are tempered out, but of course this has no effect on > the resulting tuning system. Meanwhile, a tuning representing or > having a basis of vanishing unison vectors would seem to consist of > only one note, so I'm not sure what use that would be. > > > > > > > My point is that to create a Tonespace of it, i need to > > know what to use as generators. There are already several > > possibilities: > > > > * a chain created by (4/3)^(1/33) > > > > * a chain created by 2^(1/159), with ~half the notes missing > > > > * a 4-dimensional "block" created by tempered approximations > > of prime-factors 2, 5, 7, 11 > > Why isn't prime 3 in there too? > > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Can you please explain the first paragraph in layman terms Gene? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 18 Şubat 2006 Cumartesi 7:17 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > > Has Gene or anyone else investigated any possible > > unison-vectors, or whether this tuning represents a > > TM-reduced-basis, etc.? > > It's a MOS, 79 steps per octave with generator 2 steps of 159. > Correspondng linear temperaments do not seem distinguished. In the > 7-limit we have <<33 55 95 9 58 69||, with commas 10976/10935 and the > 5-limit comma |3 -18 11> > > > > My point is that to create a Tonespace of it, i need to > > know what to use as generators. There are already several > > possibilities: > > I'd recommend a chain created by 2^(2/159), which is very little > different than (4/3)^(1/33); it has pure octaves rather than pure fourths. > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hello brother in Islam, I'm happy you enjoyed the piece: 1. For the first 15 seconds I flirt on the Hijaz tetrachord starting on A. 2. From hereon to 20 seconds I descend to D to pronounce the Buselik flavour. 3. From 20 seconds onward, I make a modulation from Hijaz on A to Buselik on high D. 4. The modulations continue and come to a stop on D with a Buselik repetition of the same motif. 5. From 33 seconds onward one hears a D minor arpeggio and I perform the same motif on high D. 6. At about 40 seconds, I make a transition to a Nikriz flavor, which requires an alteration of two notes of Buselik on high D, making another Hijaz tetrachord. 7. From 50 seconds onward, I return to Buselik on high D and rest on A Hijaz. 8. From 1:06 you hear the same motif and a transition to the Hijaz Maqam on high D instead of D. 9. By 1:25, I begin to return to Buselik on D and sound the arpeggio of D minor once more. 10. By 1:30 you hear Nikriz again. 11. By 1:40 Buselik again and a famous melody I borrowed. 12. At 1:57 minutes, I try to alterate F to F# but the mandals get stuck. Fortunately, I recover and carry on. 13. Around 2 minutes, I come to rest at low A with a Hijaz tetrachord. 14. By 2:07, Nikriz one last time. 15. By 2:15 a G minor scale with a sesquitonal Bb, in fact a requirement of Nikriz. 16. At 2:20 I have descended to low A Hijaz. Cordially, Oz. ----- Original Message ----- From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au> To: <tuning@yahoogroups.com> Sent: 18 Şubat 2006 Cumartesi 6:01 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > Ozan, > > On Fri, 17 Feb 2006, Ozan Yarman wrote: > > > > Hello Carl and Joe, > > > > Well, since you insist, I made an amateurish recording here: > > > > http://www.ozanyarman.com/anonymous/79-ton-Qanun1.mp3 > > (This is not for the faint of heart!) > > > > Fumbling as I am, I tried to show some basic modulations that are > desirable > > through the Seyir of a Taqsim. This pitiable attempt of mine makes use of > > Maqam Buselik with a Hijaz tetrachord attached to the dominant tone and > some > > Nikriz flavours even higher up. > > > Very enjoyable! Thank you. > > Could you point out the times at which you use > the Hijaz tetrachord, and also the Nikriz? > > Regards, > Yahya >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning And how does 79 notes from 33 equal divisions of the pure fourth with octave equivalances preclude the possibility of modulations Paul? Or better yet, how does 77 or 80 do not? ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 20 \ufffdubat 2006 Pazartesi 12:56 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > > > I should note, however, that 159 is interesting as a high or very > > > high limit system, and the 80&159 temperament looks better in > > > higher limits. Of course in something like the 29 limit you may > > > as well just use all 159 notes, and I really don't see why Ozan > > > doesn't do that always, > > > > He's answered that. 'Too many notes.' > > > > -Carl > > But one would think that if one chooses a subset, it would be one where the consonant intervals can be transposed once or twice by the usual intervals of modulation (fourths and fifths), wouldn't one? > > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Paul, > > > > > I should note, however, that 159 is interesting as a high or very high > > limit system, and the 80&159 temperament looks better in higher > > limits. > > So this implies an 80-note MOS rather than a 79-note one should be interesting? > I don't understand what you have against 79 anyway. > > Tempering out both 1029/1024 and > > 32805/32768, leading to "guiron", gives a generator of 31 steps of > > 159, which is an example of the sort of thing one might do by way of > > an alternative to the 79-note MOS (a 77-note MOS, perhaps). > > > Fascinating. > > It would be fascinating if we were given the chance to analyze it first.
From: Petr Parízek (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning Hi Ozan. You wrote: > The fifth should have been 3/2. The complication arises from your preference > of 159 equal divisions of the octave, which is a very close approximation to > my proposal. Am I right in assuming that the fifth is closer to 3/2 in your tuning than in 159-equal? Petr
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Petr, the default fifth is exactly 3/2 in my tuning: 0: 0.000 cents 0.000 0 0 commas C 46: 701.955 cents -0.000 0 0 commas G 13: 694.245 cents -7.710 -237 D 59: 701.955 cents -7.710 -237 A 26: 694.245 cents -15.421 -473 E 72: 701.955 cents -15.421 -473 B 39: 694.245 cents -23.131 -710 F# 6: 701.955 cents -23.131 -710 C# 52: 701.955 cents -23.131 -710 G# 19: 694.245 cents -30.842 -947 D# 65: 701.955 cents -30.842 -947 A# 32: 694.245 cents -38.552 -1183 E# 78: 701.955 cents -38.552 -1183 B# 45: 694.245 cents -46.263 -1420 G\ 12: 701.955 cents -46.263 -1420 D\ 58: 701.955 cents -46.263 -1420 A\ 25: 694.245 cents -53.973 -1656 E\ 71: 701.955 cents -53.973 -1656 B\ 38: 694.245 cents -61.684 -1893 F#\ 5: 701.955 cents -61.684 -1893 C#\ 51: 701.955 cents -61.684 -1893 G#\ 18: 694.245 cents -69.394 -2130 D#\ 64: 701.955 cents -69.394 -2130 A#\ 31: 694.245 cents -77.105 -2366 F\\ 77: 701.955 cents -77.105 -2366 C\\ 44: 694.245 cents -84.815 -2603 G\\ 11: 701.955 cents -84.815 -2603 D\\ 57: 701.955 cents -84.815 -2603 A\\ 24: 694.245 cents -92.525 -2840 E\\ 70: 701.955 cents -92.525 -2840 B\\ 37: 694.245 cents -100.236 -3076 F) 4: 701.955 cents -100.236 -3076 C) 50: 701.955 cents -100.236 -3076 G) 17: 694.245 cents -107.946 -3313 D) 63: 701.955 cents -107.946 -3313 A) 30: 694.245 cents -115.657 -3550 Fv 76: 701.955 cents -115.657 -3550 Cv 43: 694.245 cents -123.367 -3786 Gv 10: 701.955 cents -123.367 -3786 Dv 56: 701.955 cents -123.367 -3786 Av 23: 694.245 cents -131.078 -4023 Ev 69: 701.955 cents -131.078 -4023 Bv 36: 694.245 cents -138.788 -4259 F^ 3: 701.955 cents -138.788 -4259 C^ 49: 701.955 cents -138.788 -4259 G^ 16: 694.245 cents -146.499 -4496 D^ 62: 701.955 cents -146.499 -4496 A^ 29: 694.245 cents -154.209 -4733 F( 75: 701.955 cents -154.209 -4733 C( 42: 694.245 cents -161.920 -4969 G( 9: 701.955 cents -161.920 -4969 D( 55: 701.955 cents -161.920 -4969 A( 22: 694.245 cents -169.630 -5206 E( 68: 701.955 cents -169.630 -5206 B( 35: 694.245 cents -177.340 -5443 F// 2: 701.955 cents -177.340 -5443 C// 48: 701.955 cents -177.340 -5443 G// 15: 694.245 cents -185.051 -5679 D// 61: 701.955 cents -185.051 -5679 A// 28: 694.245 cents -192.761 -5916 E// 74: 701.955 cents -192.761 -5916 B// 41: 694.245 cents -200.472 -6153 Gb/ 8: 701.955 cents -200.472 -6153 Db/ 54: 701.955 cents -200.472 -6153 Ab/ 21: 694.245 cents -208.182 -6389 Eb/ 67: 701.955 cents -208.182 -6389 Bb/ 34: 694.245 cents -215.893 -6626 F/ 1: 701.955 cents -215.893 -6626 C/ 47: 701.955 cents -215.893 -6626 G/ 14: 694.245 cents -223.603 -6863 D/ 60: 701.955 cents -223.603 -6863 A/ 27: 694.245 cents -231.314 -7099 Fb 73: 701.955 cents -231.314 -7099 Cb 40: 694.245 cents -239.024 -7336 Gb 7: 701.955 cents -239.024 -7336 Db 53: 701.955 cents -239.024 -7336 Ab 20: 694.245 cents -246.735 -7572 Eb 66: 701.955 cents -246.735 -7572 Bb 33: 694.245 cents -254.445 -7809 F 79: 701.955 cents -254.445 -7809 C Average absolute difference: 129.4185 cents Root mean square difference: 149.7660 cents Maximum absolute difference: 254.4451 cents Maximum formal fifth difference: 7.7105 cents ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 18:45 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > You wrote: > > > The fifth should have been 3/2. The complication arises from your > preference > > of 159 equal divisions of the octave, which is a very close approximation > to > > my proposal. > > Am I right in assuming that the fifth is closer to 3/2 in your tuning than > in 159-equal? > > Petr > >
From: monz (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Is this lattice based on 159-eq? Or my 33 equal division of 4/3? > > > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > > > I've uploaded a screenshot of a Tonescape Lattice of Ozan's > > tuning to the tuning_files group: > > > > > http://launch.groups.yahoo.com/group/tuning_files/files/monz/ozan_79-mos_159-edo_5-7-11-space_lattice.gif > > > > > > The Lattice points are labeled with the degree numbers. 159-edo. -monz http://tonalsoft.com Tonescape microtonal music software
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. Thanks a lot for the cycle. I must admit I haven't followed the discussion very carefully. As far as I can see it, the places where there are two pure fifths in a row repeat sometimes after 5 fifths and sometimes after 7 fifths. What is the rule for that? And where does the narrow fifth come from? Petr
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Petr, the structure of the tuning comes from 33 equal divisions of the pure fourth carried to 79 tones the 79th of which is completed to the octave and the larger comma thus derived is then carried between steps 45-46 to yield a voluminous well-temperament whereby you can adequately approximate 3, 5, 7, 11 and 13 limit consonant intervals. ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 19:13 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > Thanks a lot for the cycle. I must admit I haven't followed the discussion > very carefully. As far as I can see it, the places where there are two pure > fifths in a row repeat sometimes after 5 fifths and sometimes after 7 > fifths. What is the rule for that? And where does the narrow fifth come > from? > > Petr > > > > > You can configure your subscription by sending an empty email to one > of these addresses (from the address at which you receive the list): > tuning-subscribe@yahoogroups.com - join the tuning group. > tuning-unsubscribe@yahoogroups.com - leave the group. > tuning-nomail@yahoogroups.com - turn off mail from the group. > tuning-digest@yahoogroups.com - set group to send daily digests. > tuning-normal@yahoogroups.com - set group to send individual emails. > tuning-help@yahoogroups.com - receive general help information. > > Yahoo! Groups Links > > > > > > > > > >
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. You wrote: > Petr, the structure of the tuning comes from 33 equal divisions of the pure > fourth carried to 79 tones the 79th of which is completed to the octave and > the larger comma thus derived is then carried between steps 45-46 to yield a > voluminous well-temperament whereby you can adequately approximate 3, 5, 7, > 11 and 13 limit consonant intervals. And if I rounded it off to 200-EDO instead of 159, would that work as well? Petr
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Probably so Petr, in fact 200-edo is one of my favorites nowadays. Oz. ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 21:11 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > You wrote: > > > Petr, the structure of the tuning comes from 33 equal divisions of the > pure > > fourth carried to 79 tones the 79th of which is completed to the octave > and > > the larger comma thus derived is then carried between steps 45-46 to yield > a > > voluminous well-temperament whereby you can adequately approximate 3, 5, > 7, > > 11 and 13 limit consonant intervals. > > And if I rounded it off to 200-EDO instead of 159, would that work as well? > > Petr > >
From: monz (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning Hi Paul (and Oz), --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > Hi Ozan, Yahya, et al, > > > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > I've made a Tonescape file of your 79-MOS as a subset > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > > interval, and using TM-basis for the 159-edo periodicity-block. > > Can you state this with more precision and detail, please, > for those of us attempting to follow along? TM-basis for 159-edo in 2,5,7,11-space: .. 2,5,7,11-monzo ...... ratio ........ ~cents --------------------------------------------------- .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > degree ... ~cents .. ------ monzo ------- ....... ratio > > ...................... 2 .. 5 .. 7 .. 11 > > > > <snip> > > .. 33 ... 498.113 .. [ 9 ..-1 ..-17 ..-1 > ..... 512 / 385 > > I find it pretty humorous that you didn't even get 4/3 > for 33 steps, one of the few clues Ozan has explicitly > given us . . . Well, considering that 3 is *not* one of the prime-factors in the Tonespace which i used, it's pretty obvious *why* i didn't get 4/3. But OK, yes, you're right ... since Ozan's tuning explicitly has a "pure" 3/2 5th, and since i know that his preferred version of the tuning uses (4/3)^(1/33) as the generator, i guess i should have included prime-factor 3 in the Tonespace. I'll do another one for 159-edo which includes 3, and post it. -monz http://tonalsoft.com Tonescape microtonal music software
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. > Probably so Petr, in fact 200-edo is one of my favorites nowadays. OK, I think I'm beginning to understand. Does this have something to do with the discussion on 152-EDO you were leading with Paul? I think the two fifths which that tuning has (i.e. one of 88 steps and the other of 89) could also do an acceptable approximation (though somewhat poorer, I admit) to your system. Still, I'm getting such a feeling that 200-EDO could work extremely well as the nearest fifth is amazingly close to 3/2. Petr
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Indeed, the topics revolve around a possible universal tuning that also satisfy my requirements for Maqam Music. In this regard, voluminous equal divisions of the octave are desirable such as 152, 159, 171, 193, 200, etc... But as the number increases, so do the possibilities of ever implementing such a tuning on an instrument diminish. My Qanun maker, an aging veteran in the field, exceeded his own limits by constructing the device I currently possess. Still, I'm always open to improvements. This does not in anyway imply, however, that 79 tones practically out of 159-tET are useless. On the contrary, Ruhi Ayangil, a famous Qanun virtuoso colleague of mine certified himself the revolutionary aspects of my endeavour and was mighty pleased when he performed on my Qanun. I had other Qanunists look at it as well, and heard from them little criticism, if any. As for 200-edo. I am very pleased with it since it has an excellent 1/4 Pyth-comma tempered fifth next to a just fifth. But is it good enough to be called universal? Cordially, Ozan ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 21:46 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > > Probably so Petr, in fact 200-edo is one of my favorites nowadays. > > OK, I think I'm beginning to understand. Does this have something to do with > the discussion on 152-EDO you were leading with Paul? I think the two fifths > which that tuning has (i.e. one of 88 steps and the other of 89) could also > do an acceptable approximation (though somewhat poorer, I admit) to your > system. > Still, I'm getting such a feeling that 200-EDO could work extremely well as > the nearest fifth is amazingly close to 3/2. > > Petr > > >
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Can you give the step numbers for 80? > Can you also give the step numbers for 77? Some 159-et MOS: Ozan[79] 222222222222222222222222222222222222222222222 2222222222222222222222222222222223 Ozan[80] 2222222222222222222222222222222222222222222222222 2222222222222222222222222222221 Guiron[77] 331313131313131331313131313131331313131313131331 31313131313133131313131313131
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Can you please explain the first paragraph in layman terms Gene? > > It's a MOS, 79 steps per octave with generator 2 steps of 159. It's a scale formed by means of a single generator within the octave, where the number of steps is chosen so that only two step sizes result. In this case no octave reduction is required, but it still can be classified in this way. http://tonalsoft.com/enc/m/mos.aspx > > Correspondng linear temperaments do not seem distinguished. In the > > 7-limit we have <<33 54 95 9 58 69||, with commas 10976/10935 and the > > 5-limit comma |3 -18 11> The mapping is such that 33 generators gives a fourth, 54 generators a minor sixth, and 95 generators an approximate 16/7 interval, which defines everything else in the 7-limit. It sends the small (six and a half cent) interval, or comma, 10976/10935 to the unison. That is, such an interval is "tempered out". Also tempered out is 2^3 5^11/3^18, of size 14.26 cents. The "ozan" temperament, 80&159, gets more interesting in higher prime limits. In the 11-limit, we get 4000/3993 and 3025/3024 as commas; in the 13-limit 325/324 and 364/363; and so forth.
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. > As for 200-edo. I am very pleased with it since it has an excellent 1/4 > Pyth-comma tempered fifth next to a just fifth. But is it good enough to be > called universal? Well, speaking for myself at least, what more could I wish? The only case where I might blame 200-EDO may be perhaps if I found a 3 cent detuning to be too much (I mean when approximating 7/4). Indeed, I confess, in some situations, I really do. Petr
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning You mean this: 80 MOS 159tET | 0: 1/1 C unison, perfect prime 1: 15.092 cents C/ 2: 30.185 cents C// 3: 45.277 cents C^ Db( 4: 60.369 cents C) Dbv 5: 75.461 cents C#\ Db\\ 6: 90.554 cents C# Db\ 7: 105.646 cents C#/ Db 8: 120.738 cents C#// Db/ 9: 135.830 cents C#^ D( 10: 150.923 cents C#) Dv 11: 166.015 cents D\\ 12: 181.107 cents D\ 13: 196.200 cents D 14: 211.292 cents D/ 15: 226.384 cents D// 16: 241.476 cents D^ Eb( 17: 256.569 cents D) Ebv 18: 271.661 cents D#\ Eb\\ 19: 286.753 cents D# Eb\ 20: 301.845 cents D#/ Eb 21: 316.938 cents D#// Eb/ 22: 332.030 cents D#^ E( 23: 347.122 cents D#) Ev 24: 362.215 cents E\\ 25: 377.307 cents E\ 26: 392.399 cents E 27: 407.491 cents E/ Fb 28: 422.584 cents E// Fb/ 29: 437.676 cents E^ F( 30: 452.768 cents E) Fv 31: 467.860 cents E#\ F\\ 32: 482.953 cents E# F\ 33: 4/3 F perfect fourth 34: 513.137 cents F/ 35: 528.230 cents F// 36: 543.322 cents F^ Gb( 37: 558.414 cents F) Gbv 38: 573.506 cents F#\ Gb\\ 39: 588.599 cents F# Gb\ 40: 603.691 cents F#/ Gb 41: 618.783 cents F#// Gb/ 42: 633.875 cents F#^ G( 43: 648.968 cents F#) Gv 44: 664.060 cents G\\ 45: 679.152 cents G\ 46: 694.245 cents G 47: 701.955 cents G 48: 717.047 cents G/ 49: 732.140 cents G// 50: 747.232 cents G^ Ab( 51: 762.324 cents G) Abv 52: 777.416 cents G#\ Ab\\ 53: 792.509 cents G# Ab\ 54: 807.601 cents G#/ Ab 55: 822.693 cents G#// Ab/ 56: 837.785 cents G#^ A( 57: 852.878 cents G#) Av 58: 867.970 cents A\\ 59: 883.062 cents A\ 60: 898.155 cents A 61: 913.247 cents A/ 62: 928.339 cents A// 63: 943.431 cents A^ Bb( 64: 958.524 cents A) Bbv 65: 973.616 cents A#\ Bb\\ 66: 988.708 cents A# Bb\ 67: 1003.800 cents A#/ Bb 68: 1018.893 cents A#// Bb/ 69: 1033.985 cents A#^ B( 70: 1049.077 cents A#) Bv 71: 1064.170 cents B\\ 72: 1079.262 cents B\ 73: 1094.354 cents B 74: 1109.446 cents B/ Cb 75: 1124.539 cents B// Cb/ 76: 1139.631 cents B^ C( 77: 1154.723 cents B) Cv 78: 1169.815 cents B#\ C\\ 79: 1184.908 cents B# C\ 80: 1200.000 cents C If this is all there is to it, one only requires to affix an additional mandal per octave ~8 cents just before every G. If you deem that I shall benefit from doing so, please tell me, so that I may modify my Qanun accordingly. Also, SCALA cannot extract modes from such voluminous temperaments. I get an error message saying that scale and mode sizes are unequal. Manuel, what do you make out of this? Until then, can you give me the cent values for Guiron[77] Gene? Cordially, Oz. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 21 \ufffdubat 2006 Sal\ufffd 22:07 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > Can you give the step numbers for 80? > > > Can you also give the step numbers for 77? > > Some 159-et MOS: > > Ozan[79] > > 222222222222222222222222222222222222222222222 > 2222222222222222222222222222222223 > > Ozan[80] > > 2222222222222222222222222222222222222222222222222 > 2222222222222222222222222222221 > > Guiron[77] > > 331313131313131331313131313131331313131313131331 > 31313131313133131313131313131 > > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Such is the problem I encountered myself with 7-limit consonances in 200-edo. If one chooses to deal with such high numbers, surely better options exist within that nominal region. Gene suggested 313 as a universal tuning if I'm not mistaken. The problem is, you cannot go much higher than 80 or so tones with a Qanun, or for any other practical instrument of Maqam Music for that matter. Cordially, Ozan ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 22:34 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > > As for 200-edo. I am very pleased with it since it has an excellent 1/4 > > Pyth-comma tempered fifth next to a just fifth. But is it good enough to > be > > called universal? > > Well, speaking for myself at least, what more could I wish? The only case > where I might blame 200-EDO may be perhaps if I found a 3 cent detuning to > be too much (I mean when approximating 7/4). Indeed, I confess, in some > situations, I really do. > > Petr >
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, Petr Parízek wrote: > Am I right in assuming that the fifth is closer to 3/2 in your tuning than > in 159-equal? No it isn't. In 159 equal, the fifth is flat by the same amount as in 53 equal, which is 0.068 cents. In Ozan's tuning, both the fifth and the octave are flat by the same amount, 0.164 cents. Neither figure is at all large, of course.
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Petr, the default fifth is exactly 3/2 in my tuning: OK, I misstated; but then your tuning is not based on an equal division of the fourth into 33 parts.
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Gene, you got it all wrong. The octave and the fifth are just in my tuning. ----- Original Message ----- From: "Gene Ward Smith" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 23:07 Subject: [tuning] Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, Petr Par\ufffdzek wrote: > Am I right in assuming that the fifth is closer to 3/2 in your tuning than > in 159-equal? No it isn't. In 159 equal, the fifth is flat by the same amount as in 53 equal, which is 0.068 cents. In Ozan's tuning, both the fifth and the octave are flat by the same amount, 0.164 cents. Neither figure is at all large, of course.
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Probably so Petr, in fact 200-edo is one of my favorites nowadays. Based on the numbers you gave, your scale is badly approximated by 200 edo, whereas 159 edo is pretty much perfect, and is audibly indistinguishable. The numbers below should make it clear why I think there is no point in fussing about the difference between your scale and your scale tuned to 159 edo; it's really a 159-et, 79-note MOS. Yarman scale in cents yar := [15.092000, 30.185000, 45.277000, 60.369000, 75.461000, 90.554000, 105.646000, 120.738000, 135.830000, 150.923000, 166.015000, 181.107000, 196.200000, 211.292000, 226.384000, 241.476000, 256.569000, 271.661000, 286.753000, 301.845000, 316.938000, 332.030000, 347.122000, 362.215000, 377.307000, 392.399000, 407.491000, 422.584000, 437.676000, 452.768000, 467.860000, 482.953000, 498.045000, 513.137000, 528.230000, 543.322000, 558.414000, 573.506000, 588.599000, 603.691000, 618.783000, 633.875000, 648.968000, 664.060000, 679.152000, 694.245000, 709.337000, 724.429000, 739.521000, 754.614000, 769.706000, 784.798000, 799.890000, 814.983000, 830.075000, 845.167000, 860.260000, 875.352000, 890.444000, 905.536000, 920.629000, 935.721000, 950.813000, 965.905000, 980.998000, 996.090000, 1011.182000, 1026.275000, 1041.367000, 1056.459000, 1071.551000, 1086.644000, 1101.736000, 1116.828000, 1131.920000, 1147.013000, 1162.105000, 1177.197000, 1200.000000] Yarman scale in 159-edo steps yar159 := [1.99969000, 3.99951250, 5.99920250, 7.99889250, 9.99858250, 11.9984050, 13.9980950, 15.9977850, 17.9974750, 19.9972975, 21.9969875, 23.9966775, 25.9965000, 27.9961900, 29.9958800, 31.9955700, 33.9953925, 35.9950825, 37.9947725, 39.9944625, 41.9942850, 43.9939750, 45.9936650, 47.9934875, 49.9931775, 51.9928675, 53.9925575, 55.9923800, 57.9920700, 59.9917600, 61.9914500, 63.9912725, 65.9909625, 67.9906525, 69.9904750, 71.9901650, 73.9898550, 75.9895450, 77.9893675, 79.9890575, 81.9887475, 83.9884375, 85.9882600, 87.9879500, 89.9876400, 91.9874625, 93.9871525, 95.9868425, 97.9865325, 99.9863550, 101.986045, 103.985735, 105.985425, 107.985248, 109.984938, 111.984628, 113.984450, 115.984140, 117.983830, 119.983520, 121.983342, 123.983032, 125.982722, 127.982412, 129.982235, 131.981925, 133.981615, 135.981438, 137.981128, 139.980818, 141.980508, 143.980330, 145.980020, 147.979710, 149.979400, 151.979222, 153.978912, 155.978602, 159.000000]; The Yarman scale in 200 edo yar200 := [2.51533333, 5.03083333, 7.54616667, 10.0615000, 12.5768333, 15.0923333, 17.6076667, 20.1230000, 22.6383333, 25.1538333, 27.6691667, 30.1845000, 32.7000000, 35.2153333, 37.7306667, 40.2460000, 42.7615000, 45.2768333, 47.7921667, 50.3075000, 52.8230000, 55.3383333, 57.8536667, 60.3691667, 62.8845000, 65.3998333, 67.9151667, 70.4306667, 72.9460000, 75.4613333, 77.9766667, 80.4921667, 83.0075000, 85.5228334, 88.0383334, 90.5536667, 93.0690000, 95.5843334, 98.0998334, 100.615167, 103.130500, 105.645833, 108.161333, 110.676667, 113.192000, 115.707500, 118.222833, 120.738167, 123.253500, 125.769000, 128.284333, 130.799667, 133.315000, 135.830500, 138.345833, 140.861167, 143.376667, 145.892000, 148.407333, 150.922667, 153.438167, 155.953500, 158.468833, 160.984167, 163.499667, 166.015000, 168.530333, 171.045833, 173.561167, 176.076500, 178.591833, 181.107333, 183.622667, 186.138000, 188.653333, 191.168833, 193.684167, 196.199500, 200.000000];
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning It is. You carry the comma to the 79th tone, convert it to 1200 cents, rotate the scale so that the larger comma comes between step numbers 45-46. This procedure gives a pure fifth on the 46th step. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 21 \ufffdubat 2006 Sal\ufffd 23:08 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Petr, the default fifth is exactly 3/2 in my tuning: > > OK, I misstated; but then your tuning is not based on an equal > division of the fourth into 33 parts. > >
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. > It is. You carry the comma to the 79th tone, convert it to 1200 cents, > rotate the scale so that the larger comma comes between step numbers 45-46. > This procedure gives a pure fifth on the 46th step. OK, my final question on this, I hope. Where does the number 33 come from? Petr
From: monz (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning Hi Gene, --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > Can you please explain the first paragraph in layman terms Gene? > > > > It's a MOS, 79 steps per octave with generator 2 steps of 159. > > It's a scale formed by means of a single generator within > the octave, where the number of steps is chosen so that only > two step sizes result. In this case no octave reduction is > required, but it still can be classified in this way. > > http://tonalsoft.com/enc/m/mos.aspx > > > > Correspondng linear temperaments do not seem distinguished. > > > In the 7-limit we have <<33 54 95 9 58 69||, with commas > > > 10976/10935 and the 5-limit comma |3 -18 11> > > The mapping is such that 33 generators gives a fourth, > 54 generators a minor sixth, and 95 generators an > approximate 16/7 interval, which defines everything else > in the 7-limit. It sends the small (six and a half cent) > interval, or comma, 10976/10935 to the unison. That is, > such an interval is "tempered out". Also tempered out is > 2^3 5^11/3^18, of size 14.26 cents. > > The "ozan" temperament, 80&159, gets more interesting in > higher prime limits. In the 11-limit, we get 4000/3993 and > 3025/3024 as commas; in the 13-limit 325/324 and 364/363; > and so forth. Thanks from me! This is exactly what i was looking for, for constructing Tonescape Lattices of various versions of Ozan's Qanun tuning. Now if only i had the time to spend on it ... -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I don't dispute that my scale is, just as you say, 79 MOS 159-tET Gene, since the largest error is 0.093 cents compared to my method of achieving it. However, I prefer the latter for clarity. In comparison, 200-edo is off by as much as 3 cents, which is indeed problematic: Step size is 6.0000 cents 1: 15.092: 3: 18.0000 cents, diff. 0.484621 steps, 2.9077 cents 2: 30.185: 5: 30.0000 cents, diff. -0.030758 steps, -0.1846 cents 3: 45.277: 8: 48.0000 cents, diff. 0.453863 steps, 2.7232 cents 4: 60.369: 10: 60.0000 cents, diff. -0.061515 steps, -0.3691 cents 5: 75.461: 13: 78.0000 cents, diff. 0.423106 steps, 2.5386 cents 6: 90.554: 15: 90.0000 cents, diff. -0.092273 steps, -0.5536 cents 7: 105.646: 18: 108.0000 cents, diff. 0.392348 steps, 2.3541 cents 8: 120.738: 20: 120.0000 cents, diff. -0.123031 steps, -0.7382 cents 9: 135.830: 23: 138.0000 cents, diff. 0.361590 steps, 2.1695 cents 10: 150.923: 25: 150.0000 cents, diff. -0.153788 steps, -0.9227 cents 11: 166.015: 28: 168.0000 cents, diff. 0.330833 steps, 1.9850 cents 12: 181.107: 30: 180.0000 cents, diff. -0.184546 steps, -1.1073 cents 13: 196.200: 33: 198.0000 cents, diff. 0.300075 steps, 1.8005 cents 14: 211.292: 35: 210.0000 cents, diff. -0.215303 steps, -1.2918 cents 15: 226.384: 38: 228.0000 cents, diff. 0.269318 steps, 1.6159 cents 16: 241.476: 40: 240.0000 cents, diff. -0.246061 steps, -1.4764 cents 17: 256.569: 43: 258.0000 cents, diff. 0.238560 steps, 1.4314 cents 18: 271.661: 45: 270.0000 cents, diff. -0.276818 steps, -1.6609 cents 19: 286.753: 48: 288.0000 cents, diff. 0.207801 steps, 1.2468 cents 20: 301.845: 50: 300.0000 cents, diff. -0.307576 steps, -1.8455 cents 21: 316.938: 53: 318.0000 cents, diff. 0.177045 steps, 1.0623 cents 22: 332.030: 55: 330.0000 cents, diff. -0.338333 steps, -2.0300 cents 23: 347.122: 58: 348.0000 cents, diff. 0.146286 steps, 0.8777 cents 24: 362.215: 60: 360.0000 cents, diff. -0.369091 steps, -2.2146 cents 25: 377.307: 63: 378.0000 cents, diff. 0.115530 steps, 0.6932 cents 26: 392.399: 65: 390.0000 cents, diff. -0.399848 steps, -2.3991 cents 27: 407.491: 68: 408.0000 cents, diff. 0.084771 steps, 0.5086 cents 28: 422.584: 70: 420.0000 cents, diff. -0.430606 steps, -2.5836 cents 29: 437.676: 73: 438.0000 cents, diff. 0.054015 steps, 0.3241 cents 30: 452.768: 75: 450.0000 cents, diff. -0.461363 steps, -2.7682 cents 31: 467.860: 78: 468.0000 cents, diff. 0.023256 steps, 0.1395 cents 32: 482.953: 80: 480.0000 cents, diff. -0.492121 steps, -2.9527 cents 33: 498.045: 83: 498.0000 cents, diff. -0.007500 steps, -0.0450 cents 34: 513.137: 86: 516.0000 cents, diff. 0.477120 steps, 2.8627 cents 35: 528.230: 88: 528.0000 cents, diff. -0.038258 steps, -0.2295 cents 36: 543.322: 91: 546.0000 cents, diff. 0.446363 steps, 2.6782 cents 37: 558.414: 93: 558.0000 cents, diff. -0.069015 steps, -0.4141 cents 38: 573.506: 96: 576.0000 cents, diff. 0.415605 steps, 2.4936 cents 39: 588.599: 98: 588.0000 cents, diff. -0.099773 steps, -0.5986 cents 40: 603.691: 101: 606.0000 cents, diff. 0.384848 steps, 2.3091 cents 41: 618.783: 103: 618.0000 cents, diff. -0.130530 steps, -0.7832 cents 42: 633.875: 106: 636.0000 cents, diff. 0.354090 steps, 2.1245 cents 43: 648.968: 108: 648.0000 cents, diff. -0.161288 steps, -0.9677 cents 44: 664.060: 111: 666.0000 cents, diff. 0.323333 steps, 1.9400 cents 45: 679.152: 113: 678.0000 cents, diff. -0.192046 steps, -1.1523 cents 46: 701.955: 117: 702.0000 cents, diff. 0.007500 steps, 0.0450 cents 47: 717.047: 120: 720.0000 cents, diff. 0.492120 steps, 2.9527 cents 48: 732.140: 122: 732.0000 cents, diff. -0.023258 steps, -0.1396 cents 49: 747.232: 125: 750.0000 cents, diff. 0.461363 steps, 2.7682 cents 50: 762.324: 127: 762.0000 cents, diff. -0.054016 steps, -0.3241 cents 51: 777.416: 130: 780.0000 cents, diff. 0.430605 steps, 2.5836 cents 52: 792.509: 132: 792.0000 cents, diff. -0.084773 steps, -0.5086 cents 53: 807.601: 135: 810.0000 cents, diff. 0.399848 steps, 2.3991 cents 54: 822.693: 137: 822.0000 cents, diff. -0.115531 steps, -0.6932 cents 55: 837.785: 140: 840.0000 cents, diff. 0.369090 steps, 2.2145 cents 56: 852.878: 142: 852.0000 cents, diff. -0.146288 steps, -0.8777 cents 57: 867.970: 145: 870.0000 cents, diff. 0.338333 steps, 2.0300 cents 58: 883.062: 147: 882.0000 cents, diff. -0.177046 steps, -1.0623 cents 59: 898.155: 150: 900.0000 cents, diff. 0.307575 steps, 1.8454 cents 60: 913.247: 152: 912.0000 cents, diff. -0.207803 steps, -1.2468 cents 61: 928.339: 155: 930.0000 cents, diff. 0.276816 steps, 1.6609 cents 62: 943.431: 157: 942.0000 cents, diff. -0.238561 steps, -1.4314 cents 63: 958.524: 160: 960.0000 cents, diff. 0.246060 steps, 1.4764 cents 64: 973.616: 162: 972.0000 cents, diff. -0.269318 steps, -1.6159 cents 65: 988.708: 165: 990.0000 cents, diff. 0.215301 steps, 1.2918 cents 66: 1003.800: 167: 1002.0000 cents, diff. -0.300076 steps, -1.8005 cents 67: 1018.893: 170: 1020.0000 cents, diff. 0.184545 steps, 1.1073 cents 68: 1033.985: 172: 1032.0000 cents, diff. -0.330833 steps, -1.9850 cents 69: 1049.077: 175: 1050.0000 cents, diff. 0.153786 steps, 0.9227 cents 70: 1064.170: 177: 1062.0000 cents, diff. -0.361591 steps, -2.1696 cents 71: 1079.262: 180: 1080.0000 cents, diff. 0.123030 steps, 0.7382 cents 72: 1094.354: 182: 1092.0000 cents, diff. -0.392348 steps, -2.3541 cents 73: 1109.446: 185: 1110.0000 cents, diff. 0.092271 steps, 0.5536 cents 74: 1124.539: 187: 1122.0000 cents, diff. -0.423106 steps, -2.5386 cents 75: 1139.631: 190: 1140.0000 cents, diff. 0.061515 steps, 0.3691 cents 76: 1154.723: 192: 1152.0000 cents, diff. -0.453865 steps, -2.7232 cents 77: 1169.815: 195: 1170.0000 cents, diff. 0.030756 steps, 0.1845 cents 78: 1184.908: 197: 1182.0000 cents, diff. -0.484621 steps, -2.9077 cents 79: 1200.000: 200: 1200.0000 cents, diff. 0.000000 steps, 0.0000 cents Total absolute difference : 19.59939 steps, 117.5964 cents Average absolute difference: 0.248093 steps, 1.4886 cents Root mean square difference: 0.289285 steps, 1.7357 cents Highest absolute difference: 0.492121 steps, 2.9527 cents Were it not for the fact that the narrower fifth is within the desirable range of 3/11 comma meantone, I would dump it all together. Cordially, Oz. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 21 \ufffdubat 2006 Sal\ufffd 23:38 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Probably so Petr, in fact 200-edo is one of my favorites nowadays. > > Based on the numbers you gave, your scale is badly approximated by 200 > edo, whereas 159 edo is pretty much perfect, and is audibly > indistinguishable. The numbers below should make it clear why I think > there is no point in fussing about the difference between your scale > and your scale tuned to 159 edo; it's really a 159-et, 79-note MOS. > > Yarman scale in cents > > yar := [15.092000, 30.185000, 45.277000, 60.369000, 75.461000, > 90.554000, 105.646000, 120.738000, 135.830000, 150.923000, 166.015000, > 181.107000, 196.200000, 211.292000, 226.384000, 241.476000, > 256.569000, 271.661000, 286.753000, 301.845000, 316.938000, > 332.030000, 347.122000, 362.215000, 377.307000, 392.399000, > 407.491000, 422.584000, 437.676000, 452.768000, 467.860000, > 482.953000, 498.045000, 513.137000, 528.230000, 543.322000, > 558.414000, 573.506000, 588.599000, 603.691000, 618.783000, > 633.875000, 648.968000, 664.060000, 679.152000, 694.245000, > 709.337000, 724.429000, 739.521000, 754.614000, 769.706000, > 784.798000, 799.890000, 814.983000, 830.075000, 845.167000, > 860.260000, 875.352000, 890.444000, 905.536000, 920.629000, > 935.721000, 950.813000, 965.905000, 980.998000, 996.090000, > 1011.182000, 1026.275000, 1041.367000, 1056.459000, 1071.551000, > 1086.644000, 1101.736000, 1116.828000, 1131.920000, 1147.013000, > 1162.105000, 1177.197000, 1200.000000] > > Yarman scale in 159-edo steps > > yar159 := [1.99969000, 3.99951250, 5.99920250, 7.99889250, 9.99858250, > 11.9984050, 13.9980950, 15.9977850, 17.9974750, 19.9972975, > 21.9969875, 23.9966775, 25.9965000, 27.9961900, 29.9958800, > 31.9955700, 33.9953925, 35.9950825, 37.9947725, 39.9944625, > 41.9942850, 43.9939750, 45.9936650, 47.9934875, 49.9931775, > 51.9928675, 53.9925575, 55.9923800, 57.9920700, 59.9917600, > 61.9914500, 63.9912725, 65.9909625, 67.9906525, 69.9904750, > 71.9901650, 73.9898550, 75.9895450, 77.9893675, 79.9890575, > 81.9887475, 83.9884375, 85.9882600, 87.9879500, 89.9876400, > 91.9874625, 93.9871525, 95.9868425, 97.9865325, 99.9863550, > 101.986045, 103.985735, 105.985425, 107.985248, 109.984938, > 111.984628, 113.984450, 115.984140, 117.983830, 119.983520, > 121.983342, 123.983032, 125.982722, 127.982412, 129.982235, > 131.981925, 133.981615, 135.981438, 137.981128, 139.980818, > 141.980508, 143.980330, 145.980020, 147.979710, 149.979400, > 151.979222, 153.978912, 155.978602, 159.000000]; > > The Yarman scale in 200 edo > > yar200 := [2.51533333, 5.03083333, 7.54616667, 10.0615000, 12.5768333, > 15.0923333, 17.6076667, 20.1230000, 22.6383333, 25.1538333, > 27.6691667, 30.1845000, 32.7000000, 35.2153333, 37.7306667, > 40.2460000, 42.7615000, 45.2768333, 47.7921667, 50.3075000, > 52.8230000, 55.3383333, 57.8536667, 60.3691667, 62.8845000, > 65.3998333, 67.9151667, 70.4306667, 72.9460000, 75.4613333, > 77.9766667, 80.4921667, 83.0075000, 85.5228334, 88.0383334, > 90.5536667, 93.0690000, 95.5843334, 98.0998334, 100.615167, > 103.130500, 105.645833, 108.161333, 110.676667, 113.192000, > 115.707500, 118.222833, 120.738167, 123.253500, 125.769000, > 128.284333, 130.799667, 133.315000, 135.830500, 138.345833, > 140.861167, 143.376667, 145.892000, 148.407333, 150.922667, > 153.438167, 155.953500, 158.468833, 160.984167, 163.499667, > 166.015000, 168.530333, 171.045833, 173.561167, 176.076500, > 178.591833, 181.107333, 183.622667, 186.138000, 188.653333, > 191.168833, 193.684167, 196.199500, 200.000000]; > >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Let me answer to that with a question of my own Petr: Where does the number 12 come from? ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 21 \ufffdubat 2006 Sal\ufffd 23:47 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > > It is. You carry the comma to the 79th tone, convert it to 1200 cents, > > rotate the scale so that the larger comma comes between step numbers > 45-46. > > This procedure gives a pure fifth on the 46th step. > > OK, my final question on this, I hope. Where does the number 33 come from? > > Petr > >
From: monz (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, Petr Parízek wrote: > > Hi Ozan. > > > It is. You carry the comma to the 79th tone, convert > > it to 1200 cents, rotate the scale so that the larger > > comma comes between step numbers 45-46. > > This procedure gives a pure fifth on the 46th step. > > OK, my final question on this, I hope. Where does the > number 33 come from? In Ozan's tuning, the 4/3 ratio "perfect 4th" is divided into 33 equal steps. Thus (4/3)^(1/33) is the generator of the scale. This is ~15.0922727 cents. If you take 79 steps of that size, the 79th degree is ~1192.289543 cents. Instead of using this last pitch, Ozan substitutes the octave 1200 cents. This last step thus becomes ~22 cents, a bit larger than all the other steps. Then he rotates (transposes) the scale so that this larger step comes between degrees 45 and 46. By doing this, instead of having a pseudo-meantone "5th" at the 46th degree, he now has a 3/2 "perfect-5th". Sorry if all this is obvious and i'm just repeating Ozan, but it was hard for me to understand what he meant by the way he described it, so i'm just offering my version in case it helps anyone else. It is possible to find a 79-tone subset of 159-edo which is not exactly the same as this, but is very close. -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Exactly! I apologize for wasting everyone's precious time with my horrible English. Oz. ----- Original Message ----- From: "monz" To: Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:04 Subject: [tuning] Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, Petr Par\ufffdzek wrote: > > Hi Ozan. > > > It is. You carry the comma to the 79th tone, convert > > it to 1200 cents, rotate the scale so that the larger > > comma comes between step numbers 45-46. > > This procedure gives a pure fifth on the 46th step. > > OK, my final question on this, I hope. Where does the > number 33 come from? In Ozan's tuning, the 4/3 ratio "perfect 4th" is divided into 33 equal steps. Thus (4/3)^(1/33) is the generator of the scale. This is ~15.0922727 cents. If you take 79 steps of that size, the 79th degree is ~1192.289543 cents. Instead of using this last pitch, Ozan substitutes the octave 1200 cents. This last step thus becomes ~22 cents, a bit larger than all the other steps. Then he rotates (transposes) the scale so that this larger step comes between degrees 45 and 46. By doing this, instead of having a pseudo-meantone "5th" at the 46th degree, he now has a 3/2 "perfect-5th". Sorry if all this is obvious and i'm just repeating Ozan, but it was hard for me to understand what he meant by the way he described it, so i'm just offering my version in case it helps anyone else. It is possible to find a 79-tone subset of 159-edo which is not exactly the same as this, but is very close. -monz http://tonalsoft.com Tonescape microtonal music software
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. > Let me answer to that with a question of my own Petr: Where does the number > 12 come from? I'm not sure I understand. The idea of 12 tones in the octave (no matter if spaced equally or unequally) is centuries old, maybe even millenia. I thought the idea of 33 steps in a fourth was something like a result of your own experience. That's why I was asking how you had found it. Petr
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Aha! So you don't question the validity of 12 tones simply because it has historical precedence and my tuning does not? Surely you see the dichotomy. 33 equal divisions of the fourth is just a number that is convenient for my purposes. Other than that, there is nothing terribly magical about it. Oz. ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:09 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > > Let me answer to that with a question of my own Petr: Where does the > number > > 12 come from? > > I'm not sure I understand. The idea of 12 tones in the octave (no matter if > spaced equally or unequally) is centuries old, maybe even millenia. I > thought the idea of 33 steps in a fourth was something like a result of your > own experience. That's why I was asking how you had found it. > > Petr > >
From: Manuel Op de Coul (2006-02-21) Subject: Re: Re: Ozan's 159-edo-based tuning Ozan wrote: >Also, SCALA cannot extract modes from such voluminous temperaments. I get an >error message saying that scale and mode sizes are unequal. Manuel, what do >you make out of this? You have to make sure that the steps add up to the number of notes in the scale. Otherwise the program concludes that you made a typo. So you cannot delete the last note this way. If you want to, you must do it separately. Manuel
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Re: Ozan's 159-edo-based tuning This probably means that Gene gave me numbers that don't add up. ----- Original Message ----- From: "Manuel Op de Coul" <coul@hccnet.nl> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:20 Subject: [tuning] Re: Re: Ozan's 159-edo-based tuning > Ozan wrote: > > >Also, SCALA cannot extract modes from such voluminous temperaments. I get an > >error message saying that scale and mode sizes are unequal. Manuel, what do > >you make out of this? > > You have to make sure that the steps add up to the number of notes in the > scale. Otherwise the program concludes that you made a typo. So you cannot > delete the last note this way. If you want to, you must do it separately. > > Manuel > >
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Indeed, the topics revolve around a possible universal tuning that also > satisfy my requirements for Maqam Music. In this regard, voluminous equal > divisions of the octave are desirable such as 152, 159, 171, 193, 200, > etc... But as the number increases, so do the possibilities of ever > implementing such a tuning on an instrument diminish. One tuning which has been much on my mind recently (because I'm working with it) is 224-et. This has an extremely good meantone fifth, the meantone fifth of 112-edo. It also has an excellent schismatic fifth. It is an excellent division up to the 13 limit, and supports the octoid temperament. This is relevant since Octoid[72], the octoid temperament on 72 notes, seems to have a lot of the properties you want, as well as other interesting properties involving harmony. Octoid[72] can be described as six different well-temperaments stacked next to each other, giving the kind of alternation of fifths you seem to be looking for. It, of course, involves fewer notes than your 79-note scale, and gives much greater scope to harmony and nearly-just intervals. Anyway here is one mode of it: ! octoid72.scl Octoid[72] in 224-et tuning 72 ! 16.071429 32.142857 48.214286 64.285714 85.714286 101.785714 117.857143 133.928571 150.000000 166.071429 182.142857 198.214286 214.285714 235.714286 251.785714 267.857143 283.928571 300.000000 316.071429 332.142857 348.214286 364.285714 385.714286 401.785714 417.857143 433.928571 450.000000 466.071429 482.142857 498.214286 514.285714 535.714286 551.785714 567.857143 583.928571 600.000000 616.071429 632.142857 648.214286 664.285714 685.714286 701.785714 717.857143 733.928571 750.000000 766.071429 782.142857 798.214286 814.285714 835.714286 851.785714 867.857143 883.928571 900.000000 916.071429 932.142857 948.214286 964.285714 985.714286 1001.785714 1017.857143 1033.928571 1050.000000 1066.071429 1082.142857 1098.214286 1114.285714 1135.714286 1151.785714 1167.857143 1183.928571 1200.000000
From: Petr Parízek (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Hi Ozan. > Aha! So you don't question the validity of 12 tones simply because it has > historical precedence and my tuning does not? Surely you see the dichotomy. I'm realizing I have to be pretty careful about how to say something to make others understand my words in the way they were really meant. At this time, either my statement was totally unclear or my questions made you misunderstandd my view. OK, I'll try to make things clearer. 1. The number 12 is easily explainable for me not for its historical precedence but for the acoustical properties of the intervals, no matter if pure or approximated. Since I've never examined 33 equal divisions of the fourth, I was just unaware. 2. We all know that, for instance, 13-EDO or 11-EDO doesn't have the properties wich are being so valued in 12-EDO. So I was interested if, for example, dividing the fourth into 32 or 34 equal steps instead of 33 would harm the system, and if so, how much. Or, in other words, if you found the number 33 using some formulas while trying to meet some of your requirements (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good tuning for common tonal music), or if it was just one of your free decisions. 3. Neither I speak some great English, and ... Well, who cares? Is it worth it? Petr
From: wallyesterpaulrus (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > monz, > > ----- Original Message ----- > From: "monz" <monz@...> > To: <tuning@yahoogroups.com> > Sent: 18 Þubat 2006 Cumartesi 23:43 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > Hi Ozan, Yahya, et al, > > > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > I've made a Tonescape file of your 79-MOS as a subset > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > > interval, and using TM-basis for the 159-edo periodicity-block. > > > I'll post the 79-MOS-degree_to_ratio correspondence as soon > > > as i get a chance. > > > > > > And here it is ... Ozan, see how well it agrees/disagrees > > with your perceptions. > > > > > Let me see. > > > > > > > > Ozan Yarman's Qanun tuning > > as 79-MOS out of 159-edo, in 5-7-11-space > > identity interval = 2/1 ratio > > > > > > degree ... ~cents .. ------ monzo ------- ....... ratio > > ...................... 2 .. 5 .. 7 .. 11 > > > > ... 0 ..... 0.000 .. [ 0 .. 0 .. 0 .. 0 > ....... 1 / 1 > > ... 1 .... 15.094 .. [ 4 ..-2 ..-1 .. 1 > ..... 176 / 175 > > ... 2 .... 30.189 .. [ 3 ..-1 .. 1 ..-1 > ...... 56 / 55 > > ... 3 .... 45.283 .. [ 7 ..-3 .. 0 .. 0 > ..... 128 / 125 > > ... 4 .... 60.377 .. [ 6 ..-2 .. 2 ..-2 > .... 3136 / 3025 > > ... 5 .... 75.472 .. [10 ..-4 .. 1 ..-1 > .... 7168 / 6875 > > ... 6 .... 90.566 .. [ 1 .. 5 ..-2 ..-2 > .... 6250 / 5929 > > ... 7 ... 105.660 .. [-7 .. 1 ..-2 .. 3 > .... 6655 / 6272 > > ... 8 ... 120.755 .. [-8 .. 2 .. 0 .. 1 > ..... 275 / 256 > > ... 9 ... 135.849 .. [-4 .. 0 ..-1 .. 2 > ..... 121 / 112 > > .. 10 ... 150.943 .. [-5 .. 1 .. 1 .. 0 > ...... 35 / 32 > > .. 11 ... 166.038 .. [-1 ..-1 .. 0 .. 1 > ...... 11 / 10 > > .. 12 ... 181.132 .. [-2 .. 0 .. 2 ..-1 > ...... 49 / 44 > > .. 13 ... 196.226 .. [ 2 ..-2 .. 1 .. 0 > ...... 28 / 25 > > .. 14 ... 211.321 .. [ 1 ..-1 .. 3 ..-2 > ..... 686 / 605 > > .. 15 ... 226.415 .. [ 5 ..-3 .. 2 ..-1 > .... 1568 / 1375 > > .. 16 ... 241.509 .. [ 1 .. 3 ..-4 .. 1 > .... 2750 / 2401 > > .. 17 ... 256.604 .. [ 0 .. 4 ..-2 ..-1 > ..... 625 / 539 > > .. 18 ... 271.698 .. [ 4 .. 2 ..-3 .. 0 > ..... 400 / 343 > > .. 19 ... 286.792 .. [ 3 .. 3 ..-1 ..-2 > .... 1000 / 847 > > .. 20 ... 301.887 .. [ 7 .. 1 ..-2 ..-1 > ..... 640 / 539 > > .. 21 ... 316.981 .. [-6 .. 0 .. 1 .. 1 > ...... 77 / 64 > > .. 22 ... 332.075 .. [-2 ..-2 .. 0 .. 2 > ..... 121 / 100 > > .. 23 ... 347.170 .. [-3 ..-1 .. 2 .. 0 > ...... 49 / 40 > > .. 24 ... 362.264 .. [ 1 ..-3 .. 1 .. 1 > ..... 154 / 125 > > .. 25 ... 377.358 .. [ 0 ..-2 .. 3 ..-1 > ..... 343 / 275 > > .. 26 ... 392.453 .. [ 4 ..-4 .. 2 .. 0 > ..... 784 / 625 > > .. 27 ... 407.547 .. [-5 .. 5 ..-1 ..-1 > .... 3125 / 2464 > > .. 28 ... 422.642 .. [-1 .. 3 ..-2 .. 0 > ..... 125 / 98 > > .. 29 ... 437.736 .. [ 3 .. 1 ..-3 .. 1 > ..... 440 / 343 > > .. 30 ... 452.830 .. [ 2 .. 2 ..-1 ..-1 > ..... 100 / 77 > > .. 31 ... 467.925 .. [ 6 .. 0 ..-2 .. 0 > ...... 64 / 49 > > .. 32 ... 483.019 .. [ 5 .. 1 .. 0 ..-2 > ..... 160 / 121 > > .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385 > > This is the reason why I prefer a pure fourth to the 53-edo fourth, although > they differ by 0.068 cents. I don't understand. Monz gave you a JI scale, not EDO intervals. It's true that Monz is trying to give you a 'rationalization' that derives circuitously from 159-tET, but it's simply his poor methodology that caused him to arrive at 512/385 rather than 4/3 here, not the fact that he started with an ET (not an EDO, BTW) > > .. 34 ... 513.208 .. [-4 ..-2 .. 2 .. 1 > ..... 539 / 400 > > .. 35 ... 528.302 .. [ 0 ..-4 .. 1 .. 2 > ..... 847 / 625 > > .. 36 ... 543.396 .. [-1 ..-3 .. 3 .. 0 > ..... 343 / 250 > > .. 37 ... 558.491 .. [-5 .. 3 ..-3 .. 2 > ... 15125 / 10976 > > .. 38 ... 573.585 .. [-6 .. 4 ..-1 .. 0 > ..... 625 / 448 > > .. 39 ... 588.679 .. [-2 .. 2 ..-2 .. 1 > ..... 275 / 196 > > .. 40 ... 603.774 .. [-3 .. 3 .. 0 ..-1 > ..... 125 / 88 > > .. 41 ... 618.868 .. [ 1 .. 1 ..-1 .. 0 > ...... 10 / 7 > > .. 42 ... 633.962 .. [ 0 .. 2 .. 1 ..-2 > ..... 175 / 121 > > .. 43 ... 649.057 .. [ 4 .. 0 .. 0 ..-1 > ...... 16 / 11 > > .. 44 ... 664.151 .. [ 8 ..-2 ..-1 .. 0 > ..... 256 / 175 > > .. 45 ... 679.245 .. [ 7 ..-1 .. 1 ..-2 > ..... 896 / 605 > > .. 46 ... 701.887 .. [ 4 .. 3 .. 0 ..-3 > .... 2000 / 1331 > > The fifth should have been 3/2. The complication arises from your preference > of 159 equal divisions of the octave, Not so. See my comments above, which apply here as well. > which is a very close approximation to > my proposal. > > > .. 47 ... 716.981 .. [-4 ..-1 .. 0 .. 2 > ..... 121 / 80 > > .. 48 ... 732.075 .. [-5 .. 0 .. 2 .. 0 > ...... 49 / 32 > > .. 49 ... 747.170 .. [-1 ..-2 .. 1 .. 1 > ...... 77 / 50 > > .. 50 ... 762.264 .. [ 3 ..-4 .. 0 .. 2 > ..... 968 / 625 > > .. 51 ... 777.358 .. [ 2 ..-3 .. 2 .. 0 > ..... 196 / 125 > > .. 52 ... 792.453 .. [ 6 ..-5 .. 1 .. 1 > .... 4928 / 3125 > > .. 53 ... 807.547 .. [-3 .. 4 ..-2 .. 0 > ..... 625 / 392 > > .. 54 ... 822.642 .. [ 1 .. 2 ..-3 .. 1 > ..... 550 / 343 > > .. 55 ... 837.736 .. [ 0 .. 3 ..-1 ..-1 > ..... 125 / 77 > > .. 56 ... 852.830 .. [ 4 .. 1 ..-2 .. 0 > ...... 80 / 49 > > .. 57 ... 867.925 .. [ 3 .. 2 .. 0 ..-2 > ..... 200 / 121 > > .. 58 ... 883.019 .. [ 7 .. 0 ..-1 ..-1 > ..... 128 / 77 > > .. 59 ... 898.113 .. [ 6 .. 1 .. 1 ..-3 > .... 2240 / 1331 > > .. 60 ... 913.208 .. [-2 ..-3 .. 1 .. 2 > ..... 847 / 500 > > .. 61 ... 928.302 .. [-3 ..-2 .. 3 .. 0 > ..... 343 / 200 > > .. 62 ... 943.396 .. [ 1 ..-4 .. 2 .. 1 > .... 1078 / 625 > > .. 63 ... 958.491 .. [-8 .. 5 ..-1 .. 0 > .... 3125 / 1792 > > .. 64 ... 973.585 .. [-4 .. 3 ..-2 .. 1 > .... 1375 / 784 > > .. 65 ... 988.679 .. [ 0 .. 1 ..-3 .. 2 > ..... 605 / 343 > > .. 66 .. 1003.774 .. [-1 .. 2 ..-1 .. 0 > ...... 25 / 14 > > .. 67 .. 1018.868 .. [ 3 .. 0 ..-2 .. 1 > ...... 88 / 49 > > .. 68 .. 1033.962 .. [ 2 .. 1 .. 0 ..-1 > ...... 20 / 11 > > .. 69 .. 1049.057 .. [ 6 ..-1 ..-1 .. 0 > ...... 64 / 35 > > .. 70 .. 1064.151 .. [ 5 .. 0 .. 1 ..-2 > ..... 224 / 121 > > .. 71 .. 1079.245 .. [ 9 ..-2 .. 0 ..-1 > ..... 512 / 275 > > .. 72 .. 1094.340 .. [ 8 ..-1 .. 2 ..-3 > ... 12544 / 6655 > > .. 73 .. 1109.434 .. [ 0 ..-5 .. 2 .. 2 > .... 5929 / 3125 > > .. 74 .. 1124.528 .. [-9 .. 4 ..-1 .. 1 > .... 6875 / 3584 > > .. 75 .. 1139.623 .. [-5 .. 2 ..-2 .. 2 > .... 3025 / 1568 > > .. 76 .. 1154.717 .. [-6 .. 3 .. 0 .. 0 > ..... 125 / 64 > > .. 77 .. 1169.811 .. [-2 .. 1 ..-1 .. 1 > ...... 55 / 28 > > .. 78 .. 1184.906 .. [-3 .. 2 .. 1 ..-1 > ..... 175 / 88 > > (. 79 .. 1200.000 .. [ 1 .. 0 .. 0 .. 0 > ....... 2 / 1) > > > > > > > Some famous intervals made their way in, but would you not prefer my version > instead? I'm dying to see "your version", especially if it allows us more insight into your system than we could get before.
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > This probably means that Gene gave me numbers that don't add up. Which numbers were these?
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning It is interesting indeed! However, the octoid just doesn't do everything I require from a voluminous temperament or MOS. Can you suggest something a little higher at about 80 or so tones? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:33 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Indeed, the topics revolve around a possible universal tuning that also > > satisfy my requirements for Maqam Music. In this regard, voluminous > equal > > divisions of the octave are desirable such as 152, 159, 171, 193, 200, > > etc... But as the number increases, so do the possibilities of ever > > implementing such a tuning on an instrument diminish. > > One tuning which has been much on my mind recently (because I'm > working with it) is 224-et. This has an extremely good meantone fifth, > the meantone fifth of 112-edo. It also has an excellent schismatic > fifth. It is an excellent division up to the 13 limit, and supports > the octoid temperament. This is relevant since Octoid[72], the octoid > temperament on 72 notes, seems to have a lot of the properties you > want, as well as other interesting properties involving harmony. > Octoid[72] can be described as six different well-temperaments stacked > next to each other, giving the kind of alternation of fifths you seem > to be looking for. It, of course, involves fewer notes than your > 79-note scale, and gives much greater scope to harmony and nearly-just > intervals. > SNIP
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning These: Some 159-et MOS: Ozan[79] 222222222222222222222222222222222222222222222 2222222222222222222222222222222223 Ozan[80] 2222222222222222222222222222222222222222222222222 2222222222222222222222222222221 Guiron[77] 331313131313131331313131313131331313131313131331 31313131313133131313131313131 Do they add up? Or did I do something wrong perhaps? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:50 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > This probably means that Gene gave me numbers that don't add up. > > Which numbers were these? > >
From: wallyesterpaulrus (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning I agree with Gene that the current version of Scala does not produce sensible results when using e31 with 103-equal, e79 with 159-equal, etc. Of course you may have your own reasons for liking or disliking what it's doing, but one should not take the SCALA output for granted. For but one thing, the result will be sensitive to the choice of starting note, usually taken as C. -- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Dear monz, > > Thanks very much for the praises. I have uploaded to pictures of my Qanun > to: > > http://www.ozanyarman.com/anonymous/ > > Sorry for the bad quality. My webcam can do no better and the Qanun just > won't fit in my flatbed scanner! > > A score is very easy to prepare with a frequency analyzer program. > Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and could > not transcribe the piece. > > The unalterated notes used are these according to SCALA e79: > > A B( C# D Fb F G A B( C# D E( F# G A B( C# D > > Fb equates to E buselik, not E segah, hence the characteristic of the > Buselik Maqam, whose tonic is lower D. However, I finished on lower A > Ashiran with a Hijaz flavor. > > Cordially, > Oz. > > ----- Original Message ----- > From: "monz" <monz@...> > To: <tuning@yahoogroups.com> > Sent: 18 Þubat 2006 Cumartesi 1:23 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > Hi Oz, > > > I agree with the others: this sounds great! > > Can you post any photos of your Qanun? > > How about a score of what you played on this mp3? > (Doesn't have to be in regular notation, any format is fine, > even ASCII. I'd love to make a Tonescape file of it.) > > > BTW, thanks for clarifying how you constructed the tuning. > Now i've got it. > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software >
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning SNIP > > This is the reason why I prefer a pure fourth to the 53-edo fourth, although > they differ by 0.068 cents. [PA] I don't understand. Monz gave you a JI scale, not EDO intervals. It's true that Monz is trying to give you a 'rationalization' that derives circuitously from 159-tET, but it's simply his poor methodology that caused him to arrive at 512/385 rather than 4/3 here, not the fact that he started with an ET (not an EDO, BTW) [OZ] Sorry! I was just looking at the cent values before I calculated the ratios. Moz omitted 3 limit intervals and messed up the entire scale as a result, which I am sure he will correct at his earliest convenience. SNIP Cordially, Ozan
From: Ozan Yarman (2006-02-21) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I found no faults with SCALA e79 notation for 79 MOS 159-tET beforehand. Or do you believe that I take everything for granted before putting them to good use? ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:57 Subject: [tuning] Re: Ozan's 159-edo-based tuning I agree with Gene that the current version of Scala does not produce sensible results when using e31 with 103-equal, e79 with 159-equal, etc. Of course you may have your own reasons for liking or disliking what it's doing, but one should not take the SCALA output for granted. For but one thing, the result will be sensitive to the choice of starting note, usually taken as C. -- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Dear monz, > > Thanks very much for the praises. I have uploaded to pictures of my Qanun > to: > > http://www.ozanyarman.com/anonymous/ > > Sorry for the bad quality. My webcam can do no better and the Qanun just > won't fit in my flatbed scanner! > > A score is very easy to prepare with a frequency analyzer program. > Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and could > not transcribe the piece. > > The unalterated notes used are these according to SCALA e79: > > A B( C# D Fb F G A B( C# D E( F# G A B( C# D > > Fb equates to E buselik, not E segah, hence the characteristic of the > Buselik Maqam, whose tonic is lower D. However, I finished on lower A > Ashiran with a Hijaz flavor. > > Cordially, > Oz.
From: monz (2006-02-21) Subject: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > But OK, yes, you're right ... since Ozan's tuning explicitly > has a "pure" 3/2 5th, and since i know that his preferred > version of the tuning uses (4/3)^(1/33) as the generator, > i guess i should have included prime-factor 3 in the Tonespace. > I'll do another one for 159-edo which includes 3, and post it. Lo and behold ... Ozan Yarman - 79-MOS 159-edo, in (2,)3,5,7,11-space =================================================== TM-basis unison-vectors: . 2,3,5,7,11-monzo ..... ratio .........~cents ------------------------------------------------- .. [-3 2 -1 2 -1 > ... 441 / 440 .... 3.930158439 .. [-7 -1 1 1 1 > .... 385 / 384 .... 4.502561833 .. [5 -7 -1 3 0 > .. 10976 / 10935 .. 6.478999485 .. [-2 -2 4 1 -2 > .. 4375 / 4356 ... 7.534875468 The 79-MOS 159-edo tuning in 2,3,5,7,11-space: degree .. ~cents ... 2,3,5,7,11-monzo ..... ratio ---------------------------------------------------- ... 0 ..... 0.000 .. [ 0 0, 0 0 0 > ....... 1 / 1 ... 1 .... 15.094 .. [ 4 0, -2 -1 1 > ... 176 / 175 ... 2 .... 30.189 .. [ 3 0, -1 1 -1 > .... 56 / 55 ... 3 .... 45.283 .. [ 0 -1, -2 1 1 > .... 77 / 75 ... 4 .... 60.377 .. [ 2 -3, 0 1 0 > ..... 28 / 27 ... 5 .... 75.472 .. [ 6 -3, -2 0 1 > ... 704 / 675 ... 6 .... 90.566 .. [ 0 4, 0 -1 -1 > .... 81 / 77 ... 7 ... 105.660 .. [ -3 3, -1 -1 1 .... 297 / 280 ... 8 ... 120.755 .. [ -1 1, 1 -1 0 > .... 15 / 14 ... 9 ... 135.849 .. [ 3 1, -1 -2 1 > ... 264 / 245 .. 10 ... 150.943 .. [ 2 1, 0 0 -1 > ..... 12 / 11 .. 11 ... 166.038 .. [ -1 0, -1 0 1 > .... 11 / 10 .. 12 ... 181.132 .. [ 1 -2, 1 0 0 > ..... 10 / 9 .. 13 ... 196.226 .. [ 2 0, -2 1 0 > ..... 28 / 25 .. 14 ... 211.321 .. [ 4 -2, 0 1 -1 > ... 112 / 99 .. 15 ... 226.415 .. [ 1 -3, -1 1 1 > ... 154 / 135 .. 16 ... 241.509 .. [ -2 2, 2 -2 0 > ... 225 / 196 .. 17 ... 256.604 .. [ -1 4, -1 -1 0 ..... 81 / 70 .. 18 ... 271.698 .. [ 1 2, 1 -1 -1 > .... 90 / 77 .. 19 ... 286.792 .. [ -2 1, 0 -1 1 > .... 33 / 28 .. 20 ... 301.887 .. [ -3 1, 1 1 -1 > ... 105 / 88 .. 21 ... 316.981 .. [ 1 1, -1 0 0 > ...... 6 / 5 .. 22 ... 332.075 .. [ 3 -1, 1 0 -1 > .... 40 / 33 .. 23 ... 347.170 .. [ 0 -2, 0 0 1 > ..... 11 / 9 .. 24 ... 362.264 .. [ -1 -2, 1 2 -1 .... 245 / 198 .. 25 ... 377.358 .. [ 3 -2, -1 1 0 > .... 56 / 45 .. 26 ... 392.453 .. [ 5 -4, 1 1 -1 > .. 1120 / 891 .. 27 ... 407.547 .. [ -3 2, 1 -2 1 > ... 495 / 392 .. 28 ... 422.642 .. [ -4 2, 2 0 -1 > ... 225 / 176 .. 29 ... 437.736 .. [ 0 2, 0 -1 0 > ...... 9 / 7 .. 30 ... 452.830 .. [ 2 0, 2 -1 -1 > ... 100 / 77 .. 31 ... 467.925 .. [ -4 1, 0 1 0 > ..... 21 / 16 .. 32 ... 483.019 .. [ 0 1, -2 0 1 > ..... 33 / 25 .. 33 ... 498.113 .. [ 2 -1, 0 0 0 > ...... 4 / 3 .. 34 ... 513.208 .. [ 6 -1, -2 -1 1 .... 704 / 525 .. 35 ... 528.302 .. [ -2 -2, 0 2 0 > .... 49 / 36 .. 36 ... 543.396 .. [ 2 -2, -2 1 1 > ... 308 / 225 .. 37 ... 558.491 .. [ -1 3, 1 -2 0 > ... 135 / 98 .. 38 ... 573.585 .. [ 0 5, -2 -1 0 > ... 243 / 175 .. 39 ... 588.679 .. [ -5 2, 1 0 0 > ..... 45 / 32 .. 40 ... 603.774 .. [ -1 2, -1 -1 1 ..... 99 / 70 .. 41 ... 618.868 .. [ 1 0, 1 -1 0 > ..... 10 / 7 .. 42 ... 633.962 .. [ 2 2, -2 0 0 > ..... 36 / 25 .. 43 ... 649.057 .. [ -3 -1, 1 1 0 > .... 35 / 24 .. 44 ... 664.151 .. [ 1 -1, -1 0 1 > .... 22 / 15 .. 45 ... 679.245 .. [ 3 -3, 1 0 0 > ..... 40 / 27 .. 46 ... 701.887 .. [ -1 1, 0 0 0 > ...... 3 / 2 .. 47 ... 716.981 .. [ 3 1, -2 -1 1 > ... 264 / 175 .. 48 ... 732.075 .. [ 5 -1, 0 -1 0 > .... 32 / 21 .. 49 ... 747.170 .. [ -1 0, -2 1 1 > .... 77 / 50 .. 50 ... 762.264 .. [ 1 -2, 0 1 0 > ..... 14 / 9 .. 51 ... 777.358 .. [ 5 -2, -2 0 1 > ... 352 / 225 .. 52 ... 792.453 .. [ 4 -2, -1 2 -1 .... 784 / 495 .. 53 ... 807.547 .. [ -4 4, -1 -1 1 .... 891 / 560 .. 54 ... 822.642 .. [ -2 2, 1 -1 0 > .... 45 / 28 .. 55 ... 837.736 .. [ 2 2, -1 -2 1 > ... 396 / 245 .. 56 ... 852.830 .. [ 1 2, 0 0 -1 > ..... 18 / 11 .. 57 ... 867.925 .. [ -2 1, -1 0 1 > .... 33 / 20 .. 58 ... 883.019 .. [ 0 -1, 1 0 0 > ...... 5 / 3 .. 59 ... 898.113 .. [ 4 -1, -1 -1 1 .... 176 / 105 .. 60 ... 913.208 .. [ 3 -1, 0 1 -1 > .... 56 / 33 .. 61 ... 928.302 .. [ 0 -2, -1 1 1 > .... 77 / 45 .. 62 ... 943.396 .. [ 2 -4, 1 1 0 > .... 140 / 81 .. 63 ... 958.491 .. [ -2 5, -1 -1 0 .... 243 / 140 .. 64 ... 973.585 .. [ 0 3, 1 -1 -1 > ... 135 / 77 .. 65 ... 988.679 .. [ -3 2, 0 -1 1 > .... 99 / 56 .. 66 .. 1003.774 .. [ -1 0, 2 -1 0 > .... 25 / 14 .. 67 .. 1018.868 .. [ 0 2, -1 0 0 > ...... 9 / 5 .. 68 .. 1033.962 .. [ 2 0, 1 0 -1 > ..... 20 / 11 .. 69 .. 1049.057 .. [ -1 -1, 0 0 1 > .... 11 / 6 .. 70 .. 1064.151 .. [ 1 -3, 2 0 0 > ..... 50 / 27 .. 71 .. 1079.245 .. [ 2 -1, -1 1 0 > .... 28 / 15 .. 72 .. 1094.340 .. [ 4 -3, 1 1 -1 > ... 560 / 297 .. 73 .. 1109.434 .. [ 1 -4, 0 1 1 > .... 154 / 81 .. 74 .. 1124.528 .. [ -5 3, 2 0 -1 > ... 675 / 352 .. 75 .. 1139.623 .. [ -1 3, 0 -1 0 > .... 27 / 14 .. 76 .. 1154.717 .. [ 1 1, 2 -1 -1 > ... 150 / 77 .. 77 .. 1169.811 .. [ 5 1, 0 -2 0 > ..... 96 / 49 .. 78 .. 1184.906 .. [ -3 0, 2 1 -1 > ... 175 / 88 (. 79 .. 1200.000 .. [ 1 0, 0 0 0> ........ 2 / 1) -monz http://tonalsoft.com Tonescape microtonal music software
From: wallyesterpaulrus (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning Ozan, I apologize again for my manner. I simply seek mutual edification. Our past discussions on the topic contained my preliminary reactions, which you seem to be asking me to rehash, but I prefer to move forward instead of backwards. The inconsistencies I was referring to were seeming incompatibilities between your way of thinking and the assumptions behind the technical machinery that Monz, Gene, and I are used to. Whether you choose to answer my present set of questions or not, you have my heartfelt support in every musical endeavor, particularly those which will allow your rich musical heritage to survive the wave of 12-equal hegemony. --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Paul, you are not helping in the least. I am not a tuning expert nor do I > claim to possess superior knowledge in matters of consonances. For gosh > sakes, I'm still new here and English is not my mother tongue. I have > pointed out to the best of my ability all the criteria that Maqam Music > requires and am very much satisfied with the results of my proposal at this > moment. But since you are hard to please, oblige me... what inconsistencies > have you discovered that I and the others are unaware of? > > > ----- Original Message ----- > From: "wallyesterpaulrus" <wallyesterpaulrus@...> > To: <tuning@yahoogroups.com> > Sent: 18 Þubat 2006 Cumartesi 6:47 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > Hi Oz, > > > > > > > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > > > > Some degrees yield excellent 11 limit results, while > > > > others produce adorable 5 limit and sufficiently close > > > > 7 limit intervals. > > > > > > > > > Other than the one perfect 3/2 ratio, do you consider > > > this tuning to represent 3 as a prime-factor? > > > > > > Can you please post a table showing how you associate these > > > prime-factors with their respective scale degrees? It would > > > help me put together a Tonescape Tonespace of your tuning. > > > > > > Has Gene or anyone else investigated any possible > > > unison-vectors, > > > > We have been trying very hard to do so, since so many useful MOS > > (and, more generally, DE) scales arise so naturally from delimiting > > the lattice by a set of unison vectors, all but one of which is > > tempered out. So far, though, Ozan's answers to our queries have been > > inconsistent, seemingly, both with one another and with such an > > approach. I'm reserving any judgment until there's a lot more clarity > > in our mutual understanding. > > > > > or whether this tuning represents a > > > TM-reduced-basis, etc.? > > > > What would that mean, exactly? You can TM-reduce the set of unison > > vectors that are tempered out, but of course this has no effect on > > the resulting tuning system. Meanwhile, a tuning representing or > > having a basis of vanishing unison vectors would seem to consist of > > only one note, so I'm not sure what use that would be. > > > > > > > > > > > My point is that to create a Tonespace of it, i need to > > > know what to use as generators. There are already several > > > possibilities: > > > > > > * a chain created by (4/3)^(1/33) > > > > > > * a chain created by 2^(1/159), with ~half the notes missing > > > > > > * a 4-dimensional "block" created by tempered approximations > > > of prime-factors 2, 5, 7, 11 > > > > Why isn't prime 3 in there too? > > > > > > >
From: monz (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning Hi Paul and Ozan, --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > > [monz] > > > .. 33 ... 498.113 .. [ 9 ..-1 ..-1 ..-1 > ..... 512 / 385 > > > >[Ozan] > > This is the reason why I prefer a pure fourth to the > > 53-edo fourth, although they differ by 0.068 cents. > > I don't understand. Monz gave you a JI scale, not EDO > intervals. Eh? The cents values are all from 159-edo. The monzos and ratios are the approximate JI values. > It's true that Monz is trying to give you a > 'rationalization' that derives circuitously from 159-tET, > but it's simply his poor methodology that caused him to > arrive at 512/385 rather than 4/3 here, not the fact that > he started with an ET (not an EDO, BTW) Poor methodology? I deliberately left out prime-factor 3, that's what caused me to arrive at 512-385 rather than 4/3. Perhaps that was a poor judgment, but otherwise my methodology is fine. Anyway, by now i've posted the alternative which does include 3. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Sorry! I was just looking at the cent values before I > calculated the ratios. Moz [monz] omitted 3 limit intervals > and messed up the entire scale as a result, which I am > sure he will correct at his earliest convenience. Done. See message 64456. http://launch.groups.yahoo.com/group/tuning/message/64456 -monz http://tonalsoft.com Tonescape microtonal music software
From: Gene Ward Smith (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > It is interesting indeed! However, the octoid just doesn't do everything I > require from a voluminous temperament or MOS. Can you suggest something a > little higher at about 80 or so tones? I could, but in order to make sensible suggestions it would be good to hear why Octoid[72] won't work for you. For all I know, Octoid[80], with 80 notes to the octave, would.
From: wallyesterpaulrus (2006-02-21) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > And how does 79 notes from 33 equal divisions of the pure fourth with octave > equivalances preclude the possibility of modulations Paul? I didn't say that. > Or better yet, > how does 77 or 80 do not? I have yet to look at the specific scales Gene was referring to. One possibility for 80-out-of-159 is simply the complement of your 79-out-of-159 scale, so that version would share most properties in common with your scale. Actually, if the 80&159 temperament that Gene referred to yields your scale exactly, then maybe Monz would want to switch to the TM-reduced kernel basis for this temperament rather than one for 159-tone (or any other) equal temperament. > ----- Original Message ----- > From: "wallyesterpaulrus" <wallyesterpaulrus@...> > To: <tuning@yahoogroups.com> > Sent: 20 Þubat 2006 Pazartesi 12:56 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote: > > > > > > > I should note, however, that 159 is interesting as a high or very > > > > high limit system, and the 80&159 temperament looks better in > > > > higher limits. Of course in something like the 29 limit you may > > > > as well just use all 159 notes, and I really don't see why Ozan > > > > doesn't do that always, > > > > > > He's answered that. 'Too many notes.' > > > > > > -Carl > > > > But one would think that if one chooses a subset, it would be one where > the consonant intervals can be transposed once or twice by the usual > intervals of modulation (fourths and fifths), wouldn't one? > > > > > > >
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Petr, ----- Original Message ----- From: "Petr Par\ufffdzek" To: Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 0:37 Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > Hi Ozan. > > > Aha! So you don't question the validity of 12 tones simply because it has > > historical precedence and my tuning does not? Surely you see the > dichotomy. > > I'm realizing I have to be pretty careful about how to say something to make > others understand my words in the way they were really meant. At this time, > either my statement was totally unclear or my questions made you > misunderstandd my view. That happens to me a lot. > OK, I'll try to make things clearer. > > 1. The number 12 is easily explainable for me not for its historical > precedence but for the acoustical properties of the intervals, no matter if > pure or approximated. Since I've never examined 33 equal divisions of the > fourth, I was just unaware. Well, you said it. The acoustical properties of 33 equal divisions of the pure fourth are remarkable from my point of view. > 2. We all know that, for instance, 13-EDO or 11-EDO doesn't have the > properties wich are being so valued in 12-EDO. So I was interested if, for > example, dividing the fourth into 32 or 34 equal steps instead of 33 would > harm the system, and if so, how much. Pretty much, I assure you. Or, in other words, if you found the > number 33 using some formulas while trying to meet some of your requirements > (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good > tuning for common tonal music), or if it was just one of your free > decisions. I chanced upon this while I was trying to find temperaments that contained adequately tempered fifths in range. Specifically, I was focused on 79-tET, wanted to shift the two fifths so that they were equally distant from pure: 1. (log 3/2) x 1200 divided by (log 2) over 46+47/2 times 79 = 1192.56871 cents. 2. Completed the 79th tone to 1200 cents and moved the large comma between steps 45-46. Then I realized that it was possible to make the fifth pure only if one divided the pure fourth into 33 equal parts which - when carried to the 79th tone - resulted in 1192.28954 cents, practically the same as above. Afterwards, one only needed to edit the value of the octave and rotate the scale in the same manner. Here are the differences between two approaches: 1: 1: -0.004 cents -0.003536 0.0005 Hertz, 0.0323 cycles/min. 2: 2: -0.007 cents -0.007062 0.0011 Hertz, 0.0652 cycles/min. 3: 3: -0.011 cents -0.010599 0.0016 Hertz, 0.0987 cycles/min. 4: 4: -0.014 cents -0.014135 0.0022 Hertz, 0.1327 cycles/min. 5: 5: -0.018 cents -0.017672 0.0028 Hertz, 0.1674 cycles/min. 6: 6: -0.021 cents -0.021198 0.0034 Hertz, 0.2025 cycles/min. 7: 7: -0.025 cents -0.024735 0.0040 Hertz, 0.2384 cycles/min. 8: 8: -0.028 cents -0.028261 0.0046 Hertz, 0.2748 cycles/min. 9: 9: -0.032 cents -0.031798 0.0052 Hertz, 0.3119 cycles/min. 10: 10: -0.035 cents -0.035334 0.0058 Hertz, 0.3496 cycles/min. 11: 11: -0.039 cents -0.038871 0.0065 Hertz, 0.3879 cycles/min. 12: 12: -0.042 cents -0.042397 0.0071 Hertz, 0.4268 cycles/min. 13: 13: -0.046 cents -0.045934 0.0078 Hertz, 0.4665 cycles/min. 14: 14: -0.049 cents -0.049470 0.0084 Hertz, 0.5068 cycles/min. 15: 15: -0.053 cents -0.053007 0.0091 Hertz, 0.5478 cycles/min. 16: 16: -0.057 cents -0.056533 0.0098 Hertz, 0.5893 cycles/min. 17: 17: -0.060 cents -0.060070 0.0105 Hertz, 0.6317 cycles/min. 18: 18: -0.064 cents -0.063606 0.0112 Hertz, 0.6747 cycles/min. 19: 19: -0.067 cents -0.067132 0.0120 Hertz, 0.7184 cycles/min. 20: 20: -0.071 cents -0.070669 0.0127 Hertz, 0.7628 cycles/min. 21: 21: -0.074 cents -0.074205 0.0135 Hertz, 0.8080 cycles/min. 22: 22: -0.078 cents -0.077742 0.0142 Hertz, 0.8540 cycles/min. 23: 23: -0.081 cents -0.081268 0.0150 Hertz, 0.9005 cycles/min. 24: 24: -0.085 cents -0.084805 0.0158 Hertz, 0.9479 cycles/min. 25: 25: -0.088 cents -0.088341 0.0166 Hertz, 0.9961 cycles/min. 26: 26: -0.092 cents -0.091878 0.0174 Hertz, 1.0450 cycles/min. 27: 27: -0.095 cents -0.095404 0.0182 Hertz, 1.0947 cycles/min. 28: 28: -0.099 cents -0.098941 0.0191 Hertz, 1.1452 cycles/min. 29: 29: -0.102 cents -0.102477 0.0199 Hertz, 1.1965 cycles/min. 30: 30: -0.106 cents -0.106014 0.0208 Hertz, 1.2486 cycles/min. 31: 31: -0.110 cents -0.109540 0.0217 Hertz, 1.3015 cycles/min. 32: 32: -0.113 cents -0.113077 0.0226 Hertz, 1.3552 cycles/min. 33: 33: -0.117 cents -0.116613 0.0235 Hertz, 1.4099 cycles/min. 34: 34: -0.120 cents -0.120140 0.0244 Hertz, 1.4652 cycles/min. 35: 35: -0.124 cents -0.123676 0.0254 Hertz, 1.5216 cycles/min. 36: 36: -0.127 cents -0.127212 0.0263 Hertz, 1.5788 cycles/min. 37: 37: -0.131 cents -0.130749 0.0273 Hertz, 1.6369 cycles/min. 38: 38: -0.134 cents -0.134275 0.0283 Hertz, 1.6957 cycles/min. 39: 39: -0.138 cents -0.137812 0.0293 Hertz, 1.7556 cycles/min. 40: 40: -0.141 cents -0.141348 0.0303 Hertz, 1.8165 cycles/min. 41: 41: -0.145 cents -0.144885 0.0313 Hertz, 1.8782 cycles/min. 42: 42: -0.148 cents -0.148411 0.0323 Hertz, 1.9408 cycles/min. 43: 43: -0.152 cents -0.151948 0.0334 Hertz, 2.0044 cycles/min. 44: 44: -0.155 cents -0.155484 0.0345 Hertz, 2.0690 cycles/min. 45: 45: -0.159 cents -0.159011 0.0356 Hertz, 2.1345 cycles/min. 46: 46: 0.117 cents 0.116613 0.0264 Hertz, 1.5860 cycles/min. 47: 47: 0.113 cents 0.113087 0.0259 Hertz, 1.5515 cycles/min. 48: 48: 0.110 cents 0.109550 0.0253 Hertz, 1.5161 cycles/min. 49: 49: 0.106 cents 0.106014 0.0247 Hertz, 1.4800 cycles/min. 50: 50: 0.102 cents 0.102487 0.0241 Hertz, 1.4433 cycles/min. 51: 51: 0.099 cents 0.098951 0.0234 Hertz, 1.4057 cycles/min. 52: 52: 0.095 cents 0.095414 0.0228 Hertz, 1.3674 cycles/min. 53: 53: 0.092 cents 0.091878 0.0221 Hertz, 1.3282 cycles/min. 54: 54: 0.088 cents 0.088351 0.0215 Hertz, 1.2884 cycles/min. 55: 55: 0.085 cents 0.084815 0.0208 Hertz, 1.2477 cycles/min. 56: 56: 0.081 cents 0.081278 0.0201 Hertz, 1.2061 cycles/min. 57: 57: 0.078 cents 0.077742 0.0194 Hertz, 1.1638 cycles/min. 58: 58: 0.074 cents 0.074215 0.0187 Hertz, 1.1207 cycles/min. 59: 59: 0.071 cents 0.070679 0.0179 Hertz, 1.0766 cycles/min. 60: 60: 0.067 cents 0.067142 0.0172 Hertz, 1.0317 cycles/min. 61: 61: 0.064 cents 0.063616 0.0164 Hertz, 0.9861 cycles/min. 62: 62: 0.060 cents 0.060080 0.0157 Hertz, 0.9394 cycles/min. 63: 63: 0.057 cents 0.056543 0.0149 Hertz, 0.8919 cycles/min. 64: 64: 0.053 cents 0.053007 0.0141 Hertz, 0.8434 cycles/min. 65: 65: 0.049 cents 0.049480 0.0132 Hertz, 0.7942 cycles/min. 66: 66: 0.046 cents 0.045944 0.0124 Hertz, 0.7439 cycles/min. 67: 67: 0.042 cents 0.042407 0.0115 Hertz, 0.6926 cycles/min. 68: 68: 0.039 cents 0.038871 0.0107 Hertz, 0.6404 cycles/min. 69: 69: 0.035 cents 0.035344 0.0098 Hertz, 0.5874 cycles/min. 70: 70: 0.032 cents 0.031808 0.0089 Hertz, 0.5333 cycles/min. 71: 71: 0.028 cents 0.028271 0.0080 Hertz, 0.4782 cycles/min. 72: 72: 0.025 cents 0.024735 0.0070 Hertz, 0.4220 cycles/min. 73: 73: 0.021 cents 0.021208 0.0061 Hertz, 0.3650 cycles/min. 74: 74: 0.018 cents 0.017672 0.0051 Hertz, 0.3068 cycles/min. 75: 75: 0.014 cents 0.014135 0.0041 Hertz, 0.2476 cycles/min. 76: 76: 0.011 cents 0.010609 0.0031 Hertz, 0.1874 cycles/min. 77: 77: 0.007 cents 0.007072 0.0021 Hertz, 0.1260 cycles/min. 78: 78: 0.004 cents 0.003536 0.0011 Hertz, 0.0636 cycles/min. 79: 79: 1/1 0.000000 0.0000 Hertz, 0.0000 cycles/min. Total absolute difference : 5.6399 cents Average absolute difference: 0.0714 cents Root mean square difference: 0.0833 cents Highest absolute difference: 0.1590 cents Number of notes different: 78 When compared with 159-tET, `equally distant fifths from pure` approach yields tones that are 0.0660 cents different at maximum. Cordially, Ozan
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Paul, > > > > > > > > I should note, however, that 159 is interesting as a high or very high > > > limit system, and the 80&159 temperament looks better in higher > > > limits. > > > > So this implies an 80-note MOS rather than a 79-note one should be > interesting? > > > > I don't understand what you have against 79 anyway. Absolutely nothing. In fact, if it implies an 80-note MOS, it implies a 79-note MOS too, since 159-80=79. I thought of that only after I wrote the above. > > > > > Tempering out both 1029/1024 and > > > 32805/32768, leading to "guiron", gives a generator of 31 steps of > > > 159, which is an example of the sort of thing one might do by way of > > > an alternative to the 79-note MOS (a 77-note MOS, perhaps). > > > > > Fascinating. > > > > > > It would be fascinating if we were given the chance to analyze it first. > Indeed.
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space Why, it looks pretty good monz! I'm mighty pleased with your effort. ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 1:26 Subject: [tuning] Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space > --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > > But OK, yes, you're right ... since Ozan's tuning explicitly > > has a "pure" 3/2 5th, and since i know that his preferred > > version of the tuning uses (4/3)^(1/33) as the generator, > > i guess i should have included prime-factor 3 in the Tonespace. > > I'll do another one for 159-edo which includes 3, and post it. > > > Lo and behold ... > > > Ozan Yarman - 79-MOS 159-edo, in (2,)3,5,7,11-space > =================================================== > > > TM-basis unison-vectors: > > . 2,3,5,7,11-monzo ..... ratio .........~cents > ------------------------------------------------- > > .. [-3 2 -1 2 -1 > ... 441 / 440 .... 3.930158439 > .. [-7 -1 1 1 1 > .... 385 / 384 .... 4.502561833 > .. [5 -7 -1 3 0 > .. 10976 / 10935 .. 6.478999485 > .. [-2 -2 4 1 -2 > .. 4375 / 4356 ... 7.534875468 > > > > The 79-MOS 159-edo tuning in 2,3,5,7,11-space: > > degree .. ~cents ... 2,3,5,7,11-monzo ..... ratio > ---------------------------------------------------- > > ... 0 ..... 0.000 .. [ 0 0, 0 0 0 > ....... 1 / 1 > ... 1 .... 15.094 .. [ 4 0, -2 -1 1 > ... 176 / 175 > ... 2 .... 30.189 .. [ 3 0, -1 1 -1 > .... 56 / 55 > ... 3 .... 45.283 .. [ 0 -1, -2 1 1 > .... 77 / 75 > ... 4 .... 60.377 .. [ 2 -3, 0 1 0 > ..... 28 / 27 > ... 5 .... 75.472 .. [ 6 -3, -2 0 1 > ... 704 / 675 > ... 6 .... 90.566 .. [ 0 4, 0 -1 -1 > .... 81 / 77 > ... 7 ... 105.660 .. [ -3 3, -1 -1 1 .... 297 / 280 > ... 8 ... 120.755 .. [ -1 1, 1 -1 0 > .... 15 / 14 > ... 9 ... 135.849 .. [ 3 1, -1 -2 1 > ... 264 / 245 > .. 10 ... 150.943 .. [ 2 1, 0 0 -1 > ..... 12 / 11 > .. 11 ... 166.038 .. [ -1 0, -1 0 1 > .... 11 / 10 > .. 12 ... 181.132 .. [ 1 -2, 1 0 0 > ..... 10 / 9 > .. 13 ... 196.226 .. [ 2 0, -2 1 0 > ..... 28 / 25 > .. 14 ... 211.321 .. [ 4 -2, 0 1 -1 > ... 112 / 99 > .. 15 ... 226.415 .. [ 1 -3, -1 1 1 > ... 154 / 135 > .. 16 ... 241.509 .. [ -2 2, 2 -2 0 > ... 225 / 196 > .. 17 ... 256.604 .. [ -1 4, -1 -1 0 ..... 81 / 70 > .. 18 ... 271.698 .. [ 1 2, 1 -1 -1 > .... 90 / 77 > .. 19 ... 286.792 .. [ -2 1, 0 -1 1 > .... 33 / 28 > .. 20 ... 301.887 .. [ -3 1, 1 1 -1 > ... 105 / 88 > .. 21 ... 316.981 .. [ 1 1, -1 0 0 > ...... 6 / 5 > .. 22 ... 332.075 .. [ 3 -1, 1 0 -1 > .... 40 / 33 > .. 23 ... 347.170 .. [ 0 -2, 0 0 1 > ..... 11 / 9 > .. 24 ... 362.264 .. [ -1 -2, 1 2 -1 .... 245 / 198 > .. 25 ... 377.358 .. [ 3 -2, -1 1 0 > .... 56 / 45 > .. 26 ... 392.453 .. [ 5 -4, 1 1 -1 > .. 1120 / 891 > .. 27 ... 407.547 .. [ -3 2, 1 -2 1 > ... 495 / 392 > .. 28 ... 422.642 .. [ -4 2, 2 0 -1 > ... 225 / 176 > .. 29 ... 437.736 .. [ 0 2, 0 -1 0 > ...... 9 / 7 > .. 30 ... 452.830 .. [ 2 0, 2 -1 -1 > ... 100 / 77 > .. 31 ... 467.925 .. [ -4 1, 0 1 0 > ..... 21 / 16 > .. 32 ... 483.019 .. [ 0 1, -2 0 1 > ..... 33 / 25 > .. 33 ... 498.113 .. [ 2 -1, 0 0 0 > ...... 4 / 3 > .. 34 ... 513.208 .. [ 6 -1, -2 -1 1 .... 704 / 525 > .. 35 ... 528.302 .. [ -2 -2, 0 2 0 > .... 49 / 36 > .. 36 ... 543.396 .. [ 2 -2, -2 1 1 > ... 308 / 225 > .. 37 ... 558.491 .. [ -1 3, 1 -2 0 > ... 135 / 98 > .. 38 ... 573.585 .. [ 0 5, -2 -1 0 > ... 243 / 175 > .. 39 ... 588.679 .. [ -5 2, 1 0 0 > ..... 45 / 32 > .. 40 ... 603.774 .. [ -1 2, -1 -1 1 ..... 99 / 70 > .. 41 ... 618.868 .. [ 1 0, 1 -1 0 > ..... 10 / 7 > .. 42 ... 633.962 .. [ 2 2, -2 0 0 > ..... 36 / 25 > .. 43 ... 649.057 .. [ -3 -1, 1 1 0 > .... 35 / 24 > .. 44 ... 664.151 .. [ 1 -1, -1 0 1 > .... 22 / 15 > .. 45 ... 679.245 .. [ 3 -3, 1 0 0 > ..... 40 / 27 > .. 46 ... 701.887 .. [ -1 1, 0 0 0 > ...... 3 / 2 > .. 47 ... 716.981 .. [ 3 1, -2 -1 1 > ... 264 / 175 > .. 48 ... 732.075 .. [ 5 -1, 0 -1 0 > .... 32 / 21 > .. 49 ... 747.170 .. [ -1 0, -2 1 1 > .... 77 / 50 > .. 50 ... 762.264 .. [ 1 -2, 0 1 0 > ..... 14 / 9 > .. 51 ... 777.358 .. [ 5 -2, -2 0 1 > ... 352 / 225 > .. 52 ... 792.453 .. [ 4 -2, -1 2 -1 .... 784 / 495 > .. 53 ... 807.547 .. [ -4 4, -1 -1 1 .... 891 / 560 > .. 54 ... 822.642 .. [ -2 2, 1 -1 0 > .... 45 / 28 > .. 55 ... 837.736 .. [ 2 2, -1 -2 1 > ... 396 / 245 > .. 56 ... 852.830 .. [ 1 2, 0 0 -1 > ..... 18 / 11 > .. 57 ... 867.925 .. [ -2 1, -1 0 1 > .... 33 / 20 > .. 58 ... 883.019 .. [ 0 -1, 1 0 0 > ...... 5 / 3 > .. 59 ... 898.113 .. [ 4 -1, -1 -1 1 .... 176 / 105 > .. 60 ... 913.208 .. [ 3 -1, 0 1 -1 > .... 56 / 33 > .. 61 ... 928.302 .. [ 0 -2, -1 1 1 > .... 77 / 45 > .. 62 ... 943.396 .. [ 2 -4, 1 1 0 > .... 140 / 81 > .. 63 ... 958.491 .. [ -2 5, -1 -1 0 .... 243 / 140 > .. 64 ... 973.585 .. [ 0 3, 1 -1 -1 > ... 135 / 77 > .. 65 ... 988.679 .. [ -3 2, 0 -1 1 > .... 99 / 56 > .. 66 .. 1003.774 .. [ -1 0, 2 -1 0 > .... 25 / 14 > .. 67 .. 1018.868 .. [ 0 2, -1 0 0 > ...... 9 / 5 > .. 68 .. 1033.962 .. [ 2 0, 1 0 -1 > ..... 20 / 11 > .. 69 .. 1049.057 .. [ -1 -1, 0 0 1 > .... 11 / 6 > .. 70 .. 1064.151 .. [ 1 -3, 2 0 0 > ..... 50 / 27 > .. 71 .. 1079.245 .. [ 2 -1, -1 1 0 > .... 28 / 15 > .. 72 .. 1094.340 .. [ 4 -3, 1 1 -1 > ... 560 / 297 > .. 73 .. 1109.434 .. [ 1 -4, 0 1 1 > .... 154 / 81 > .. 74 .. 1124.528 .. [ -5 3, 2 0 -1 > ... 675 / 352 > .. 75 .. 1139.623 .. [ -1 3, 0 -1 0 > .... 27 / 14 > .. 76 .. 1154.717 .. [ 1 1, 2 -1 -1 > ... 150 / 77 > .. 77 .. 1169.811 .. [ 5 1, 0 -2 0 > ..... 96 / 49 > .. 78 .. 1184.906 .. [ -3 0, 2 1 -1 > ... 175 / 88 > (. 79 .. 1200.000 .. [ 1 0, 0 0 0> ........ 2 / 1) > > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > >
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Can you provide the details for Octaid 80? 72 didn't work, because the super-pythagorean fifth is intolerable to listen to. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 1:41 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > It is interesting indeed! However, the octoid just doesn't do > everything I > > require from a voluminous temperament or MOS. Can you suggest > something a > > little higher at about 80 or so tones? > > I could, but in order to make sensible suggestions it would be good to > hear why Octoid[72] won't work for you. For all I know, Octoid[80], > with 80 notes to the octave, would. >
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning Ozan, don't take this as an attack or anything, I'm just trying to tease out your thinking. Why are these 694.2-cent fifths less offensive than those of 19-equal? --- In tuning@yahoogroups.com, "Ozan Yarman" wrote: > > Petr, the default fifth is exactly 3/2 in my tuning: > > 0: 0.000 cents 0.000 0 0 commas C > 46: 701.955 cents -0.000 0 0 commas G > 13: 694.245 cents -7.710 -237 D > 59: 701.955 cents -7.710 -237 A > 26: 694.245 cents -15.421 -473 E > 72: 701.955 cents -15.421 -473 B > 39: 694.245 cents -23.131 -710 F# > 6: 701.955 cents -23.131 -710 C# > 52: 701.955 cents -23.131 -710 G# > 19: 694.245 cents -30.842 -947 D# > 65: 701.955 cents -30.842 -947 A# > 32: 694.245 cents -38.552 -1183 E# > 78: 701.955 cents -38.552 -1183 B# > 45: 694.245 cents -46.263 -1420 G\ > 12: 701.955 cents -46.263 -1420 D\ > 58: 701.955 cents -46.263 -1420 A\ > 25: 694.245 cents -53.973 -1656 E\ > 71: 701.955 cents -53.973 -1656 B\ > 38: 694.245 cents -61.684 -1893 F#\ > 5: 701.955 cents -61.684 -1893 C#\ > 51: 701.955 cents -61.684 -1893 G#\ > 18: 694.245 cents -69.394 -2130 D#\ > 64: 701.955 cents -69.394 -2130 A#\ > 31: 694.245 cents -77.105 -2366 F\\ > 77: 701.955 cents -77.105 -2366 C\\ > 44: 694.245 cents -84.815 -2603 G\\ > 11: 701.955 cents -84.815 -2603 D\\ > 57: 701.955 cents -84.815 -2603 A\\ > 24: 694.245 cents -92.525 -2840 E\\ > 70: 701.955 cents -92.525 -2840 B\\ > 37: 694.245 cents -100.236 -3076 F) > 4: 701.955 cents -100.236 -3076 C) > 50: 701.955 cents -100.236 -3076 G) > 17: 694.245 cents -107.946 -3313 D) > 63: 701.955 cents -107.946 -3313 A) > 30: 694.245 cents -115.657 -3550 Fv > 76: 701.955 cents -115.657 -3550 Cv > 43: 694.245 cents -123.367 -3786 Gv > 10: 701.955 cents -123.367 -3786 Dv > 56: 701.955 cents -123.367 -3786 Av > 23: 694.245 cents -131.078 -4023 Ev > 69: 701.955 cents -131.078 -4023 Bv > 36: 694.245 cents -138.788 -4259 F^ > 3: 701.955 cents -138.788 -4259 C^ > 49: 701.955 cents -138.788 -4259 G^ > 16: 694.245 cents -146.499 -4496 D^ > 62: 701.955 cents -146.499 -4496 A^ > 29: 694.245 cents -154.209 -4733 F( > 75: 701.955 cents -154.209 -4733 C( > 42: 694.245 cents -161.920 -4969 G( > 9: 701.955 cents -161.920 -4969 D( > 55: 701.955 cents -161.920 -4969 A( > 22: 694.245 cents -169.630 -5206 E( > 68: 701.955 cents -169.630 -5206 B( > 35: 694.245 cents -177.340 -5443 F// > 2: 701.955 cents -177.340 -5443 C// > 48: 701.955 cents -177.340 -5443 G// > 15: 694.245 cents -185.051 -5679 D// > 61: 701.955 cents -185.051 -5679 A// > 28: 694.245 cents -192.761 -5916 E// > 74: 701.955 cents -192.761 -5916 B// > 41: 694.245 cents -200.472 -6153 Gb/ > 8: 701.955 cents -200.472 -6153 Db/ > 54: 701.955 cents -200.472 -6153 Ab/ > 21: 694.245 cents -208.182 -6389 Eb/ > 67: 701.955 cents -208.182 -6389 Bb/ > 34: 694.245 cents -215.893 -6626 F/ > 1: 701.955 cents -215.893 -6626 C/ > 47: 701.955 cents -215.893 -6626 G/ > 14: 694.245 cents -223.603 -6863 D/ > 60: 701.955 cents -223.603 -6863 A/ > 27: 694.245 cents -231.314 -7099 Fb > 73: 701.955 cents -231.314 -7099 Cb > 40: 694.245 cents -239.024 -7336 Gb > 7: 701.955 cents -239.024 -7336 Db > 53: 701.955 cents -239.024 -7336 Ab > 20: 694.245 cents -246.735 -7572 Eb > 66: 701.955 cents -246.735 -7572 Bb > 33: 694.245 cents -254.445 -7809 F > 79: 701.955 cents -254.445 -7809 C > Average absolute difference: 129.4185 cents > Root mean square difference: 149.7660 cents > Maximum absolute difference: 254.4451 cents > Maximum formal fifth difference: 7.7105 cents > > > ----- Original Message ----- > From: "Petr Parízek" > To: > Sent: 21 Þubat 2006 Salý 18:45 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > Hi Ozan. > > > > You wrote: > > > > > The fifth should have been 3/2. The complication arises from your > > preference > > > of 159 equal divisions of the octave, which is a very close > approximation > > to > > > my proposal. > > > > Am I right in assuming that the fifth is closer to 3/2 in your tuning than > > in 159-equal? > > > > Petr > > > > >
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning They are not less offensive, they are very very offensive, but that is the price I have to pay while retaining all the benefits of 79 tones, unless of course you can suggest something else as a substitute. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 2:47 Subject: [tuning] Re: Ozan's 159-edo-based tuning Ozan, don't take this as an attack or anything, I'm just trying to tease out your thinking. Why are these 694.2-cent fifths less offensive than those of 19-equal?
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Oh well, we are all human! Thanx for your encouragement though. Just remember that I am entitled to making less sense most of the time than not, given my eccentric disposition and absolute ignorance of the world. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 1:29 Subject: [tuning] Re: Ozan's 159-edo-based tuning Ozan, I apologize again for my manner. I simply seek mutual edification. Our past discussions on the topic contained my preliminary reactions, which you seem to be asking me to rehash, but I prefer to move forward instead of backwards. The inconsistencies I was referring to were seeming incompatibilities between your way of thinking and the assumptions behind the technical machinery that Monz, Gene, and I are used to. Whether you choose to answer my present set of questions or not, you have my heartfelt support in every musical endeavor, particularly those which will allow your rich musical heritage to survive the wave of 12-equal hegemony.
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Paul (and Oz), > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > Hi Ozan, Yahya, et al, > > > > > > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > > I've made a Tonescape file of your 79-MOS as a subset > > > > of 159-edo in (2,)5,7,11-space, with 2 as the identity > > > > interval, and using TM-basis for the 159-edo periodicity-block. > > > > Can you state this with more precision and detail, please, > > for those of us attempting to follow along? > > > TM-basis for 159-edo in 2,5,7,11-space: > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents > --------------------------------------------------- > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > How did you arrive at this? Which "val" are you assuming? And as usual, I think it would make a lot more sense to reduce the pitches (thus making the choice of kernel basis irrelevant) instead of reducing the kernel basis and then constructing an FPB. > > > > > degree ... ~cents .. ------ monzo ------- ....... ratio > > > ...................... 2 .. 5 .. 7 .. 11 > > > > > > <snip> > > > .. 33 ... 498.113 .. [ 9 ..-1 ..-17 ..-1 > ..... 512 / 385 > > > > I find it pretty humorous that you didn't even get 4/3 > > for 33 steps, one of the few clues Ozan has explicitly > > given us . . . > > > > Well, considering that 3 is *not* one of the prime-factors > in the Tonespace which i used, it's pretty obvious *why* > i didn't get 4/3. > > But OK, yes, you're right ... since Ozan's tuning explicitly > has a "pure" 3/2 5th, and since i know that his preferred > version of the tuning uses (4/3)^(1/33) as the generator, > i guess i should have included prime-factor 3 in the Tonespace. > I'll do another one for 159-edo which includes 3, and post it. > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software >
From: monz (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning Hi Paul, --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > [monz] > > TM-basis for 159-edo in 2,5,7,11-space: > > > > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents > > --------------------------------------------------- > > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > > > How did you arrive at this? I didn't have to do anything myself, Tonescape did it. > Which "val" are you assuming? The 2,5,7,11-val is < 159 369 446 550 ] . > And as usual, I think it would make a lot more sense to > reduce the pitches (thus making the choice of kernel basis > irrelevant) instead of reducing the kernel basis and then > constructing an FPB. Ah yes, i could tell Tonescape to construct a 79-tone periodicity-block first, *then* use 159-edo for the tuning. Why do you say that reducing the number of pitches makes "the choice of kernel basis irrelevant"? The choice of kernel basis still determines how compact the periodicity-block is. -monz http://tonalsoft.com Tonescape microtonal music software
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > Until then, can you give me the cent values for Guiron[77] Gene? ! guiron77.scl Guiron[77] (118&159 temperament) in 159-et 77 ! 22.641509 30.188679 52.830189 60.377358 83.018868 90.566038 113.207547 120.754717 143.396226 150.943396 173.584906 181.132075 203.773585 211.320755 233.962264 256.603774 264.150943 286.792453 294.339623 316.981132 324.528302 347.169811 354.716981 377.358491 384.905660 407.547170 415.094340 437.735849 445.283019 467.924528 490.566038 498.113208 520.754717 528.301887 550.943396 558.490566 581.132075 588.679245 611.320755 618.867925 641.509434 649.056604 671.698113 679.245283 701.886792 709.433962 732.075472 754.716981 762.264151 784.905660 792.452830 815.094340 822.641509 845.283019 852.830189 875.471698 883.018868 905.660377 913.207547 935.849057 943.396226 966.037736 988.679245 996.226415 1018.867925 1026.415094 1049.056604 1056.603774 1079.245283 1086.792453 1109.433962 1116.981132 1139.622642 1147.169811 1169.811321 1177.358491 1200.000000 Here's how I would do Ozan[80]: ! ozan80.scl Ozan[80] (80&159 temperament) in 159-et 80 ! 15.094340 30.188679 45.283019 60.377358 75.471698 90.566038 105.660377 120.754717 135.849057 150.943396 166.037736 181.132075 196.226415 211.320755 226.415094 241.509434 256.603774 271.698113 286.792453 301.886792 316.981132 332.075472 347.169811 362.264151 377.358491 392.452830 407.547170 422.641509 437.735849 452.830189 467.924528 483.018868 498.113208 513.207547 528.301887 543.396226 558.490566 573.584906 588.679245 603.773585 618.867925 633.962264 649.056604 664.150943 679.245283 694.339623 709.433962 724.528302 739.622642 754.716981 769.811321 784.905660 800.000000 815.094340 830.188679 845.283019 860.377358 875.471698 890.566038 905.660377 920.754717 935.849057 950.943396 966.037736 981.132075 996.226415 1011.320755 1026.415094 1041.509434 1056.603774 1071.698113 1086.792453 1101.886792 1116.981132 1132.075472 1147.169811 1162.264151 1177.358491 1192.452830 1200.000000
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > > > How did you arrive at this? Which "val" are you assuming? Just run the numbers, and you get <159 .. 369 446 550|. > > But OK, yes, you're right ... since Ozan's tuning explicitly > > has a "pure" 3/2 5th, and since i know that his preferred > > version of the tuning uses (4/3)^(1/33) as the generator, > > i guess i should have included prime-factor 3 in the Tonespace. > > I'll do another one for 159-edo which includes 3, and post it. Considering how good the 3 of 159 is, this doesn't make a hell of a lot of sense.
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Gene, thank you for posting these. I see that Guiron doesn't serve my purposes, but 79 and 80 do. However, I wonder why you prefer to keep the smaller comma in 80 toward the end instead? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 3:43 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > Until then, can you give me the cent values for Guiron[77] Gene? > > ! guiron77.scl > Guiron[77] (118&159 temperament) in 159-et > 77 > ! > 22.641509 > 30.188679 > 52.830189 > 60.377358 > 83.018868 > 90.566038 > 113.207547 > 120.754717 > 143.396226 > 150.943396 > 173.584906 > 181.132075 > 203.773585 > 211.320755 > 233.962264 > 256.603774 > 264.150943 > 286.792453 > 294.339623 > 316.981132 > 324.528302 > 347.169811 > 354.716981 > 377.358491 > 384.905660 > 407.547170 > 415.094340 > 437.735849 > 445.283019 > 467.924528 > 490.566038 > 498.113208 > 520.754717 > 528.301887 > 550.943396 > 558.490566 > 581.132075 > 588.679245 > 611.320755 > 618.867925 > 641.509434 > 649.056604 > 671.698113 > 679.245283 > 701.886792 > 709.433962 > 732.075472 > 754.716981 > 762.264151 > 784.905660 > 792.452830 > 815.094340 > 822.641509 > 845.283019 > 852.830189 > 875.471698 > 883.018868 > 905.660377 > 913.207547 > 935.849057 > 943.396226 > 966.037736 > 988.679245 > 996.226415 > 1018.867925 > 1026.415094 > 1049.056604 > 1056.603774 > 1079.245283 > 1086.792453 > 1109.433962 > 1116.981132 > 1139.622642 > 1147.169811 > 1169.811321 > 1177.358491 > 1200.000000 > > Here's how I would do Ozan[80]: > > ! ozan80.scl > Ozan[80] (80&159 temperament) in 159-et > 80 > ! > 15.094340 > 30.188679 > 45.283019 > 60.377358 > 75.471698 > 90.566038 > 105.660377 > 120.754717 > 135.849057 > 150.943396 > 166.037736 > 181.132075 > 196.226415 > 211.320755 > 226.415094 > 241.509434 > 256.603774 > 271.698113 > 286.792453 > 301.886792 > 316.981132 > 332.075472 > 347.169811 > 362.264151 > 377.358491 > 392.452830 > 407.547170 > 422.641509 > 437.735849 > 452.830189 > 467.924528 > 483.018868 > 498.113208 > 513.207547 > 528.301887 > 543.396226 > 558.490566 > 573.584906 > 588.679245 > 603.773585 > 618.867925 > 633.962264 > 649.056604 > 664.150943 > 679.245283 > 694.339623 > 709.433962 > 724.528302 > 739.622642 > 754.716981 > 769.811321 > 784.905660 > 800.000000 > 815.094340 > 830.188679 > 845.283019 > 860.377358 > 875.471698 > 890.566038 > 905.660377 > 920.754717 > 935.849057 > 950.943396 > 966.037736 > 981.132075 > 996.226415 > 1011.320755 > 1026.415094 > 1041.509434 > 1056.603774 > 1071.698113 > 1086.792453 > 1101.886792 > 1116.981132 > 1132.075472 > 1147.169811 > 1162.264151 > 1177.358491 > 1192.452830 > 1200.000000 >
From: Haresh BAKSHI (2006-02-22) Subject: No drone in Indian music before 12th century (was: Re: More on shruti-s) Dear Ozan, I have the same question that Carl has: The key is there; where is the modulation, or, where are the modulations? Regards, Haresh.
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Gene, thank you for posting these. I see that Guiron doesn't serve my > purposes, but 79 and 80 do. However, I wonder why you prefer to keep the > smaller comma in 80 toward the end instead? I made a guess that you'd prefer it there.
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Can you provide the details for Octaid 80? 72 didn't work, because the > super-pythagorean fifth is intolerable to listen to. Octoid[80] does not put the meantone fifth and the nearly pure (schismatic) fifth in the same interval class, so I doubt it is what you want. Octoid[72] does, however. There are no intolerable super-pythagorean fifths in the six closed chains of fifths you get in this way. As I said, these are in fact well-temperaments; two almost-pure fifths followed by a meantone fifth, and repeat. The minor thirds are all 300 cents exactly, and the triads differ in that the ones with the meantone fifths have better major thirds, as they clearly must, given that the minor thirds are fixed in size. ! octoid80.scl Octoid[80] in 224-et tuning 80 ! 16.071429 32.142857 48.214286 64.285714 80.357143 85.714286 101.785714 117.857143 133.928571 150.000000 166.071429 182.142857 198.214286 214.285714 230.357143 235.714286 251.785714 267.857143 283.928571 300.000000 316.071429 332.142857 348.214286 364.285714 380.357143 385.714286 401.785714 417.857143 433.928571 450.000000 466.071429 482.142857 498.214286 514.285714 530.357143 535.714286 551.785714 567.857143 583.928571 600.000000 616.071429 632.142857 648.214286 664.285714 680.357143 685.714286 701.785714 717.857143 733.928571 750.000000 766.071429 782.142857 798.214286 814.285714 830.357143 835.714286 851.785714 867.857143 883.928571 900.000000 916.071429 932.142857 948.214286 964.285714 980.357143 985.714286 1001.785714 1017.857143 1033.928571 1050.000000 1066.071429 1082.142857 1098.214286 1114.285714 1130.357143 1135.714286 1151.785714 1167.857143 1183.928571 1200.000000
From: Carl Lumma (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning > Gene, thank you for posting these. I see that Guiron doesn't > serve my purposes, but 79 and 80 do. Why is that? -Carl
From: coul@hccnet.nl (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning Ozan, Did you consider using E101 for your tuning? It has the benefit that the best third is notated as E\. Manuel
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Dear Manuel, I'm afraid it won't do. Perde segah of ~390 cents has to be a natural E to begin with. Ozan ----- Original Message ----- From: <coul@hccnet.nl> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 19:20 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Ozan, > > Did you consider using E101 for your tuning? It has the benefit that the > best third is notated as E\. > > Manuel > >
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning If you can only have 79 tones on your instrument, what does it matter whether they're from a superset which has 171, 217, 224, 270, 311, or even an infinite number of tones per octave? It seems that only the number of tones on the instrument which has to conform to practical constraints, not the number of notes in the superset -- right? Just curious (the MOS scales in my paper are *not* drawn from any equal-tempered supersets). --- In tuning@yahoogroups.com, "Ozan Yarman" wrote: > > Such is the problem I encountered myself with 7-limit consonances in > 200-edo. If one chooses to deal with such high numbers, surely better > options exist within that nominal region. Gene suggested 313 as a universal > tuning if I'm not mistaken. The problem is, you cannot go much higher than > 80 or so tones with a Qanun, or for any other practical instrument of Maqam > Music for that matter. > > Cordially, > Ozan > > ----- Original Message ----- > From: "Petr Parízek" > To: > Sent: 21 Þubat 2006 Salý 22:34 > Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > > > > Hi Ozan. > > > > > As for 200-edo. I am very pleased with it since it has an excellent 1/4 > > > Pyth-comma tempered fifth next to a just fifth. But is it good enough to > > be > > > called universal? > > > > Well, speaking for myself at least, what more could I wish? The only case > > where I might blame 200-EDO may be perhaps if I found a 3 cent detuning to > > be too much (I mean when approximating 7/4). Indeed, I confess, in some > > situations, I really do. > > > > Petr > > >
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > Petr, the default fifth is exactly 3/2 in my tuning: > > OK, I misstated; but then your tuning is not based on an equal > division of the fourth into 33 parts. > So what is it?
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning By all means, it IS a 33 equal division of the pure fourth carried to the 79th tone that is completed to the octave whereby the resultant scale is rotated to yield an exact pure fourth as well as fifth. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 21:30 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > > > Petr, the default fifth is exactly 3/2 in my tuning: > > > > OK, I misstated; but then your tuning is not based on an equal > > division of the fourth into 33 parts. > > > So what is it? > >
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning > (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good > tuning for common tonal music), 22-equal is absolutely terrible for common tonal music. The comma problems, which I've discussed before, turn into comma disasters. I've been playing in 22-equal for over 10 years and any attempt at common-practice tonality quickly degenerates into a comedy. Blackwood's and other composers' attempts to do this sound to me like a perversion, and give 22 a bad name, given 22-equal's many wonderful non-common-practice resources.
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I wholeheartedly agree with you Paul. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 22:14 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > (like I could find 19-EDO, 22, 31, 50, or 53 while trying to find a good > > tuning for common tonal music), > > 22-equal is absolutely terrible for common tonal music. The comma problems, which I've discussed before, turn into comma disasters. I've been playing in 22-equal for over 10 years and any attempt at common-practice tonality quickly degenerates into a comedy. Blackwood's and other composers' attempts to do this sound to me like a perversion, and give 22 a bad name, given 22-equal's many wonderful non-common-practice resources. > > >
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I found no faults with SCALA e79 notation for 79 MOS 159-tET beforehand. Or > do you believe that I take everything for granted before putting them to > good use? Absolutely not what I believe, given what I wrote below. You continue to misintepret the spirit of my inquiries, which is to open up mutual understanding. Also, this post was not primarily directed toward you, but toward Manuel and Gene. > ----- Original Message ----- > From: "wallyesterpaulrus" <wallyesterpaulrus@...> > To: <tuning@yahoogroups.com> > Sent: 22 Þubat 2006 Çarþamba 0:57 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > I agree with Gene that the current version of Scala does not produce > sensible results when using e31 with 103-equal, e79 with 159-equal, etc. Of > course you may have your own reasons for liking or disliking what it's > doing, but one should not take the SCALA output for granted. For but one > thing, the result will be sensitive to the choice of starting note, usually > taken as C. > > -- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > Dear monz, > > > > Thanks very much for the praises. I have uploaded to pictures of my Qanun > > to: > > > > http://www.ozanyarman.com/anonymous/ > > > > Sorry for the bad quality. My webcam can do no better and the Qanun just > > won't fit in my flatbed scanner! > > > > A score is very easy to prepare with a frequency analyzer program. > > Unfortunately Solo Explorer by Gailius Raskinis detected polyphony and > could > > not transcribe the piece. > > > > The unalterated notes used are these according to SCALA e79: > > > > A B( C# D Fb F G A B( C# D E( F# G A B( C# D > > > > Fb equates to E buselik, not E segah, hence the characteristic of the > > Buselik Maqam, whose tonic is lower D. However, I finished on lower A > > Ashiran with a Hijaz flavor. > > > > Cordially, > > Oz. >
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Sorry about that! It's becoming a habit of mine these day. My apologies. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 22:29 Subject: [tuning] Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I found no faults with SCALA e79 notation for 79 MOS 159-tET beforehand. Or > do you believe that I take everything for granted before putting them to > good use? Absolutely not what I believe, given what I wrote below. You continue to misintepret the spirit of my inquiries, which is to open up mutual understanding. Also, this post was not primarily directed toward you, but toward Manuel and Gene.
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Certainly not. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 9:07 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Gene, thank you for posting these. I see that Guiron doesn't serve my > > purposes, but 79 and 80 do. However, I wonder why you prefer to keep the > > smaller comma in 80 toward the end instead? > > I made a guess that you'd prefer it there. > > >
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I have given ample explanations why, have I not? ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 12:38 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > Gene, thank you for posting these. I see that Guiron doesn't > > serve my purposes, but 79 and 80 do. > > Why is that? > > -Carl >
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning It certainly matters how you place those tones and how much of them you are able to handle before one is constrained by the instrument in question. I find 79 MOS 159-tET to be a very good choice with its three sizes of fifths, adequate approximation of 3,5,7,11,13 limit intervals, and a myriad of transposition capabilities. Besides, the notation is just right for Maqam Music. What other subset would you suggest that appeals to me then? ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 21:07 Subject: [tuning] Re: Ozan's 159-edo-based tuning If you can only have 79 tones on your instrument, what does it matter whether they're from a superset which has 171, 217, 224, 270, 311, or even an infinite number of tones per octave? It seems that only the number of tones on the instrument which has to conform to practical constraints, not the number of notes in the superset -- right? Just curious (the MOS scales in my paper are *not* drawn from any equal-tempered supersets).
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I have given ample explanations why, have I not? Evidently not. Guiron provides a great multitude of nearly pure fifths, but does not do very well with 112/75, which tempers to the meantone fifth; this has a complexity of 44 generators. Is that why not? I can easily enough find temperaments in which the complexity of the fifth and meantone fifth are both low; in fact I have.
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space Now how about a 13-limit version, since Gene gave the 13-limit TM basis for the 2D temperament that gives you this MOS scale? 13-limit would be a step closer to the much higher-prime-limit ratios Ozan said he was interested in approximating with this scale (a while back). --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > But OK, yes, you're right ... since Ozan's tuning explicitly > > has a "pure" 3/2 5th, and since i know that his preferred > > version of the tuning uses (4/3)^(1/33) as the generator, > > i guess i should have included prime-factor 3 in the Tonespace. > > I'll do another one for 159-edo which includes 3, and post it. > > > Lo and behold ... > > > Ozan Yarman - 79-MOS 159-edo, in (2,)3,5,7,11-space > =================================================== > > > TM-basis unison-vectors: > > . 2,3,5,7,11-monzo ..... ratio .........~cents > ------------------------------------------------- > > .. [-3 2 -1 2 -1 > ... 441 / 440 .... 3.930158439 > .. [-7 -1 1 1 1 > .... 385 / 384 .... 4.502561833 > .. [5 -7 -1 3 0 > .. 10976 / 10935 .. 6.478999485 > .. [-2 -2 4 1 -2 > .. 4375 / 4356 ... 7.534875468 > > > > The 79-MOS 159-edo tuning in 2,3,5,7,11-space: > > degree .. ~cents ... 2,3,5,7,11-monzo ..... ratio > ---------------------------------------------------- > > ... 0 ..... 0.000 .. [ 0 0, 0 0 0 > ....... 1 / 1 > ... 1 .... 15.094 .. [ 4 0, -2 -1 1 > ... 176 / 175 > ... 2 .... 30.189 .. [ 3 0, -1 1 -1 > .... 56 / 55 > ... 3 .... 45.283 .. [ 0 -1, -2 1 1 > .... 77 / 75 > ... 4 .... 60.377 .. [ 2 -3, 0 1 0 > ..... 28 / 27 > ... 5 .... 75.472 .. [ 6 -3, -2 0 1 > ... 704 / 675 > ... 6 .... 90.566 .. [ 0 4, 0 -1 -1 > .... 81 / 77 > ... 7 ... 105.660 .. [ -3 3, -1 -1 1 .... 297 / 280 > ... 8 ... 120.755 .. [ -1 1, 1 -1 0 > .... 15 / 14 > ... 9 ... 135.849 .. [ 3 1, -1 -2 1 > ... 264 / 245 > .. 10 ... 150.943 .. [ 2 1, 0 0 -1 > ..... 12 / 11 > .. 11 ... 166.038 .. [ -1 0, -1 0 1 > .... 11 / 10 > .. 12 ... 181.132 .. [ 1 -2, 1 0 0 > ..... 10 / 9 > .. 13 ... 196.226 .. [ 2 0, -2 1 0 > ..... 28 / 25 > .. 14 ... 211.321 .. [ 4 -2, 0 1 -1 > ... 112 / 99 > .. 15 ... 226.415 .. [ 1 -3, -1 1 1 > ... 154 / 135 > .. 16 ... 241.509 .. [ -2 2, 2 -2 0 > ... 225 / 196 > .. 17 ... 256.604 .. [ -1 4, -1 -1 0 ..... 81 / 70 > .. 18 ... 271.698 .. [ 1 2, 1 -1 -1 > .... 90 / 77 > .. 19 ... 286.792 .. [ -2 1, 0 -1 1 > .... 33 / 28 > .. 20 ... 301.887 .. [ -3 1, 1 1 -1 > ... 105 / 88 > .. 21 ... 316.981 .. [ 1 1, -1 0 0 > ...... 6 / 5 > .. 22 ... 332.075 .. [ 3 -1, 1 0 -1 > .... 40 / 33 > .. 23 ... 347.170 .. [ 0 -2, 0 0 1 > ..... 11 / 9 > .. 24 ... 362.264 .. [ -1 -2, 1 2 -1 .... 245 / 198 > .. 25 ... 377.358 .. [ 3 -2, -1 1 0 > .... 56 / 45 > .. 26 ... 392.453 .. [ 5 -4, 1 1 -1 > .. 1120 / 891 > .. 27 ... 407.547 .. [ -3 2, 1 -2 1 > ... 495 / 392 > .. 28 ... 422.642 .. [ -4 2, 2 0 -1 > ... 225 / 176 > .. 29 ... 437.736 .. [ 0 2, 0 -1 0 > ...... 9 / 7 > .. 30 ... 452.830 .. [ 2 0, 2 -1 -1 > ... 100 / 77 > .. 31 ... 467.925 .. [ -4 1, 0 1 0 > ..... 21 / 16 > .. 32 ... 483.019 .. [ 0 1, -2 0 1 > ..... 33 / 25 > .. 33 ... 498.113 .. [ 2 -1, 0 0 0 > ...... 4 / 3 > .. 34 ... 513.208 .. [ 6 -1, -2 -1 1 .... 704 / 525 > .. 35 ... 528.302 .. [ -2 -2, 0 2 0 > .... 49 / 36 > .. 36 ... 543.396 .. [ 2 -2, -2 1 1 > ... 308 / 225 > .. 37 ... 558.491 .. [ -1 3, 1 -2 0 > ... 135 / 98 > .. 38 ... 573.585 .. [ 0 5, -2 -1 0 > ... 243 / 175 > .. 39 ... 588.679 .. [ -5 2, 1 0 0 > ..... 45 / 32 > .. 40 ... 603.774 .. [ -1 2, -1 -1 1 ..... 99 / 70 > .. 41 ... 618.868 .. [ 1 0, 1 -1 0 > ..... 10 / 7 > .. 42 ... 633.962 .. [ 2 2, -2 0 0 > ..... 36 / 25 > .. 43 ... 649.057 .. [ -3 -1, 1 1 0 > .... 35 / 24 > .. 44 ... 664.151 .. [ 1 -1, -1 0 1 > .... 22 / 15 > .. 45 ... 679.245 .. [ 3 -3, 1 0 0 > ..... 40 / 27 > .. 46 ... 701.887 .. [ -1 1, 0 0 0 > ...... 3 / 2 > .. 47 ... 716.981 .. [ 3 1, -2 -1 1 > ... 264 / 175 > .. 48 ... 732.075 .. [ 5 -1, 0 -1 0 > .... 32 / 21 > .. 49 ... 747.170 .. [ -1 0, -2 1 1 > .... 77 / 50 > .. 50 ... 762.264 .. [ 1 -2, 0 1 0 > ..... 14 / 9 > .. 51 ... 777.358 .. [ 5 -2, -2 0 1 > ... 352 / 225 > .. 52 ... 792.453 .. [ 4 -2, -1 2 -1 .... 784 / 495 > .. 53 ... 807.547 .. [ -4 4, -1 -1 1 .... 891 / 560 > .. 54 ... 822.642 .. [ -2 2, 1 -1 0 > .... 45 / 28 > .. 55 ... 837.736 .. [ 2 2, -1 -2 1 > ... 396 / 245 > .. 56 ... 852.830 .. [ 1 2, 0 0 -1 > ..... 18 / 11 > .. 57 ... 867.925 .. [ -2 1, -1 0 1 > .... 33 / 20 > .. 58 ... 883.019 .. [ 0 -1, 1 0 0 > ...... 5 / 3 > .. 59 ... 898.113 .. [ 4 -1, -1 -1 1 .... 176 / 105 > .. 60 ... 913.208 .. [ 3 -1, 0 1 -1 > .... 56 / 33 > .. 61 ... 928.302 .. [ 0 -2, -1 1 1 > .... 77 / 45 > .. 62 ... 943.396 .. [ 2 -4, 1 1 0 > .... 140 / 81 > .. 63 ... 958.491 .. [ -2 5, -1 -1 0 .... 243 / 140 > .. 64 ... 973.585 .. [ 0 3, 1 -1 -1 > ... 135 / 77 > .. 65 ... 988.679 .. [ -3 2, 0 -1 1 > .... 99 / 56 > .. 66 .. 1003.774 .. [ -1 0, 2 -1 0 > .... 25 / 14 > .. 67 .. 1018.868 .. [ 0 2, -1 0 0 > ...... 9 / 5 > .. 68 .. 1033.962 .. [ 2 0, 1 0 -1 > ..... 20 / 11 > .. 69 .. 1049.057 .. [ -1 -1, 0 0 1 > .... 11 / 6 > .. 70 .. 1064.151 .. [ 1 -3, 2 0 0 > ..... 50 / 27 > .. 71 .. 1079.245 .. [ 2 -1, -1 1 0 > .... 28 / 15 > .. 72 .. 1094.340 .. [ 4 -3, 1 1 -1 > ... 560 / 297 > .. 73 .. 1109.434 .. [ 1 -4, 0 1 1 > .... 154 / 81 > .. 74 .. 1124.528 .. [ -5 3, 2 0 -1 > ... 675 / 352 > .. 75 .. 1139.623 .. [ -1 3, 0 -1 0 > .... 27 / 14 > .. 76 .. 1154.717 .. [ 1 1, 2 -1 -1 > ... 150 / 77 > .. 77 .. 1169.811 .. [ 5 1, 0 -2 0 > ..... 96 / 49 > .. 78 .. 1184.906 .. [ -3 0, 2 1 -1 > ... 175 / 88 > (. 79 .. 1200.000 .. [ 1 0, 0 0 0> ........ 2 / 1) > > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software >
From: monz (2006-02-22) Subject: Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > Now how about a 13-limit version, since Gene gave the > 13-limit TM basis for the 2D temperament that gives you > this MOS scale? 13-limit would be a step closer to the > much higher-prime-limit ratios Ozan said he was interested > in approximating with this scale (a while back). Sure -- just point me to the numbers, and i'll whip one up. (did Gene post it here, or on tuning-math?) So this will only be a 2D Lattice? I hope so, because 2D temperaments are my favorite viewing in Tonescape, since we have the "Closed Curved" geometry which warps it into a helix when the 3rd dimension is used. -monz http://tonalsoft.com Tonescape microtonal music software
From: Carl Lumma (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning > > I have given ample explanations why, have I not? You apparently desire three kinds of fifths as well as good higher-limit approximations. What, in a perfect world, would these three sizes of fifth be? One of the fifths in your 79-tone scale seems to be over your stated maximum tolerable size of 708 cents. And you haven't said which higher-limit intervals are absolutely essential, and how many of them (in how many modes they) should appear. -Carl
From: Ozan Yarman (2006-02-22) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning > > > I have given ample explanations why, have I not? > > You apparently desire three kinds of fifths as well as > good higher-limit approximations. > > What, in a perfect world, would these three sizes of > fifth be? 696, 702, 708 cents or so. > > One of the fifths in your 79-tone scale seems to be over > your stated maximum tolerable size of 708 cents. > In an ideal world. Still, it's not so horrible. > And you haven't said which higher-limit intervals are > absolutely essential, and how many of them (in how > many modes they) should appear. > One may need to go as high as 17 at minumum. > -Carl > > Oz.
From: Carl Lumma (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning > > What, in a perfect world, would these three sizes of > > fifth be? > > 696, 702, 708 cents or so. Alright, Gene, what have you got for that in 80 tones or less? Guiron doesn't do it. -Carl
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning I would like very much to suggest something else that would offend you less, so I'm taking my time in asking you many pertinent questions first. With the right information, the tuning-math folks can run an efficient computer search for alternative systems that could save months of human labor time. I'm still quite unclear as to why a decent fifth, similar to that of 79-equal, wouldn't make more sense as an interval by which to generate the spine or circle of fifths, rather than alternating a nearly pure fifth with a "very very offensive one". The alternation does not in any way allow the system to function more flexibly, only less flexibly, unless I'm missing something. Isn't a fifth the most common interval by which a scale is modulated? If you have a mode/scale/key with some pure fifths in it, and you modulate by a fifth, why should most of the formerly pure fifths now become "very very offensive"? In my very limited understanding of your system and its motivations, this confuses me, since I thought modulation was of major importance to you. --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > They are not less offensive, they are very very offensive, but that is the > price I have to pay while retaining all the benefits of 79 tones, unless of > course you can suggest something else as a substitute. > > ----- Original Message ----- > From: "wallyesterpaulrus" <wallyesterpaulrus@...> > To: <tuning@yahoogroups.com> > Sent: 22 Þubat 2006 Çarþamba 2:47 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > Ozan, don't take this as an attack or anything, I'm just trying to tease out > your thinking. Why are these 694.2-cent fifths less offensive than those of > 19-equal? >
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Paul, > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > > [monz] > > > TM-basis for 159-edo in 2,5,7,11-space: > > > > > > > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents > > > --------------------------------------------------- > > > > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > > > > > > How did you arrive at this? > > > I didn't have to do anything myself, Tonescape did it. So you're selling us a product which has a mind of its own? > > Which "val" are you assuming? > > The 2,5,7,11-val is < 159 369 446 550 ] . Did you consider any other possibilities? And it's been quite a few days since I asked why you (initially) omitted prime 3 -- if you're never going to answer me, oh well, I'll drop that question. > > And as usual, I think it would make a lot more sense to > > reduce the pitches (thus making the choice of kernel basis > > irrelevant) instead of reducing the kernel basis and then > > constructing an FPB. > > > > Ah yes, i could tell Tonescape to construct a 79-tone > periodicity-block first, *then* use 159-edo for the tuning. Not what I meant, but worth considering. > Why do you say that reducing the number of pitches > makes "the choice of kernel basis irrelevant"? No, I meant Tenney-reducing the pitches (or better yet, Kees-reducing them), rather than Tenney-reducing the kernel basis. > The choice of kernel basis still determines how > compact the periodicity-block is. Not at all true, if you reduce the pitches. Then the choice of kernel basis becomes irrelevant -- any valid kernel basis yields the same final result. Which, BTW, is more compact than any Fokker periodicity block arising from any valid kernel basis.
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > > > > > > How did you arrive at this? Which "val" are you assuming? > > Just run the numbers, and you get <159 .. 369 446 550|. What do you mean, "just run the numbers"?
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > It certainly matters how you place those tones No doubt! > and how much of them you are > able to handle before one is constrained by the instrument in >question. I don't think you understood my question, which was about some constraint that appears to lie well beyond the instrument itself. Would you re-read it then? > I > find 79 MOS 159-tET to be a very good choice with its three sizes of fifths, > adequate approximation of 3,5,7,11,13 limit intervals, and a myriad of > transposition capabilities. Besides, the notation is just right for Maqam > Music. > > What other subset would you suggest that appeals to me then? In the context of this particular discussion/thread/post, I would simply ask what you think of a 79-tone MOS that does *not* arise as a subset of any EDO. If there aren't more than 79 tones per octave on the instrument, what could it matter if the superset from which the tones are chosen form 159-equal, or any equal tuning at all for that matter? 'Cause you'll never have an opportunity to use more than 79 of them anyway, so you'll never become aware of the closure, or lack thereof, of the "universe set" of 159 or >159 pitches. Gene has determined a 13-limit kernel basis (IIRC) for the 2D temperament which yields your 79-note MOS (or an 80-note MOS with one extra note). If this turns out to correspond to your desires, why not use the TOP or Kees tuning for this temperament, rather than drawing the notes from an EDO? > ----- Original Message ----- > From: "wallyesterpaulrus" <wallyesterpaulrus@...> > To: <tuning@yahoogroups.com> > Sent: 22 Þubat 2006 Çarþamba 21:07 > Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > If you can only have 79 tones on your instrument, what does it matter > whether they're from a superset which has 171, 217, 224, 270, 311, or even > an infinite number of tones per octave? It seems that only the number of > tones on the instrument which has to conform to practical constraints, not > the number of notes in the superset -- right? Just curious (the MOS scales > in my paper are *not* drawn from any equal-tempered supersets). >
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > What, in a perfect world, would these three sizes of > > fifth be? > > 696, 702, 708 cents or so. 224-et seems like a good choice then.
From: Gene Ward Smith (2006-02-22) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > Just run the numbers, and you get <159 .. 369 446 550|. > > What do you mean, "just run the numbers"? Solve the linear equations you can derive from the commas, or do what I did and take wedge products.
From: wallyesterpaulrus (2006-02-22) Subject: Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > > Now how about a 13-limit version, since Gene gave the > > 13-limit TM basis for the 2D temperament that gives you > > this MOS scale? 13-limit would be a step closer to the > > much higher-prime-limit ratios Ozan said he was interested > > in approximating with this scale (a while back). > > > > Sure -- just point me to the numbers, and i'll whip one up. > (did Gene post it here, or on tuning-math?) Here, and you replied that this was just was you were looking for (so I know you saw the numbers already), but didn't proceed any further. > So this will only be a 2D Lattice? No, but it's a 2D temperament, while ETs are 1D temperaments, in terms of the number of independent generators you need to generate it. The generators aren't what your lattices are based on, though. > I hope so, because > 2D temperaments are my favorite viewing in Tonescape, > since we have the "Closed Curved" geometry which warps > it into a helix when the 3rd dimension is used. I'm glad you adopted this suggestion of mine for displaying meantone tunings, and this all makes sense for most 2D temperaments of the 5- limit. But any of these 2D temperaments you're referring to derived from the 7-limit (as more than half the 2D temperaments in my "Middle Path" paper are) or any higher limit?
From: monz (2006-02-22) Subject: Tenny-reduced and Kees-reduced pitches (was: Ozan's 159-edo-based tuning) Hi Paul, --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > TM-basis for 159-edo in 2,5,7,11-space: > > > > > > > > > > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents > > > > --------------------------------------------------- > > > > > > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > > > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > > > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > > > > > > > > > How did you arrive at this? > > > > > > I didn't have to do anything myself, Tonescape did it. > > So you're selling us a product which has a mind of its own? Almost! ;-) Seriously -- the whole idea behind Tonescape's tuning capabilities is that the user doesn't have to fuss with all the mathematical stuff (unless he/she wants to). The computer handles all of that. If you have the "TM-basis" box checked, Tonescape does all the calculating for you. If you want don't want TM-basis and would prefer to pick your own unison-vectors, you simply uncheck the box, and Tonescape provides a big list of possibilities. > > > Which "val" are you assuming? > > > > The 2,5,7,11-val is < 159 369 446 550 ] . > > Did you consider any other possibilities? As i said, Tonescape did it automatically. It normally doesn't say anything about a val unless the tuning you're trying to develop has torsion. We'll eventually add in features that let you pick vals, similar to the way you can choose your own unison-vector basis. I know these are essentially the same process ... Tonescape just doesn't offer val notation yet. > And it's been quite a few days since I asked why > you (initially) omitted prime 3 -- if you're > never going to answer me, oh well, I'll drop that question. I thought you already had the answer to that: in the post which started this thread, Ozan said that his tuning gives good approximations to 5,7, and 11, and he didn't mention 3 except for the fact that 4/3 is the interval to be divided. To which i can only respond: duh! My bad. > > > And as usual, I think it would make a lot more sense to > > > reduce the pitches (thus making the choice of kernel basis > > > irrelevant) instead of reducing the kernel basis and then > > > constructing an FPB. > > > > > > > > Ah yes, i could tell Tonescape to construct a 79-tone > > periodicity-block first, *then* use 159-edo for the tuning. > > Not what I meant, but worth considering. Then can you please elaborate on what you did mean? It seems i'm not understanding you well here. > > Why do you say that reducing the number of pitches > > makes "the choice of kernel basis irrelevant"? > > No, I meant Tenney-reducing the pitches (or better > yet, Kees-reducing them), rather than Tenney-reducing > the kernel basis. > > > The choice of kernel basis still determines how > > compact the periodicity-block is. > > Not at all true, if you reduce the pitches. Then the > choice of kernel basis becomes irrelevant -- any valid > kernel basis yields the same final result. Which, BTW, > is more compact than any Fokker periodicity block > arising from any valid kernel basis. OK, now i have to confess my ignorance. I've spent a lot of time in the past year working on Tonescape and only skimming past many posts on these lists. What does it mean to Tenney- (or Kees-) reduce the pitches? It seems that this can apply directly to how Tonescape works, so i definitely want to learn more. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-22) Subject: Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space Hi Paul, --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > > <wallyesterpaulrus@> wrote: > > > > > > Now how about a 13-limit version, since Gene gave the > > > 13-limit TM basis for the 2D temperament that gives you > > > this MOS scale? 13-limit would be a step closer to the > > > much higher-prime-limit ratios Ozan said he was interested > > > in approximating with this scale (a while back). > > > > > > > > Sure -- just point me to the numbers, and i'll whip one up. > > (did Gene post it here, or on tuning-math?) > > Here, and you replied that this was just was you were > looking for (so I know you saw the numbers already), but > didn't proceed any further. Hmm ... OK, i'll have to search then later, when i have time. Are you talking about this? ... http://launch.groups.yahoo.com/group/tuning/message/64412 --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > > > Correspondng linear temperaments do not seem > > > distinguished. In the 7-limit we have <<33 54 95 9 58 69||, > > > with commas 10976/10935 and the 5-limit comma |3 -18 11> > > The mapping is such that 33 generators gives a fourth, > 54 generators a minor sixth, and 95 generators an > approximate 16/7 interval, which defines everything else > in the 7-limit. It sends the small (six and a half cent) > interval, or comma, 10976/10935 to the unison. That is, > such an interval is "tempered out". Also tempered out is > 2^3 5^11/3^18, of size 14.26 cents. > > The "ozan" temperament, 80&159, gets more interesting > in higher prime limits. In the 11-limit, we get 4000/3993 > and 3025/3024 as commas; in the 13-limit 325/324 and > 364/363; and so forth. > > So this will only be a 2D Lattice? > > No, but it's a 2D temperament, while ETs are 1D temperaments, > in terms of the number of independent generators you need > to generate it. The generators aren't what your lattices > are based on, though. Just to clarify: i used the "usual" prime-factors as generators in the Lattice of Ozan's tuning which i posted. But Tonescape can use anything you'd like as generators. > > I hope so, because > > 2D temperaments are my favorite viewing in Tonescape, > > since we have the "Closed Curved" geometry which warps > > it into a helix when the 3rd dimension is used. > > I'm glad you adopted this suggestion of mine for displaying > meantone tunings, and this all makes sense for most 2D > temperaments of the 5-limit. But any of these 2D temperaments > you're referring to derived from the 7-limit (as more than > half the 2D temperaments in my "Middle Path" paper are) or > any higher limit? If you give me details of one example (cents values of generators and the ratios they're supposed to represent), i'll make a Tonescape file of it and post the pretty pictures. Tonescape will do "Geometry|Closed Curved" for any temperament. However, when the un-closed Lattice has more than 2 dimensions, the closed version doesn't convey much meaningful visual information, IMO -- it just looks like a cluttered mess, altho you can still see the symmetry in the form. -monz http://tonalsoft.com Tonescape microtonal music software
From: wallyesterpaulrus (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > > Just run the numbers, and you get <159 .. 369 446 550|. > > > > What do you mean, "just run the numbers"? > > Solve the linear equations you can derive from the commas, or do what > I did and take wedge products. Gene, you're obviously not reading very carefully. Monz gave the commas. I asked where he got them. He said from the val. I asked where he got that. You're answering for him, "from the commas". Geez! Can't you see that you're just leading me around a logical circle?
From: wallyesterpaulrus (2006-02-23) Subject: Re: Tenny-reduced and Kees-reduced pitches (was: Ozan's 159-edo-based tuning) --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Paul, > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > > TM-basis for 159-edo in 2,5,7,11-space: > > > > > > > > > > > > > > > .. 2,5,7,11-monzo ...... ratio ........ ~cents > > > > > --------------------------------------------------- > > > > > > > > > > .. [-12 -2 1 4 > .. 102487 / 102400 ... 1.470248198 > > > > > .. [8 -8 5 -1 > .. 4302592 / 4296875 .. 2.301879062 > > > > > .. [-5 3 3 -3 > .... 42875 / 42592 ... 11.46503391 > > > > > > > > > > > > > How did you arrive at this? > > > > > > > > > I didn't have to do anything myself, Tonescape did it. > > > > So you're selling us a product which has a mind of its own? > > > > Almost! ;-) > > Seriously -- the whole idea behind Tonescape's tuning > capabilities is that the user doesn't have to fuss with > all the mathematical stuff (unless he/she wants to). > The computer handles all of that. If you have the > "TM-basis" box checked, Tonescape does all the calculating > for you. But why can't you tell me how? Am I just supposed to accept this "black box"? > If you want don't want TM-basis and would prefer to > pick your own unison-vectors, you simply uncheck the > box, and Tonescape provides a big list of possibilities. Oh? But what about the "val"? > > > > Which "val" are you assuming? > > > > > > The 2,5,7,11-val is < 159 369 446 550 ] . > > > > Did you consider any other possibilities? > > > As i said, Tonescape did it automatically. It normally > doesn't say anything about a val unless the tuning > you're trying to develop has torsion. > > We'll eventually add in features that let you pick > vals, similar to the way you can choose your own > unison-vector basis. Aha. But why the current "black box", and what is it doing? > > > > And as usual, I think it would make a lot more sense to > > > > reduce the pitches (thus making the choice of kernel basis > > > > irrelevant) instead of reducing the kernel basis and then > > > > constructing an FPB. > > > > > > > > > > > > Ah yes, i could tell Tonescape to construct a 79-tone > > > periodicity-block first, *then* use 159-edo for the tuning. > > > > Not what I meant, but worth considering. > > Then can you please elaborate on what you did mean? Do the same kind of reduction you did to the kernel basis, only do it to the pitch ratios instead. > It seems i'm not understanding you well here. I tried to explain below. > > > Why do you say that reducing the number of pitches > > > makes "the choice of kernel basis irrelevant"? > > > > No, I meant Tenney-reducing the pitches (or better > > yet, Kees-reducing them), rather than Tenney-reducing > > the kernel basis. > > > > > The choice of kernel basis still determines how > > > compact the periodicity-block is. > > > > Not at all true, if you reduce the pitches. Then the > > choice of kernel basis becomes irrelevant -- any valid > > kernel basis yields the same final result. Which, BTW, > > is more compact than any Fokker periodicity block > > arising from any valid kernel basis. > > > OK, now i have to confess my ignorance. I've spent a > lot of time in the past year working on Tonescape and > only skimming past many posts on these lists. What does > it mean to Tenney- (or Kees-) reduce the pitches? One way of saying it is that it means to find the simplest ratio for each pitch that you can obtain by starting with the pitch's ratio in the Fokker periodicity block, periodicity strip, or periodicity sheet (whichever vanishing commas you use to define that) and transposing it by any number/combination of vanishing commas. The result will be the same no matter which Fokker periodicity block, strip, or sheet you start with. Gene does this a whole lot on the tuning-math list. > It seems that this can apply directly to how Tonescape > works, You better believe it! > so i definitely want to learn more. I suggest posting your questions on this to the tuning-math list.
From: wallyesterpaulrus (2006-02-23) Subject: Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > Hi Paul, > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > <wallyesterpaulrus@> wrote: > > > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" > > > <wallyesterpaulrus@> wrote: > > > > > > > > Now how about a 13-limit version, since Gene gave the > > > > 13-limit TM basis for the 2D temperament that gives you > > > > this MOS scale? 13-limit would be a step closer to the > > > > much higher-prime-limit ratios Ozan said he was interested > > > > in approximating with this scale (a while back). > > > > > > > > > > > > Sure -- just point me to the numbers, and i'll whip one up. > > > (did Gene post it here, or on tuning-math?) > > > > Here, and you replied that this was just was you were > > looking for (so I know you saw the numbers already), but > > didn't proceed any further. > > > Hmm ... OK, i'll have to search then later, when i have time. > > Are you talking about this? ... > > > http://launch.groups.yahoo.com/group/tuning/message/64412 Yes, at the bottom. > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@> > wrote: > > > > > > Correspondng linear temperaments do not seem > > > > distinguished. In the 7-limit we have <<33 54 95 9 58 69||, > > > > with commas 10976/10935 and the 5-limit comma |3 -18 11> > > > > The mapping is such that 33 generators gives a fourth, > > 54 generators a minor sixth, and 95 generators an > > approximate 16/7 interval, which defines everything else > > in the 7-limit. It sends the small (six and a half cent) > > interval, or comma, 10976/10935 to the unison. That is, > > such an interval is "tempered out". Also tempered out is > > 2^3 5^11/3^18, of size 14.26 cents. > > > > The "ozan" temperament, 80&159, gets more interesting > > in higher prime limits. In the 11-limit, we get 4000/3993 > > and 3025/3024 as commas; in the 13-limit 325/324 and > > 364/363; and so forth. > > > > > > So this will only be a 2D Lattice? > > > > No, but it's a 2D temperament, while ETs are 1D temperaments, > > in terms of the number of independent generators you need > > to generate it. The generators aren't what your lattices > > are based on, though. > > > > Just to clarify: i used the "usual" prime-factors as > generators in the Lattice of Ozan's tuning which i posted. > But Tonescape can use anything you'd like as generators. Don't confuse "generators" with "rungs". Ozan's tuning is 2D in terms of generators but clearly you needed more than two directions of rungs to make an 11-limit harmonic lattice of it. > > > I hope so, because > > > 2D temperaments are my favorite viewing in Tonescape, > > > since we have the "Closed Curved" geometry which warps > > > it into a helix when the 3rd dimension is used. > > > > I'm glad you adopted this suggestion of mine for displaying > > meantone tunings, and this all makes sense for most 2D > > temperaments of the 5-limit. But any of these 2D temperaments > > you're referring to derived from the 7-limit (as more than > > half the 2D temperaments in my "Middle Path" paper are) or > > any higher limit? > > > > If you give me details of one example (cents values of > generators Why are cents values relevant when dealing with temperament in the abstract? Surely your meantone helix doesn't depend on any cents values . . . (?) > and the ratios they're supposed to represent), > i'll make a Tonescape file of it and post the pretty pictures. How about 7-limit meantone, as in my paper? The generators can be said to represent 2:1 and 3:2. Since you asked, in the TOP tuning (just one of many possibilities), these generators are 1201.7 and 697.57 cents -- exactly the same as they are in the TOP tuning for 5- limit meantone. But generators of 2D temperaments are often ambiguous between different ratio-interpretations, but this never mattered to you before, so I don't know why you now need ratio-interpretations for the generators all of a sudden. Can't you simply take the specification of the original JI lattice, plus the set of vanishing commas, as input? For example, to get meantone, I'd start with the 5- limit lattice, and temper out 81:80. Does this work for you?
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > > What, in a perfect world, would these three sizes of > > > fifth be? > > > > 696, 702, 708 cents or so. > > Alright, Gene, what have you got for that in 80 tones > or less? Guiron doesn't do it. The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size 707.1 cents. Thus the fifth situation is very well in hand; I hope Ozan take a look at it.
From: monz (2006-02-23)
Subject: Re: Ozan's 159-edo-based tuning
Hi Paul (and Gene)
--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@> wrote:
> >
> > > > Just run the numbers, and you get <159 .. 369 446 550|.
> > >
> > > What do you mean, "just run the numbers"?
> >
> > Solve the linear equations you can derive from the commas,
> > or do what I did and take wedge products.
>
> Gene, you're obviously not reading very carefully. Monz gave
> the commas. I asked where he got them. He said from the val.
> I asked where he got that. You're answering for him, "from
> the commas". Geez! Can't you see that you're just leading
> me around a logical circle?
I already explained that Tonescape used the TM-basis
for 159-edo in 2,5,7,11-space. Doing TM-reduction on
the kernel for this tuning yields the val Gene posted
above, and the unison-vectors ("commas") which i posted
earlier.
It would be tough for me to provide you with a more
detailed explanation than that ... Chris and i figured
out how to do it based on Gene's posts here and on
tuning-math, and after Chris coded it into Tonescape,
i moved on to other important things, like creating
the so-necessary Help menu files (which i'm working
on right now) to teach people how to use the damn thing.
:)
I do recall that it's a process which uses Hermite
reduction first, and then something else after that
... i think was "LL reduction" ...?
-monz
http://tonalsoft.com
Tonescape microtonal music software
From: Carl Lumma (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning > > > > What, in a perfect world, would these three sizes of > > > > fifth be? > > > > > > 696, 702, 708 cents or so. > > > > Alright, Gene, what have you got for that in 80 tones > > or less? Guiron doesn't do it. > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size > 707.1 cents. Thus the fifth situation is very well in hand; I > hope Ozan take a look at it. That's great. Have you posted a Scala file? -Carl
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, > > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size > > 707.1 cents. Thus the fifth situation is very well in hand; I > > hope Ozan take a look at it. > > That's great. Have you posted a Scala file? It's toof1.scl. I wonder what could be done with it musically.
From: monz (2006-02-23) Subject: generators vs. rungs (was: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space) Hi Paul, --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > > > > So this will only be a 2D Lattice? > > > > > > No, but it's a 2D temperament, while ETs are 1D temperaments, > > > in terms of the number of independent generators you need > > > to generate it. The generators aren't what your lattices > > > are based on, though. > > > > > > Just to clarify: i used the "usual" prime-factors as > > generators in the Lattice of Ozan's tuning which i posted. > > But Tonescape can use anything you'd like as generators. > > Don't confuse "generators" with "rungs". Yikes! ... what the heck is a "rung" in tuning theory? I presume there's a new Encyclopedia page waiting to be created about this ...? > Ozan's tuning is 2D in terms of generators To clarify: "2D in terms of generators" means: 1st dimension = the ~15-cent step which makes almost the whole tuning; and 2nd dimension = the ~22 cent step which "completes the octave" as Ozan puts it. Yes? If this is not correct, then please elaborate on what "2D in terms of generators" refers to. > but clearly you needed more than two directions > of rungs to make an 11-limit harmonic lattice of it. Please elaborate on this a bit. I have no idea what you mean. > > > > I hope so, because > > > > 2D temperaments are my favorite viewing in Tonescape, > > > > since we have the "Closed Curved" geometry which warps > > > > it into a helix when the 3rd dimension is used. > > > > > > I'm glad you adopted this suggestion of mine for displaying > > > meantone tunings, and this all makes sense for most 2D > > > temperaments of the 5-limit. But any of these 2D temperaments > > > you're referring to derived from the 7-limit (as more than > > > half the 2D temperaments in my "Middle Path" paper are) or > > > any higher limit? > > > > > > If you give me details of one example (cents values of > > generators > > Why are cents values relevant when dealing with temperament > in the abstract? Surely your meantone helix doesn't depend > on any cents values . . . (?) I have more to say on this "abstract" aspect, below. > > and the ratios they're supposed to represent), > > i'll make a Tonescape file of it and post the pretty pictures. > > How about 7-limit meantone, as in my paper? The generators > can be said to represent 2:1 and 3:2. Since you asked, in > the TOP tuning (just one of many possibilities), these > generators are 1201.7 and 697.57 cents -- exactly the same > as they are in the TOP tuning for 5-limit meantone. Hmm ... so you call it "7-limit" because it gives good approximations of ratios-of-7 (as well as ratios-of-5) ... but it's really constructed as a "linear temperament" (i know, we don't like that term anymore ...) -- that is, the generator representing 2:1 is considered to be the "identity interval", and the generator representing 3:2 is iterated to build up the tuning, exactly as in pythagorean and "ordinary" (non-TOP) meantones. To create a Tonescape Lattice of this tuning, i'd say that we want to make it 4D, since the tuning is intended to represent prime-factors 3, 5, and 7 (and 2) -- or, more accurately, the ratios 3:2, 5:4, and 7:4 (and the identity-interval 2:1). > But generators of 2D temperaments are often ambiguous > between different ratio-interpretations, but this never > mattered to you before, so I don't know why you now need > ratio-interpretations for the generators all of a sudden. > Can't you simply take the specification of the original > JI lattice, plus the set of vanishing commas, as input? > For example, to get meantone, I'd start with the 5- > limit lattice, and temper out 81:80. Does this work > for you? Sure, that's exactly how Tonescape works. But a tuning in Tonescape can never be abstract, because the purpose of Tonescape is not just to work out theoretical concepts, but to enable the user to compose music. You have to nail down exactly what frequencies the pitches represent before you can create music. When you use this method to create meantone in Tonescape, the default result is 1/4-comma meantone. Then if you desire a different flavor of meantone, you just go into the Tuning Editor and change the fraction-of-a-comma. Using "the specification of the original JI lattice, plus the set of vanishing commas, as input" already implies a set of ratio approximations. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-23) Subject: Re: Tenny-reduced and Kees-reduced pitches (was: Ozan's 159-edo-based tuning) --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > I suggest posting your questions on this to the tuning-math list. OK, will do. -monz http://tonalsoft.com Tonescape microtonal music software
From: Carl Lumma (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning > > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, > > > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size > > > 707.1 cents. Thus the fifth situation is very well in hand; I > > > hope Ozan take a look at it. > > > > That's great. Have you posted a Scala file? > > It's toof1.scl. I wonder what could be done with it musically. Humph, that's not in the current version (52) of the scale archive. -Carl
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > That's great. Have you posted a Scala file? > > > > It's toof1.scl. I wonder what could be done with it musically. > > Humph, that's not in the current version (52) of the scale > archive. You asked if I posted it, which I did here: http://launch.groups.yahoo.com/group/tuning/message/64578
From: monz (2006-02-23) Subject: Paul Erlich's 7-limit TOP meantone (was: Ozan's 79-MOS ...) Hi Paul, --- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@...> wrote: > How about 7-limit meantone, as in my paper? The generators > can be said to represent 2:1 and 3:2. Since you asked, in > the TOP tuning (just one of many possibilities), these > generators are 1201.7 and 697.57 cents -- exactly the same > as they are in the TOP tuning for 5-limit meantone. Hmm ... this is a very interesting tuning. I notice that this TOP meantone forms a nearly-closed system at 31 tones, but that if you continue it past that, you get an adaptive-JI system. Anyway, i made a Tonescape Lattice of the 31-tone version, in pseudo-2,3,5,7-space: http://launch.groups.yahoo.com/group/tuning_files/files/monz/erlich_7-limit-TOP-meantone_31-tone-chain.gif For the notation, i used 1,200,000-edo, so that you can consider it to be cents with the last three digits representing those which come after the decimal point. I didn't use any mathematical formula to calculate the shape of the block -- i just added each pitch manually, trying to keep all the pitches as close as possible to the origin. I was so intrigued by this that i already started composing a piece in it (it's so easy in Tonescape [shameless plug]) ... let's hope that i finish it, which is something i haven't done for quite some time. -monz http://tonalsoft.com Tonescape microtonal music software
From: Carl Lumma (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning > > > > That's great. Have you posted a Scala file? > > > > > > It's toof1.scl. I wonder what could be done with it musically. > > > > Humph, that's not in the current version (52) of the scale > > archive. > > You asked if I posted it, which I did here: > > http://launch.groups.yahoo.com/group/tuning/message/64578 Aha! So let's compare: toof1 72 696.429 76 701.786 64 707.143 ozan[79] 33 694.340 46 701.887 32 709.434 On the left is the number of occurrances in the modes of the scale of the given fifth (size shown on the right). So not only are toof1's fifths closer to Ozan's stated targets, there's more of them. What do you think, Ozan? And will it be possible for you to add one more note to your qanun? -Carl
From: Carl Lumma (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning > -- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > Dear monz, > > > > Thanks very much for the praises. I have uploaded to pictures > > of my Qanun to: > > > > http://www.ozanyarman.com/anonymous/ I see this instrument looks as beautiful as it sounds. -Carl
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I'm afraid neither Guiron77 nor Octoid80 serve my purposes. The chain of fifths are not right, and neither is the notation thus. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 9:17 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Can you provide the details for Octaid 80? 72 didn't work, because the > > super-pythagorean fifth is intolerable to listen to. > > Octoid[80] does not put the meantone fifth and the nearly pure > (schismatic) fifth in the same interval class, so I doubt it is what > you want. Octoid[72] does, however. There are no intolerable > super-pythagorean fifths in the six closed chains of fifths you get in > this way. As I said, these are in fact well-temperaments; two > almost-pure fifths followed by a meantone fifth, and repeat. The minor > thirds are all 300 cents exactly, and the triads differ in that the > ones with the meantone fifths have better major thirds, as they > clearly must, given that the minor thirds are fixed in size. > > ! octoid80.scl > Octoid[80] in 224-et tuning > 80 > ! > 16.071429 > 32.142857 > 48.214286 > 64.285714 > 80.357143 > 85.714286 > 101.785714 > 117.857143 > 133.928571 > 150.000000 > 166.071429 > 182.142857 > 198.214286 > 214.285714 > 230.357143 > 235.714286 > 251.785714 > 267.857143 > 283.928571 > 300.000000 > 316.071429 > 332.142857 > 348.214286 > 364.285714 > 380.357143 > 385.714286 > 401.785714 > 417.857143 > 433.928571 > 450.000000 > 466.071429 > 482.142857 > 498.214286 > 514.285714 > 530.357143 > 535.714286 > 551.785714 > 567.857143 > 583.928571 > 600.000000 > 616.071429 > 632.142857 > 648.214286 > 664.285714 > 680.357143 > 685.714286 > 701.785714 > 717.857143 > 733.928571 > 750.000000 > 766.071429 > 782.142857 > 798.214286 > 814.285714 > 830.357143 > 835.714286 > 851.785714 > 867.857143 > 883.928571 > 900.000000 > 916.071429 > 932.142857 > 948.214286 > 964.285714 > 980.357143 > 985.714286 > 1001.785714 > 1017.857143 > 1033.928571 > 1050.000000 > 1066.071429 > 1082.142857 > 1098.214286 > 1114.285714 > 1130.357143 > 1135.714286 > 1151.785714 > 1167.857143 > 1183.928571 > 1200.000000 >
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space Perhaps as high a prime-limit as 17 will yield interesting results too. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 22 \ufffdubat 2006 \ufffdar\ufffdamba 23:48 Subject: [tuning] Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space > Now how about a 13-limit version, since Gene gave the 13-limit TM > basis for the 2D temperament that gives you this MOS scale? 13-limit > would be a step closer to the much higher-prime-limit ratios Ozan > said he was interested in approximating with this scale (a while > back). > >
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I'm afraid neither Guiron77 nor Octoid80 serve my purposes. The chain of > fifths are not right, and neither is the notation thus. I don't see why you would worry about notation at this point. What do you want in chains of fifths?
From: Gene Ward Smith (2006-02-23)
Subject: Re: Ozan's 79-MOS 159-edo tuning in 2,3,5,7,11-space
--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Perhaps as high a prime-limit as 17 will yield interesting results too.
The patent val for 159 gives the best tuning through the 17-limit;
here aren TM bases:
c7: {1029/1024, 10976/10935, 15625/15552}
c11: {385/384, 441/440, 4000/3993, 10976/10935}
c13: {325/324, 364/363, 385/384, 625/624, 10976/10935}
c17: {273/272, 325/324, 364/363, 375/374, 385/384, 3773/3757}
In the 13 and 17 limits particularly, the most complex comma is
clearly cheesier than the rest, which suggests the characteristic
temperament, meaning the one obtained by tossing the most complex
comma, should be interesting. These are
7 limit: <<3 -24 -1 -45 -10 65|| guiron, the 118&159 temperament
11, 13 and 17 limits: <<18 15 -6 9 42 54 ... || tritikleismic, the
72&87 temperament.
Here I give only the octave equivalent part of the wedgie; the
temperament has a period of 1/3 octave and a hanson-type generator of
a minor third, tempering out 15625/15552. It's a good way of getting
to the 11-limit, but not such a good way of getting to meantone
fifths, which have a rather high complexity--54, the same as 17/16.
From: monz (2006-02-23) Subject: definition: "patent val" (was: Ozan's 79-MOS...) Hi Gene, --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > Perhaps as high a prime-limit as 17 will yield > > interesting results too. > > The patent val for 159 gives the best tuning through > the 17-limit; I want to put "patent val" into the Encyclopedia. Should it be described on the "val" page, or have its own separate page? Can you please write up a definition for me? Thanks. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-23)
Subject: definition: "a&b temperament" (was: Ozan's 79-MOS...)
Hi Gene,
Another request for an Encyclopedia defintion ...
--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
> The patent val for 159 gives the best tuning through the
> 17-limit; here aren TM bases:
>
> c7: {1029/1024, 10976/10935, 15625/15552}
> c11: {385/384, 441/440, 4000/3993, 10976/10935}
> c13: {325/324, 364/363, 385/384, 625/624, 10976/10935}
> c17: {273/272, 325/324, 364/363, 375/374, 385/384, 3773/3757}
>
> In the 13 and 17 limits particularly, the most complex
> comma is clearly cheesier than the rest, which suggests
> the characteristic temperament, meaning the one obtained
> by tossing the most complex comma, should be interesting.
> These are
>
> 7 limit: <<3 -24 -1 -45 -10 65|| guiron, the
> 118&159 temperament
>
> 11, 13 and 17 limits: <<18 15 -6 9 42 54 ... ||
> tritikleismic, the 72&87 temperament.
Becausae of some big gaps in my reading the tuning lists
over the last couple of years, i never fully grasped this
the meaning of this "a&b temperament" type of notation.
Definition, please. Thanks.
-monz
http://tonalsoft.com
Tonescape microtonal music software
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Given my satisfaction for the moment with 79 MOS 159-tET (generator, notation and approximation-wise), and the myriad of explanations I have already given, I do not know what prevents you from settling with what I demonstrated to work already. As for the horribly low fifth, the intonation of my instrument or minute tuning calibrations does help change it by a few cents, whereby I can acquire a 2/7 comma fifth at certain degrees if I so desire. Moreover, I need alternating fifths for transition from Rast to Suz-i Dilara, or Buselik to Nishabur. Otherwise the chain of fifths is broken. Oz. ----- Original Message ----- From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> To: <tuning@yahoogroups.com> Sent: 23 \ufffdubat 2006 Per\ufffdembe 0:23 Subject: [tuning] Re: Ozan's 159-edo-based tuning I would like very much to suggest something else that would offend you less, so I'm taking my time in asking you many pertinent questions first. With the right information, the tuning-math folks can run an efficient computer search for alternative systems that could save months of human labor time. I'm still quite unclear as to why a decent fifth, similar to that of 79-equal, wouldn't make more sense as an interval by which to generate the spine or circle of fifths, rather than alternating a nearly pure fifth with a "very very offensive one". The alternation does not in any way allow the system to function more flexibly, only less flexibly, unless I'm missing something. Isn't a fifth the most common interval by which a scale is modulated? If you have a mode/scale/key with some pure fifths in it, and you modulate by a fifth, why should most of the formerly pure fifths now become "very very offensive"? In my very limited understanding of your system and its motivations, this confuses me, since I thought modulation was of major importance to you.
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning [PA] I don't think you understood my question, which was about some constraint that appears to lie well beyond the instrument itself. Would you re-read it then? [OZ] Would you be kind enough to rephrase and ask me again? > > What other subset would you suggest that appeals to me then? [PA] In the context of this particular discussion/thread/post, I would simply ask what you think of a 79-tone MOS that does *not* arise as a subset of any EDO. If there aren't more than 79 tones per octave on the instrument, what could it matter if the superset from which the tones are chosen form 159-equal, or any equal tuning at all for that matter? 'Cause you'll never have an opportunity to use more than 79 of them anyway, so you'll never become aware of the closure, or lack thereof, of the "universe set" of 159 or >159 pitches. Gene has determined a 13-limit kernel basis (IIRC) for the 2D temperament which yields your 79-note MOS (or an 80-note MOS with one extra note). If this turns out to correspond to your desires, why not use the TOP or Kees tuning for this temperament, rather than drawing the notes from an EDO? [OZ] How many times do I need to repeat that I do not derive my tuning from any EDO, but from the equal division of the pure fourth? It was Gene himself who pointed out months ago the similarity of my tuning to 79 MOS 159, a definition which I accepted at the cost of being misunderstood. So, if you think you are able to suggest something better, why not provide me the TOP or Kees tuning that I dare not comprehend? Oz.
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Indeed! Can we obtain a 80 or so tone MOS out of it? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 23 \ufffdubat 2006 Per\ufffdembe 1:28 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > What, in a perfect world, would these three sizes of > > > fifth be? > > > > 696, 702, 708 cents or so. > > 224-et seems like a good choice then. > >
From: Gene Ward Smith (2006-02-23) Subject: Re: definition: "patent val" (was: Ozan's 79-MOS...) --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > I want to put "patent val" into the Encyclopedia. > Should it be described on the "val" page, or have > its own separate page? Can you please write up a > definition for me? Thanks. It's the same as "standard val", a term I am abandoning because of numerous objections. For any positive integer n and prime limit p, the patent val for n and p is defined to be the following: <n round(n log2(3)) round(n log2(5)) ... round(n log2(p)| Here "round" means the function rounding to the nearest integer, also called the nint function, and written round(x), nint(x), [x] or ||x|| for a real number x.
From: Gene Ward Smith (2006-02-23) Subject: Re: definition: "a&b temperament" (was: Ozan's 79-MOS...) --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > Becausae of some big gaps in my reading the tuning lists > over the last couple of years, i never fully grasped this > the meaning of this "a&b temperament" type of notation. > Definition, please. Thanks. I have a precise definition for this, but other people are more loose about it. In my usage, a&b, for positive integers a and b and prime limit p, is the temperament defined by the wedgie for the patent vals for a and b in the prime limit p.
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > Given my satisfaction for the moment with 79 MOS 159-tET (generator, > notation and approximation-wise), and the myriad of explanations I have > already given, I do not know what prevents you from settling with what I > demonstrated to work already. No one understands why you prefer it, so the questions keep coming.
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Neither do I understand why nobody understands my continuing explanations. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 0:33 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > Given my satisfaction for the moment with 79 MOS 159-tET (generator, > > notation and approximation-wise), and the myriad of explanations I have > > already given, I do not know what prevents you from settling with what I > > demonstrated to work already. > > No one understands why you prefer it, so the questions keep coming. > > > >
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning An 80-note MOS out of 224 sounds intriguing. Can we have the cent values or the step numbers please? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 23 \ufffdubat 2006 Per\ufffdembe 5:32 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > > > > What, in a perfect world, would these three sizes of > > > > fifth be? > > > > > > 696, 702, 708 cents or so. > > > > Alright, Gene, what have you got for that in 80 tones > > or less? Guiron doesn't do it. > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, 72 very > nice 696.4 meantone fifths, and 64 sharp fifths of size 707.1 cents. > Thus the fifth situation is very well in hand; I hope Ozan take a look > at it. > > >
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I am not sure I liked it. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 23 \ufffdubat 2006 Per\ufffdembe 7:02 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > > > The 80-note MOS 12&224[80] does. It has 76 sensibly JI fifths, > > > 72 very nice 696.4 meantone fifths, and 64 sharp fifths of size > > > 707.1 cents. Thus the fifth situation is very well in hand; I > > > hope Ozan take a look at it. > > > > That's great. Have you posted a Scala file? > > It's toof1.scl. I wonder what could be done with it musically. > >
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I'm not sure if this appeals to me Carl, despite the fifths. The scale is very irregular for my requirements and 5-limit consonances are problematic. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 23 \ufffdubat 2006 Per\ufffdembe 11:59 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > > That's great. Have you posted a Scala file? > > > > > > > > It's toof1.scl. I wonder what could be done with it musically. > > > > > > Humph, that's not in the current version (52) of the scale > > > archive. > > > > You asked if I posted it, which I did here: > > > > http://launch.groups.yahoo.com/group/tuning/message/64578 > > Aha! So let's compare: > > toof1 > 72 696.429 > 76 701.786 > 64 707.143 > > ozan[79] > 33 694.340 > 46 701.887 > 32 709.434 > > On the left is the number of occurrances in the modes of > the scale of the given fifth (size shown on the right). > So not only are toof1's fifths closer to Ozan's stated > targets, there's more of them. > > What do you think, Ozan? And will it be possible for you > to add one more note to your qanun? > > -Carl > >
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Notation has everything to do with my purposes. I'm trying to revolutionize Maqam Music transcription, remember? I desire that a diatonical scale can be meantone/well and pythagorean at every degree. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 23 \ufffdubat 2006 Per\ufffdembe 19:28 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > I'm afraid neither Guiron77 nor Octoid80 serve my purposes. The chain of > > fifths are not right, and neither is the notation thus. > > I don't see why you would worry about notation at this point. What do > you want in chains of fifths? > > >
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > An 80-note MOS out of 224 sounds intriguing. Can we have the cent values or > the step numbers please? The scale "toof1" which we've been discussing seems like the most plausible candidate for now. Another was Octoid[80], which you didn't like. You should have both scales in terms of cents already.
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I'm not sure if this appeals to me Carl, despite the fifths. The scale is > very irregular for my requirements and 5-limit consonances are problematic. The scale is very irregular in terms of step size, but *any* scale with a lot of three different kinds of fifth is going to be, because the differences between the fifths are small. The 5-limit consonances are not a problem so far as I can see. For one thing, we've got lots of copies of the diatonic scale in there, and as well as a lot of nearly pure fifths, a lot of nearly pure major thirds. Toof1 has 44 nearly pure major triads and 44 nearly pure minor triads. It also has 8 otonal and 8 utonal tetrads to close accuracy, and of course less closely tuned versions as well. Your scale has 25 of each kind of triad in its best tuning, and the accuracy while very good (the same as 53) isn't as close as 224. Nor does it have any near-pure tetrads to boast of. I would say toof1 clearly has it beat in the 5-limit consonances department.
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I cannot even get a decent Rast scale on C! ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 1:19 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > I'm not sure if this appeals to me Carl, despite the fifths. The > scale is > > very irregular for my requirements and 5-limit consonances are > problematic. > > The scale is very irregular in terms of step size, but *any* scale > with a lot of three different kinds of fifth is going to be, because > the differences between the fifths are small. The 5-limit consonances > are not a problem so far as I can see. For one thing, we've got lots > of copies of the diatonic scale in there, and as well as a lot of > nearly pure fifths, a lot of nearly pure major thirds. > > Toof1 has 44 nearly pure major triads and 44 nearly pure minor triads. > It also has 8 otonal and 8 utonal tetrads to close accuracy, and of > course less closely tuned versions as well. Your scale has 25 of each > kind of triad in its best tuning, and the accuracy while very good > (the same as 53) isn't as close as 224. Nor does it have any near-pure > tetrads to boast of. I would say toof1 clearly has it beat in the > 5-limit consonances department. > >
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I'm not sure if this appeals to me Carl, despite the fifths. The scale is > very irregular for my requirements and 5-limit consonances are problematic. One way of thinking about it is that it's a sort of adaptive version of 12-et. There are twelve note-groups, each consisting of six or seven alternative notes. By choosing your alternative, you can get a huge number of different 12-note scales out of toof1; subscales of these are probably, most of the time, what you'd be looking for. Certainly, you can find sensibly just 5-limit harmony in abudence.
From: Gene Ward Smith (2006-02-23) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I cannot even get a decent Rast scale on C! If Rast is the same as a diatonic scale, then you certainly can. It has them in vast abundence. I think perhaps it would be better if we moved 1/1 somewhere else, as you seem to not like where it is.
From: Ozan Yarman (2006-02-23) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning What about 13/12, 12/11 and 11/10? ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 1:55 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > I cannot even get a decent Rast scale on C! > > If Rast is the same as a diatonic scale, then you certainly can. It > has them in vast abundence. I think perhaps it would be better if we > moved 1/1 somewhere else, as you seem to not like where it is. > > > >
From: Carl Lumma (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning > Neither do I understand why nobody understands my continuing > explanations. You haven't given a complete statement of your criteria in precise terms. We now know that you require three types of fifth and what sizes they should be. We know you want higher-limit approximations but not precisely what will work and what would be unacceptable. Now we see you have restrictions on how a chain of fifths will produce a third. Can you state it in a precise manner? -Carl
From: Carl Lumma (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning > > > > > > That's great. Have you posted a Scala file? > > > > > > > > > > It's toof1.scl. // > > > You asked if I posted it, which I did here: > > > > > > http://launch.groups.yahoo.com/group/tuning/message/64578 > > > > Aha! So let's compare: > > > > toof1 > > 72 696.429 > > 76 701.786 > > 64 707.143 > > > > ozan[79] > > 33 694.340 > > 46 701.887 > > 32 709.434 > > > > On the left is the number of occurrances in the modes of > > the scale of the given fifth (size shown on the right). > > So not only are toof1's fifths closer to Ozan's stated > > targets, there's more of them. > > > > What do you think, Ozan? And will it be possible for you > > to add one more note to your qanun? > > I'm not sure if this appeals to me Carl, despite the fifths. > The scale is very irregular for my requirements and 5-limit > consonances are problematic. In what way are they problematic? -Carl
From: Ozan Yarman (2006-02-24) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I thought I had made precise statements on how both the Rast and the Suz-i Dilara scales must be achieved via an unbroken chain of fifths. I have specified already the desirable sizes and tried to show to the best of my ability how these have to alterate on several degrees. I have also made precise statements concerning how I desired high prime limit approximations by giving several Maqam scales. I have repeated myself to the extent that I don't know what else to say anymore. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 2:07 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > Neither do I understand why nobody understands my continuing > > explanations. > > You haven't given a complete statement of your criteria in > precise terms. We now know that you require three types of > fifth and what sizes they should be. We know you want > higher-limit approximations but not precisely what will work > and what would be unacceptable. Now we see you have > restrictions on how a chain of fifths will produce a third. > Can you state it in a precise manner? > > -Carl > >
From: Ozan Yarman (2006-02-24) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning If Gene can start 1/1 on a more convenient degree, I may re-evaluate the scale once more. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 2:09 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > > > > That's great. Have you posted a Scala file? > > > > > > > > > > > > It's toof1.scl. > // > > > > You asked if I posted it, which I did here: > > > > > > > > http://launch.groups.yahoo.com/group/tuning/message/64578 > > > > > > Aha! So let's compare: > > > > > > toof1 > > > 72 696.429 > > > 76 701.786 > > > 64 707.143 > > > > > > ozan[79] > > > 33 694.340 > > > 46 701.887 > > > 32 709.434 > > > > > > On the left is the number of occurrances in the modes of > > > the scale of the given fifth (size shown on the right). > > > So not only are toof1's fifths closer to Ozan's stated > > > targets, there's more of them. > > > > > > What do you think, Ozan? And will it be possible for you > > > to add one more note to your qanun? > > > > I'm not sure if this appeals to me Carl, despite the fifths. > > The scale is very irregular for my requirements and 5-limit > > consonances are problematic. > > In what way are they problematic? > > -Carl > >
From: Gene Ward Smith (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > What about 13/12, 12/11 and 11/10? These have complexities of 88, 112, and 76 respectively, so using the best tuning of 224 only 11/10 appears in toof1. The complexities of these in your "ozan" temperament, 80&159, are 9, 10, and 11 respectively, so they are everywhere.
From: Gene Ward Smith (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I thought I had made precise statements on how both the Rast and the Suz-i > Dilara scales must be achieved via an unbroken chain of fifths. What does the chain of fifths need to look like?
From: Ozan Yarman (2006-02-24) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning That is where you get clobbered! ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 2:25 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > What about 13/12, 12/11 and 11/10? > > These have complexities of 88, 112, and 76 respectively, so using the > best tuning of 224 only 11/10 appears in toof1. > > The complexities of these in your "ozan" temperament, 80&159, are 9, > 10, and 11 respectively, so they are everywhere. > > >
From: Ozan Yarman (2006-02-24) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning 2/7 comma meantone and 707-8 cent super-pythagorean fifths. For smoother transition, they need to be interspersed with pure fifths. 224-edo is excellent for MOS scales. Let's see if you can improve on that 80 tones. ----- Original Message ----- From: "Gene Ward Smith" <genewardsmith@coolgoose.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 2:26 Subject: [tuning] Re: Ozan's 159-edo-based tuning > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > > > I thought I had made precise statements on how both the Rast and the > Suz-i > > Dilara scales must be achieved via an unbroken chain of fifths. > > What does the chain of fifths need to look like? > >
From: Graham Breed (2006-02-24)
Subject: Re: [tuning] definition: "a&b temperament"
monz wrote:
>>7 limit: <<3 -24 -1 -45 -10 65|| guiron, the
>>118&159 temperament
>>
>>11, 13 and 17 limits: <<18 15 -6 9 42 54 ... ||
>>tritikleismic, the 72&87 temperament.
>
> Becausae of some big gaps in my reading the tuning lists
> over the last couple of years, i never fully grasped this
> the meaning of this "a&b temperament" type of notation.
> Definition, please. Thanks.
I've been using the "a&b" notation longer than most (all?) and I use it
to refer to a family of MOS scales as well as a temperament class.
Where it refers to an MOS family, a and b are integers. There are
different ways of thinking about the results (I abandoned standardization):
- There could be a+b notes with a steps of one size and b of another
- There could be max(a,b) notes with min(a,b) steps of one size
In both cases we're looking at the number of notes to an equivalence
interval, which is usually an octave.
Where a&b refers to a temperament, a and b should be equal temperaments.
How to go from a pair of equal temperaments to a rank 2 (what I'd
still rather call linear) temperament is best explained here:
http://riters.com/microtonal/index.cgi/FindingLinearTemperaments
Wedgies don't work in the general case because they can't handle
contorsion. However, we can define "temperament" such that a
temperament can never be contorted.
Where integers refer to equal temperaments, I prefer to state how to
find the mappings whenever I use the notation. Usually I take the best
mapping in the light of whatever error measure I'm working with. If I
only give the numbers it should be because there are obviously best
mappings that will be optimal for any sensible error measure. With odd
limits, this is true if the ETs are consistent. With prime limits I
don't have a standard rule.
Graham
From: Gene Ward Smith (2006-02-24) Subject: Re: definition: "a&b temperament" --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote: > I've been using the "a&b" notation longer than most (all?) and I use it > to refer to a family of MOS scales as well as a temperament class. Which means you use it ambiguously. I prefer a+b for MOS scales.
From: Carl Lumma (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning > > > Neither do I understand why nobody understands my continuing > > > explanations. > > > > You haven't given a complete statement of your criteria in > > precise terms. We now know that you require three types of > > fifth and what sizes they should be. We know you want > > higher-limit approximations but not precisely what will work > > and what would be unacceptable. Now we see you have > > restrictions on how a chain of fifths will produce a third. > > Can you state it in a precise manner? > > I thought I had made precise statements on how both the Rast > and the Suz-i Dilara scales must be achieved via an unbroken > chain of fifths. I have specified already the desirable sizes > and tried to show to the best of my ability how these have to > alterate on several degrees. I have also made precise > statements concerning how I desired high prime limit > approximations by giving several Maqam scales. I have repeated > myself to the extent that I don't know what else to say anymore. Sorry, maybe I missed that stuff. I wasn't reading the list for a few months. Is it all collected in a single message somewhere? -Carl
From: Carl Lumma (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning > If Gene can start 1/1 on a more convenient degree, I may > re-evaluate the scale once more. Usually scales are meant to be good or bad based on all of their modes. When doing these cursory investigations, I don't think either Gene or I would neccesarily take the time to present any kind of 'best' mode in the scl file. You're expected to use Scala's key command, or "show locations", or whatever floats your boat. -Carl
From: Ozan Yarman (2006-02-24) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning It is collected in several of my messages put together going back several months for those who have been following. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 3:40 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > > > Neither do I understand why nobody understands my continuing > > > > explanations. > > > > > > You haven't given a complete statement of your criteria in > > > precise terms. We now know that you require three types of > > > fifth and what sizes they should be. We know you want > > > higher-limit approximations but not precisely what will work > > > and what would be unacceptable. Now we see you have > > > restrictions on how a chain of fifths will produce a third. > > > Can you state it in a precise manner? > > > > I thought I had made precise statements on how both the Rast > > and the Suz-i Dilara scales must be achieved via an unbroken > > chain of fifths. I have specified already the desirable sizes > > and tried to show to the best of my ability how these have to > > alterate on several degrees. I have also made precise > > statements concerning how I desired high prime limit > > approximations by giving several Maqam scales. I have repeated > > myself to the extent that I don't know what else to say anymore. > > Sorry, maybe I missed that stuff. I wasn't reading the list > for a few months. Is it all collected in a single message > somewhere? > > -Carl >
From: Ozan Yarman (2006-02-24) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I did and am considering it once more. Oz. ----- Original Message ----- From: "Carl Lumma" <clumma@yahoo.com> To: <tuning@yahoogroups.com> Sent: 24 \ufffdubat 2006 Cuma 3:43 Subject: [tuning] Re: Ozan's 159-edo-based tuning > > If Gene can start 1/1 on a more convenient degree, I may > > re-evaluate the scale once more. > > Usually scales are meant to be good or bad based on all > of their modes. When doing these cursory investigations, I > don't think either Gene or I would neccesarily take the > time to present any kind of 'best' mode in the scl file. > You're expected to use Scala's key command, or > "show locations", or whatever floats your boat. > > -Carl > >
From: Graham Breed (2006-02-24)
Subject: Re: [tuning] Re: definition: "a&b temperament"
Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
>>I've been using the "a&b" notation longer than most (all?) and I use it
>>to refer to a family of MOS scales as well as a temperament class.
>
> Which means you use it ambiguously. I prefer a+b for MOS scales.
Then you must be using your own definition of "ambiguous". Most people
will still expect "+" to refer to addition. I did experiment with
distinguishing "+" and "&" here:
http://www.microtonal.co.uk/notakey.htm#gengenkey
I've since repented, but not updated the page to reflect this.
Graham
From: Gene Ward Smith (2006-02-24) Subject: Re: definition: "a&b temperament" --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote: > Then you must be using your own definition of "ambiguous". "Ambiguous" means open to more than one interpretation. Since no one knows what you mean by a&b, it's ambiguous.
From: monz (2006-02-24) Subject: Re: definition: "a&b temperament" (was: Ozan's 79-MOS...) Hi Gene, --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "monz" <monz@> wrote: > > > Becausae of some big gaps in my reading the tuning lists > > over the last couple of years, i never fully grasped this > > the meaning of this "a&b temperament" type of notation. > > Definition, please. Thanks. > > I have a precise definition for this, but other people > are more loose about it. In my usage, a&b, for positive > integers a and b and prime limit p, is the temperament > defined by the wedgie for the patent vals for a and b > in the prime limit p. Thanks for that. http://tonalsoft.com/enc/number/a-b.aspx Can you please provide some example with their wedgies and patent vals? I'd like to start the examples with 12&19 and 12&31 meantone, which i'm guessing is are valid examples. Also, i'd like to hear from those folks who "are more loose about it", with explanations and examples of their usage. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning Hi Ozan and Gene, --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > I cannot even get a decent Rast scale on C! > > From: "Gene Ward Smith" <genewardsmith@...> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote: > > > > > > I'm not sure if this appeals to me Carl, despite the > > > fifths. The scale is very irregular for my requirements > > > and 5-limit consonances are problematic. > > > > The scale is very irregular in terms of step size, > > but *any* scale with a lot of three different kinds > > of fifth is going to be, because the differences > > between the fifths are small. The 5-limit consonances > > are not a problem so far as I can see. For one thing, > > we've got lots of copies of the diatonic scale in there, > > and as well as a lot of nearly pure fifths, a lot of > > nearly pure major thirds. > > > > Toof1 has 44 nearly pure major triads and 44 nearly > > pure minor triads. It also has 8 otonal and 8 utonal > > tetrads to close accuracy, and of course less closely > > tuned versions as well. Your scale has 25 of each > > kind of triad in its best tuning, and the accuracy > > while very good (the same as 53) isn't as close as 224. > > Nor does it have any near-pure tetrads to boast of. > > I would say toof1 clearly has it beat in the 5-limit > > consonances department. It's clear that the two of you are having a hard time understanding each other, and i'm taking the presumption of stepping in here to try and make this discussion work before you both get frustrated. I think examples would help some of us understand what you're both talking about. Oz, can you post a comparative table of the various different Maqam modes (or whatever term is used here) with names of modes and notes in Turkish, Persian, and Arabic, and with ratios and/or cents values? Can you also tell us what are published as the "usual" or "standard" measurements of these scales, and how your work on them does or doesn't correspond? Gene, can you post tables of the various different diatonic scales, triads, tetrads, etc., with the relevant ratios and/or cents values? I could use all this stuff to make a nice Encyclopedia page about Maqam, and perhaps Ozan's work merits a separate page too. -monz http://tonalsoft.com Tonescape microtonal music software
From: Graham Breed (2006-02-24)
Subject: Re: [tuning] Re: definition: "a&b temperament" (was: Ozan's 79-MOS...)
monz wrote:
> Hi Gene,
>
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
> wrote:
>
>>--- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>>
>>
>>>Becausae of some big gaps in my reading the tuning lists
>>>over the last couple of years, i never fully grasped this
>>>the meaning of this "a&b temperament" type of notation.
>>>Definition, please. Thanks.
>>
>>I have a precise definition for this, but other people
>>are more loose about it. In my usage, a&b, for positive
>>integers a and b and prime limit p, is the temperament
>>defined by the wedgie for the patent vals for a and b
>>in the prime limit p.
>
>
>
>
> Thanks for that.
>
> http://tonalsoft.com/enc/number/a-b.aspx
>
>
> Can you please provide some example with their wedgies
> and patent vals? I'd like to start the examples with
> 12&19 and 12&31 meantone, which i'm guessing is are
> valid examples.
>
>
> Also, i'd like to hear from those folks who "are more
> loose about it", with explanations and examples of
> their usage.
I don't agree that I'm more loose about this. My usage handles
contorsion whereas Gene's doesn't. Anyway, the simple definition, where
everything is a strict temperament, is:
A&B denotes the rank 2 temperament class that includes the equal
temperaments A and B as special cases.
Note that A and B do *not* have to be numbers. If you have some other
way of defining equal temperaments (or even equal temperament classes,
now that we work with stretched octaves) you can use that instead. It
happens to be a good shorthand to use numbers because most good equal
temperaments can be identified by the number of notes to the octave
without any ambiguity.
In general terms A, B and A&B do not have to be strict temperaments --
that is they may be contorted. In this case the melodic structure fits
the MOS defined by oct(A)&oct(B) where oct() is the number of notes to
the octave (the numbers you supply as a shorthand).
I give 5, 7, 12 and 19 as examples in:
http://riters.com/microtonal/index.cgi/FindingLinearTemperaments
As it happens, there's nothing about the mappings there, probably
because I thought it was obvious. Anyway, 12&19 expands to <12 19 28
34] & <19 30 44 53] in the 7-limit. One optimum temperament that
describes had 12 steps of 33.4 cents and 19 steps of 42.1 cents to a
stretched octave, 19 steps of 33.4 cents and 30 steps of 42.1 cents to
an approximate 3:1, and so on.
12&31 expands to <12 19 28 34] & <31 49 72 87] which optimizes so that
there isn't a correct 43 note MOS to foul up the presentation.
For the classic contorted example, 7&31 in the 5-limit expands to <7 11
16] & <31 49 72] with 7 steps of 8.3 cents and 31 steps of 36.9 steps to
the stretched octave. It supports a 24 note MOS with large and small
steps of
L s s s L s s L s s s L s s L s s s L s s L s s
This is basically Vicentino's enharmonic. It has the same wedge product
as <5 8 12] & <19 30 44] with the 24 note scale
L s s s s L s s s s L s s s s L s s s s L s s s
hence Gene's method is either ambiguous (by his own definition of
"ambiguous") in this case or fails to produce a historically important
example.
Graham
From: Gene Ward Smith (2006-02-24) Subject: Re: definition: "a&b temperament" (was: Ozan's 79-MOS...) --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote: > Note that A and B do *not* have to be numbers. If you have some other > way of defining equal temperaments (or even equal temperament classes, > now that we work with stretched octaves) you can use that instead. In which case, if A and B *are* numbers, your notation is undefined. It > happens to be a good shorthand to use numbers because most good equal > temperaments can be identified by the number of notes to the octave > without any ambiguity. "Most" is not acceptable in a mathematical definition. Your notation is clearly ambiguous; you must guess what it means in particular cases. Moreover, your claim becomes progressively less true as you proceed to higher limits. > In general terms A, B and A&B do not have to be strict temperaments -- > that is they may be contorted. In this case the melodic structure fits > the MOS defined by oct(A)&oct(B) where oct() is the number of notes to > the octave (the numbers you supply as a shorthand). What is "melodic structure"? This is amazingly vague. > 12&31 expands to <12 19 28 34] & <31 49 72 87] which optimizes so that > there isn't a correct 43 note MOS to foul up the presentation. If you can't get a 43 note MOS for meantone, adjust the tuning or don't worry about it. What's the big deal? You keep talking about an optimized tuning you have not defined, and which should not be part of the definition in the first place. > hence Gene's method is either ambiguous (by his own definition of > "ambiguous") in this case or fails to produce a historically important > example. My definition is completely precise and entirely unambiguous; in the 5-limit, 7&31 is determined from: <7 11 16| ^ <31 49 72| = <<2 8 8|| Taking out the common factor gives <<1 4 4||, taking the complement gives |4 -4 1>, which is 80/81; inverting that gives 81/80. The temperament is, therefore, the 5-limit temperament tempering out 81/80, ie meantone. Your complaint that this does not cover contorted temperaments is true, but that's becuse I don't want it to. One could certainly extend the definition of the wedgie to define contorted temperaments; simply do the sign change, but don't take out any common factors. We could even make the sign mean something about the choice of generator if we wished. I suggest that a wedge product, normalized so that the first nonzero coefficient is positive, where the coefficients have a common factor, be called a "contorted wedgie". Then the contorted wedgie would define the corresponding contorted temperament.
From: Gene Ward Smith (2006-02-24) Subject: Re: definition: "a&b temperament" (was: Ozan's 79-MOS...) --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > Can you please provide some example with their wedgies > and patent vals? I'd like to start the examples with > 12&19 and 12&31 meantone, which i'm guessing is are > valid examples. In the 5-limit, we have <12 19 28| ^ <19 30 44| = <<-1 -4 -4|| >12 19 28| ^ <31 49 72| = <<-1 -4 -4|| Normally we'd take the complement, ~<<=1 -4 -4|| = |-1 4 -4>, which is 81/80, and use that to define the temperament. In the 7-limit <12 19 28 34| ^ <19 30 44 53| = <<-1 -4 -10 -4 -13 -12|| <12 19 28 34| ^ <31 49 72 87| = <<-1 -4 -10 -4 -13 -12|| Here we would reduce to the wedgie by chaning signs, since the first non-zero coefficient of the wedige is positive, and get <<1 4 10 4 13 12|| as the wedgie.
From: Gene Ward Smith (2006-02-24) Subject: Re: Ozan's 159-edo-based tuning --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > Gene, can you post tables of the various different > diatonic scales, triads, tetrads, etc., with the > relevant ratios and/or cents values? Rather than do that, I'll just point out I was primarily thinking of the diatonic scale of the meantone of 112-et. Toof1 has many copies of that. > I could use all this stuff to make a nice Encyclopedia > page about Maqam, and perhaps Ozan's work merits a > separate page too. As yet we haven't gotten this figured out.
From: Graham Breed (2006-02-24)
Subject: Re: [tuning] Re: definition: "a&b temperament" (was: Ozan's 79-MOS...)
On 2/25/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
> "Most" is not acceptable in a mathematical definition. Your notation
> is clearly ambiguous; you must guess what it means in particular
> cases. Moreover, your claim becomes progressively less true as you
> proceed to higher limits.
Newsflash, Gene! This is "tuning"!
Graham
From: Ozan Yarman (2006-03-06) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning monz, sorry for the late reply, my mother is trying to recover from an unfortuitous accident which requires my constant attention and I lost my grandfather the day before at the age of 97. His advanced age and deteriorating health occupied us all and the funeral event was exhausting. I did all my duties for the burial of his body as his favorite grandson, and thus enter into a period of mourning for my muslim senior, during which time I shall try to answer briefly to everyone. What you ask for, or something in that quarter, shall have to await my doctorate dissertation I'm afraid. I know I have said it all too often, but a diligent academical work needs great concentration for which I am too tired to attend to nowadays. But still, if you have the time in the near future to commit a page about Maqamat in your famed encyclopedia, I would be most pleased to be able to edit and contribute. Cordially, Ozan SNIP > > It's clear that the two of you are having a hard time > understanding each other, and i'm taking the presumption > of stepping in here to try and make this discussion work > before you both get frustrated. > > I think examples would help some of us understand what > you're both talking about. > > Oz, can you post a comparative table of the various > different Maqam modes (or whatever term is used here) > with names of modes and notes in Turkish, Persian, > and Arabic, and with ratios and/or cents values? > > Can you also tell us what are published as the > "usual" or "standard" measurements of these scales, > and how your work on them does or doesn't correspond? > > > Gene, can you post tables of the various different > diatonic scales, triads, tetrads, etc., with the > relevant ratios and/or cents values? > > > I could use all this stuff to make a nice Encyclopedia > page about Maqam, and perhaps Ozan's work merits a > separate page too. > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > >
From: Yahya Abdal-Aziz (2006-03-07) Subject: Re: Ozan's 159-edo-based tuning On Mon, 6 Mar 2006, Ozan Yarman wrote in [tuning]: > > monz, sorry for the late reply, my mother is trying to recover from an > unfortuitous accident which requires my constant attention and I lost my > grandfather the day before at the age of 97. His advanced age and > deteriorating health occupied us all and the funeral event was exhausting. I > did all my duties for the burial of his body as his favorite grandson, and > thus enter into a period of mourning for my muslim senior, during which time > I shall try to answer briefly to everyone. > > What you ask for, or something in that quarter, shall have to await my > doctorate dissertation I'm afraid. I know I have said it all too often, but > a diligent academical work needs great concentration for which I am too > tired to attend to nowadays. > > But still, if you have the time in the near future to commit a page about > Maqamat in your famed encyclopedia, I would be most pleased to be able to > edit and contribute. Hi Ozan, My condolences to you and your family in your time of sorrow. Insha'Allah your mother will soon mend, and you will be able to complete your work well. Thinking of you, Yahya -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.375 / Virus Database: 268.2.0/275 - Release Date: 6/3/06
From: Ozan Yarman (2006-03-07) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning You are most gracious my dear brothers in faith. May the blessings of our Lord be with you and your close ones. Cordially, Ozan SNIP > Hi Ozan, > > My condolences to you and your family in your time of sorrow. > Insha'Allah your mother will soon mend, and you will be able to > complete your work well. > > Thinking of you, > Yahya > Dear brother ozan Doroud bar to ba'ad ( that is as-salam-o alaik in arabic word) Very sorry to hear such events. Be sure my heart is with you and I wish I were there to embrace you to feel my sense about \ufffd.. I want god the fast recovery of your mother and bless of your grand father soul. Shaahin Mohaajeri Tombak Player & Researcher , Composer
From: monz (2006-03-08) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > monz, sorry for the late reply, my mother is trying to > recover from an unfortuitous accident which requires my > constant attention and I lost my grandfather the day > before at the age of 97. <snip> > > What you ask for, or something in that quarter, shall have > to await my doctorate dissertation I'm afraid. <snip> > > But still, if you have the time in the near future to > commit a page about Maqamat in your famed encyclopedia, > I would be most pleased to be able to edit and contribute. You see that i'm responding no less than 67 posts later, and as i said i too have been otherwise occupied lately. When i get around to creating a Maqamat page, i will happily encourage you to submit as much information, graphics, and audio examples as you'd like. Don't forget that fairly soon i'll be engaged in incorporating the entire Encyclopedia into the Tonescape help menu ... so i'm looking forward to being able to explain to Tonescape users how to explore Maqam music, and in particular your theories about it, using Tonescape. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2006-03-08) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > You see that i'm responding no less than 67 posts later, > and as i said i too have been otherwise occupied lately. Arrgh ... i was in a hurry when i wrote that response to you, and didn't say everything that i wanted to ... I meant to include condolences for your grandfather's passing, and sympathy and prayers for the rest of your family situation. -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-03-08) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I will be glad to be able to help, provided that I can keep up with all the expectations. 8-) Oz. SNIP > > When i get around to creating a Maqamat page, i will > happily encourage you to submit as much information, > graphics, and audio examples as you'd like. > > Don't forget that fairly soon i'll be engaged in > incorporating the entire Encyclopedia into the Tonescape > help menu ... so i'm looking forward to being able to > explain to Tonescape users how to explore Maqam music, > and in particular your theories about it, using Tonescape. > > > -monz > http://tonalsoft.com > Tonescape microtonal music software >
From: Ozan Yarman (2006-03-08) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning You are most gracious, as always. 8-) Excuse my amazement, but.... you pray???? I never would have guessed. (Doomsday, here we come!) Cordially, Oz. ----- Original Message ----- From: "monz" <monz@tonalsoft.com> To: <tuning@yahoogroups.com> Sent: 08 Mart 2006 \ufffdar\ufffdamba 7:33 Subject: [tuning] Re: Ozan's 159-edo-based tuning > Hi Oz, > > > --- In tuning@yahoogroups.com, "monz" <monz@...> wrote: > > > You see that i'm responding no less than 67 posts later, > > and as i said i too have been otherwise occupied lately. > > > Arrgh ... i was in a hurry when i wrote that response to you, > and didn't say everything that i wanted to ... > > I meant to include condolences for your grandfather's passing, > and sympathy and prayers for the rest of your family situation. > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software >
From: monz (2006-03-10) Subject: Re: Ozan's 159-edo-based tuning Hi Oz, --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote: > > You are most gracious, as always. 8-) > > Excuse my amazement, but.... you pray???? > > I never would have guessed. > > (Doomsday, here we come!) I would write more about it on metatuning, but you don't read that ... so maybe we can talk about it privately. Didn't i mention here once that i've been toying for years with the idea of setting up a "Church of Mahler"? -monz http://tonalsoft.com Tonescape microtonal music software
From: Ozan Yarman (2006-03-10) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning I answered to you on hypertuning. SNIP > > I would write more about it on metatuning, but you > don't read that ... so maybe we can talk about it > privately. > > Didn't i mention here once that i've been toying for > years with the idea of setting up a "Church of Mahler"? > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > >
From: Chris Mohr (2006-03-15) Subject: Re: [tuning] Re: Ozan's 159-edo-based tuning Monz, Did you know I founded the Church of Good Music in 1979? That evolved into Harmony Community Church, which I now run. If you pray, pray that Mt. Mahler gets named officially this year! The US Board On Geographic Names will be voting on it after all the local boards here in Colorado weigh in on it. Rev. Chris Mohr --- monz <monz@tonalsoft.com> wrote: > Hi Oz, > > > --- In tuning@yahoogroups.com, "Ozan Yarman" > <ozanyarman@...> wrote: > > > > You are most gracious, as always. 8-) > > > > Excuse my amazement, but.... you pray???? > > > > I never would have guessed. > > > > (Doomsday, here we come!) > > > I would write more about it on metatuning, but you > don't read that ... so maybe we can talk about it > privately. > > Didn't i mention here once that i've been toying for > > years with the idea of setting up a "Church of > Mahler"? > > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > > > > > > > > > > > > > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com