Topic: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic?
13 scales
| File | Description | Notes | Period (¢) |
|---|---|---|---|
| 43-46 | 43 notes of 43&46 regular temperament | 43 | 1200.0 |
| cal42 | 42-n 4 Cal by G.W.Smith "required" | 42 | 1200.0 |
| caleb44 | caleb46 massacred | 44 | 1200.0 |
| caleb46_4 | caleb46 re-tweaked | 46 | 1200.0 |
| caleb46_tuning_92330_92333 | 46 note tweaked epimorphic scale by G.W.Smith, mod by caleb | 46 | 1200.0 |
| compton48 | Compton[48] 11-limit tweaked | 48 | 1200.0 |
| dwarf27_7tempered | Irregularly tempered Dwarf(<27 43 63 76|) | 27 | 1200.0 |
| hemifamity27 | (3/2)^9 * (10/9)^3 hemifamity tempered | 27 | 1200.0 |
| miracle3 | 41 out of 72-tET Pythagorean scale "Miracle/Studloco", Erlich/Keenan 2001 | 41 | 1200.0 |
| miracle41s | Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976 | 41 | 1200.0 |
| newts | 11-limit scale with boatload of neutral thirds | 41 | 1200.0 |
| octacot27 | Octacot[27] in 88 cent (150et) tuning | 27 | 1200.0 |
| studwacko | Tweaked miracle41s.scl | 41 | 1200.0 |
Thread (111 messages)
From: calebmrgn (2010-09-04) Subject: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Help, o wise ones. 46EDO is nearly perfect, Gene Ward Smith's epimorphic Just scale is nearly perfect. Can I somehow split the difference to make something better than either? I've tweaked GWS's epi scale to make it even more to my liking. I include 46EDO and my tweaked GWS scale below. All the important 8:9:10:11:12:13:14:15:16 approximations sound good, and on a standard keyboard, they go 8,7,6,6,5,5,5,4 steps apart. These are the two essential things to keep that I like. 48 pitches per 2/1 is my maximum practical limit, so 46 is fine. The only problem with the current tweaked scale, below, is that other intervallic patterns have slightly inconsistent patterns of keys. Such as, a chain of 4ths from 15/14, or C#, if the scale begins on A. The 4/3 interval *should* be 19 tones apart, or an octave plus 7 keys. It isn't. Is it possible to make a subtle tweak to my mod2 version so that the fingering is slightly more consistent? I want to keep the basic pitch relations I've got, but make just make the key patterns slightly more consistent. Not every starting point needs to have "good" 4ths or 5ths. Just the important ones. The tweak might be impossible. Or it might involve adjusting a few pitches, or adding or subtracting a few. I'd even accept a tweak with a repetition of the identical pitch on two adjacent keys, if that would make the key-patterns more consistent. What's *not" important is consistent steps between adjacent keys, that is, the small intervals between adjacent keys don't need to be exactly the same. What *is* important: chains of 3/2 approximations, 4/3 approx., and 8:9:10:11:12:13:14:15:16s, with leeway allowed in the 11s, 13s and 15s. The desired result is close to 46 EDO or some other EDO perhaps, but is a sort of large "well" temperament, perhaps. It has better 7's and 11's and 13's than 46 EDO--being closer to JI. Is this simply impossible by definition? Here are my two starting-points, below. ! 46et.scl 46-note equal temp 46 ! 0 26.08696 1 52.17391 2 78.261 3 104.34 4 b2 130.435 5 156.52 6 182.609 7 208.696 8 2 234.783 9 260.8696 10 286.9565 11 b3 narrow ! 313.0435 12 b3 wide 339.13 13 365.2174 14 391.3043 15 3 417.3913 16 443.4783 17 469.5652 18 495.6522 19 4 !4th= 1 oct + fifth 521.7391 20 547.8261 21 573.913 22 600 23 #4/b5 middle-!tritone= 1 oct + major seventh----------------------------------- ! 626.087 24 652.1739 25 678.2609 26 704.3478 27 5 !fifth= 2 oct + minor third 730.4348 28 756.5217 29 782.6087 30 808.6957 31 b6 834.7826 32 860.8696 33 886.9565 34 913.0435 35 6 ! 939.1304 36 965.2174 37 991.3043 38 1017.391 39 1043.478 40 1069.565 41 1095.652 42 1121.739 43 1147.826 44 1173.913 45 1200 46 ! caleb46.scl 46 note 13-lim tweaked epiby G.W.Smith, mod2 by caleb 46 ! a ************keep 8,7,6,6,5,5,5,4, 30 53. 4th below 11/8, 5th above 11/8 21/20 c 84.46 ********keep 15/14 c# 119.4 (was 16/15 in previous)************* 13/12 d 138.57 150.68 12/11 d# changed to give "5th" above /11 179.1 e 10/9 was 182.4 *******keep 207.2 f 9/8 wide with 3/2 *********keep 8/7 f# 231 7/6 g 266 13/11 g# 289 32/27 is 294.13 *************keep ! 313.6 a was 6/5 315.6 ************keep 11/9 a# 347.4 16/13 b 385.0 c 5/4 was 386.3 ************ 14/11 c# 417.5 9/7 d 435 21/16 d# 470.8 496.4 e 4/3 low/narrow 27/20 f 519.55 11/8 f# 551.3 7/5 g 582 *********keep 593 ! ! 10/7 a 617.5 ********keep 648.68 16/11 a# 40/27 b 4th above our 10/9 is 677, 22/15 is 663, 40/27 is 680.4 703.6 3/2 wide *******keep 32/21 c# 14/9 d 764 11/7 d# 782.49 keep************** 819. e high 8/5, keep8*************** 13/8 f 840.52 18/11 f# 852 882.7 g 5/3 was orig 884.35 ********keep 22/13 g# 911 ! 12/7 a 933 7/4 a# 968 992.8 b 16/9 low/narrow with 4/3, was 996 ************ 1013.6 ********keep, end of +5ths chain, was 9/5, 1017.59 11/6 c# 24/13 d 1085.0 eb 15/8 lower--was 1088.3 ***********keep 40/21 1115.5 *******keep 1147 1170 2/1 g
From: genewardsmith (2010-09-04) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, "calebmrgn" <calebmrgn@...> wrote: > > > ! caleb46.scl > 46 note 13-lim tweaked epiby G.W.Smith, mod2 by caleb You've got all kinds of comments which prevent it from being a valid scl file. Could you post a version with only either a rational number or a floating point number (representing cents) on each line? You can also place comments after a ! on a line.
From: caleb morgan (2010-09-04) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Sorry 'bout that! The file below should work better. I changed 45/32 to be higher @ 605 cents, from 590.22. ! keep 8,7,6,6,5,5,5,4, on "important" tonalities, ! keep 19 steps to a 4th, keep "wide, high" 5ths, allow some inconsistencies where less important--somehow! (or is that impossible?) I guess the way I understand it is, is there any wiggle room to get closer to JI, while still having good chains of 4ths and 5ths, and consistent fingering? And, if I were patient enough, (which I am) how to search for other things that are very close to this? You, Gene, were the one who gave me the idea of 46-note JI, and also you've composed in 46EDO. Is there some tuning that sort of splits the difference in a way that's better than either? Caleb ! caleb46.scl 46 note tweaked epimorphic scale by G.W.Smith, mod by caleb 46 ! a 35.69 48.77 84.46 119.4 138.572 150.68 179.1 207.2 231.17 266.87 289.2 ! 313.6 347.4 359.47 385.0 417.5 435.1 470.78 496.4 519.55 551.31 582.5 605.0 ! ! 617.5 648.68 680.45 703.6 729.22 764.9 782.49 819.0 840.53 852.6 882.7 910.79 ! 933.12 968.82 992.8 1013.6 1049.36 1061.43 1085.0 1115.53 1151.23 1168.8 1200.0 On Sep 4, 2010, at 4:04 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, "calebmrgn" <calebmrgn@...> wrote: > > > > > > ! caleb46.scl > > 46 note 13-lim tweaked epiby G.W.Smith, mod2 by caleb > > You've got all kinds of comments which prevent it from being a valid scl file. Could you post a version with only either a rational number or a floating point number (representing cents) on each line? You can also place comments after a ! on a line. > >
From: caleb morgan (2010-09-04) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? For example, what would happen if you divided 7/5 in 23 equal parts, then divided 10/7 in 23 equal parts? Probably nothing good, but I'm just trying to brainstorm. Caleb On Sep 4, 2010, at 4:40 PM, caleb morgan wrote: > Sorry 'bout that! The file below should work better. > > > I changed 45/32 to be higher @ 605 cents, from 590.22. > > ! keep 8,7,6,6,5,5,5,4, on "important" tonalities, ! keep 19 steps to a 4th, keep "wide, high" 5ths, allow some inconsistencies where less important--somehow! (or is that impossible?) > > I guess the way I understand it is, is there any wiggle room to get closer to JI, while still having good chains of 4ths and 5ths, and consistent fingering? > > And, if I were patient enough, (which I am) how to search for other things that are very close to this? > > You, Gene, were the one who gave me the idea of 46-note JI, and also you've composed in 46EDO. > > Is there some tuning that sort of splits the difference in a way that's better than either? > > Caleb > > > > > > ! caleb46.scl > 46 note tweaked epimorphic scale by G.W.Smith, mod by caleb > 46 > ! a > 35.69 > 48.77 > 84.46 > 119.4 > 138.572 > 150.68 > 179.1 > 207.2 > 231.17 > 266.87 > 289.2 > ! > 313.6 > 347.4 > 359.47 > 385.0 > 417.5 > 435.1 > 470.78 > 496.4 > 519.55 > 551.31 > 582.5 > 605.0 > ! > ! > 617.5 > 648.68 > 680.45 > 703.6 > 729.22 > 764.9 > 782.49 > 819.0 > 840.53 > 852.6 > 882.7 > 910.79 > ! > 933.12 > 968.82 > 992.8 > 1013.6 > 1049.36 > 1061.43 > 1085.0 > 1115.53 > 1151.23 > 1168.8 > 1200.0 > > > > On Sep 4, 2010, at 4:04 PM, genewardsmith wrote: > >> >> >> >> --- In tuning@yahoogroups.com, "calebmrgn" <calebmrgn@...> wrote: >> > >> > >> > ! caleb46.scl >> > 46 note 13-lim tweaked epiby G.W.Smith, mod2 by caleb >> >> You've got all kinds of comments which prevent it from being a valid scl file. Could you post a version with only either a rational number or a floating point number (representing cents) on each line? You can also place comments after a ! on a line. >> > > >
From: genewardsmith (2010-09-04) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > I guess the way I understand it is, is there any wiggle room to get closer to JI, while still having good chains of 4ths and 5ths, and consistent fingering? It's not what you seemed to be asking for, but below are two scales I derived from yours. The wide fifths are now narrow ones, and 13 is a little screwed over, but there are advantages also. Maybe you can use it as another starting point, or see if it gives you ideas. ! caleb46_4.scl caleb46 re-tweaked 46 ! 34.1041 51.1932 83.0422 117.8827 133.9278 150.5304 184.4619 201.5270 234.4075 267.4520 285.5358 315.1545 350.9402 365.5360 384.7127 417.5425 433.6369 467.8656 501.1001 517.6815 551.1279 582.6132 602.9948 618.2099 651.4617 682.860 700.5025 733.4973 768.0480 784.1441 818.4160 835.7333 850.7061 885.6155 917.1322 934.7707 967.3138 1000.3701 1016.1738 1050.3968 1067.8418 1085.1891 1117.9017 1152.6154 1167.7300 1200.0000 ! caleb44.scl caleb46 massacred 44 ! 33.3285 49.1413 82.5632 116.9509 133.7225 149.7450 183.7235 199.9940 232.9493 266.1797 284.0458 314.9424 350.1557 383.6852 416.3771 433.0033 466.3924 499.8415 516.4081 550.5131 582.7073 600.3996 617.0051 649.5010 683.3140 699.7916 733.0869 766.9046 783.3466 816.2088 849.5745 884.3029 915.4063 933.4554 966.7936 999.6010 1016.0054 1050.0168 1066.1453 1082.7801 1117.1462 1150.7489 1166.3940 1200.0000
From: caleb morgan (2010-09-04) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Thanks!, I'm checking them out now. Will have something to say tomorrow. -c On Sep 4, 2010, at 6:00 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > I guess the way I understand it is, is there any wiggle room to get closer to JI, while still having good chains of 4ths and 5ths, and consistent fingering? > > It's not what you seemed to be asking for, but below are two scales I derived from yours. The wide fifths are now narrow ones, and 13 is a little screwed over, but there are advantages also. Maybe you can use it as another starting point, or see if it gives you ideas. > > ! caleb46_4.scl > caleb46 re-tweaked > 46 > ! > 34.1041 > 51.1932 > 83.0422 > 117.8827 > 133.9278 > 150.5304 > 184.4619 > 201.5270 > 234.4075 > 267.4520 > 285.5358 > 315.1545 > 350.9402 > 365.5360 > 384.7127 > 417.5425 > 433.6369 > 467.8656 > 501.1001 > 517.6815 > 551.1279 > 582.6132 > 602.9948 > 618.2099 > 651.4617 > 682.860 > 700.5025 > 733.4973 > 768.0480 > 784.1441 > 818.4160 > 835.7333 > 850.7061 > 885.6155 > 917.1322 > 934.7707 > 967.3138 > 1000.3701 > 1016.1738 > 1050.3968 > 1067.8418 > 1085.1891 > 1117.9017 > 1152.6154 > 1167.7300 > 1200.0000 > > ! caleb44.scl > caleb46 massacred > 44 > ! > 33.3285 > 49.1413 > 82.5632 > 116.9509 > 133.7225 > 149.7450 > 183.7235 > 199.9940 > 232.9493 > 266.1797 > 284.0458 > 314.9424 > 350.1557 > 383.6852 > 416.3771 > 433.0033 > 466.3924 > 499.8415 > 516.4081 > 550.5131 > 582.7073 > 600.3996 > 617.0051 > 649.5010 > 683.3140 > 699.7916 > 733.0869 > 766.9046 > 783.3466 > 816.2088 > 849.5745 > 884.3029 > 915.4063 > 933.4554 > 966.7936 > 999.6010 > 1016.0054 > 1050.0168 > 1066.1453 > 1082.7801 > 1117.1462 > 1150.7489 > 1166.3940 > 1200.0000 > >
From: genewardsmith (2010-09-04) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > I guess the way I understand it is, is there any wiggle room to get closer to JI, while still having good chains of 4ths and 5ths, and consistent fingering? The most obvious way to do this is to use a 46 note MOS of an appropriate rank two temperament such as the 17-limit versions of wizard, valentine, rodan or diaschismic. Wizard would be excellent but for the fact that you want long chains of wide fifths, so it seems to me rodan or diaschismic would be the best choices. I could give 46 note MOS for those if you want them.
From: Graham Breed (2010-09-04)
Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic?
On 5 September 2010 06:24, genewardsmith <genewardsmith@...> wrote:
> The most obvious way to do this is to use a 46 note MOS of an appropriate
> rank two temperament such as the 17-limit versions of wizard, valentine,
> rodan or diaschismic. Wizard would be excellent but for the fact that you want
> long chains of wide fifths, so it seems to me rodan or diaschismic would be
> the best choices. I could give 46 note MOS for those if you want them.
Why 17? I don't see any mention of 17 in the thread above. Anyway,
I'll give URLs to the automatically generated pages, in the hope that
they'll be understood. This is diaschismic, which is an obvious
choice if you want the fifths:
http://tinyurl.com/29zs84h
Rodan:
http://tinyurl.com/258ngvy
Valentino, which must be the Valentine variant:
http://tinyurl.com/23h89ye
Wizard only comes up in the 17-limit search, so here's that:
http://tinyurl.com/2bnlamt
Unidec looks better, but may or may not be so in reality.
13-limit:
http://tinyurl.com/23cno9d
17-limit:
http://tinyurl.com/26oodsl
You can take any rank 2 temperament and smooth the edges to get a well
temperament.
Graham
From: caleb morgan (2010-09-05) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Tuning lightweight Caleb is overwhelmed by talking to the heavy cats. Thank you both, and, really, I'm embarrassed to admit I'm not sure if I understand, but I'm determined to understand this. I'd be delighted with chains of 5ths either slightly wide or slightly narrow, and with something approximating a 13-limit. 17 isn't necessary. I like the octave slightly off--not too much, though. I do seem to prefer the sound of higher fifths. I've also found that I prefer a *little* detuning or beating to absolutely perfect JI, but I prefer something less consistent and closer to JI than 46 EDO. Because of checking out some of the scales by GWS and others, I've come to appreciate the importance of regular fingering patterns. Regular fingering patterns are more important than repeating at some multiple of 12, which I *formerly* thought was one way to make a scale easier to learn. Easy learning becomes increasingly important as more pitches are added. I will learn about the theory by generating these tunings, I hope. I can't plug them into Scala, because I don't have that running on my Mac, but I hope to in the future. Therefore, I can't follow the instructions literally, as given on one of your pages. However, let me guess, and try using LMSO, and a calculator. Let's take them one at a time. http://tinyurl.com/29zs84h Diaschismic I use 103.608 as a generator inside a modulus of 599.447 for 23 iterations, then take each of those cent values and add 599.447 cents to get all 46? Or do I add *600* cents? Rodan I use 234.48 inside a modulus of 1199.989 up to 46? Valentino I use 77.971 inside a mod of 1200.201 etc.? Unidec I do 23 iterations of 183.315 inside 600.383, then add 600.383 for the remaining 23? Or do I add 600? Unidec one dimension higher 23 interations of 183.318 inside 600.4, then add 600.4 for the remaining 23? Or do I add 600? I'm sorry you have to be so literal and concrete, but that's my level. If I may hazard a very small joke: when it comes to your mastery of tuning, *both* of you are two dimensions higher. I'm exhausted right now, I'll work on this tomorrow. Thanks, Caleb On Sep 4, 2010, at 7:29 PM, Graham Breed wrote: > On 5 September 2010 06:24, genewardsmith <genewardsmith@...> wrote: > > > The most obvious way to do this is to use a 46 note MOS of an appropriate > > rank two temperament such as the 17-limit versions of wizard, valentine, > > rodan or diaschismic. Wizard would be excellent but for the fact that you want > > long chains of wide fifths, so it seems to me rodan or diaschismic would be > > the best choices. I could give 46 note MOS for those if you want them. > > Why 17? I don't see any mention of 17 in the thread above. Anyway, > I'll give URLs to the automatically generated pages, in the hope that > they'll be understood. This is diaschismic, which is an obvious > choice if you want the fifths: > > http://tinyurl.com/29zs84h > > Rodan: > > http://tinyurl.com/258ngvy > > Valentino, which must be the Valentine variant: > > http://tinyurl.com/23h89ye > > Wizard only comes up in the 17-limit search, so here's that: > > http://tinyurl.com/2bnlamt > > Unidec looks better, but may or may not be so in reality. > > 13-limit: > > http://tinyurl.com/23cno9d > > 17-limit: > > http://tinyurl.com/26oodsl > > You can take any rank 2 temperament and smooth the edges to get a well > temperament. > > Graham >
From: Graham Breed (2010-09-05)
Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic?
On 5 September 2010 08:35, caleb morgan <calebmrgn@...> wrote:
> Because of checking out some of the scales by GWS and others, I've come to appreciate the importance of regular fingering patterns. Regular fingering patterns are more important than repeating at some multiple of 12, which I *formerly* thought was one way to make a scale easier to learn. Easy learning becomes increasingly important as more pitches are added.
I still think 46 is a lot of notes if you don't have a generalized
keyboard. But, given that, regular temperaments will have this
consistency.
> I will learn about the theory by generating these tunings, I hope.
> I can't plug them into Scala, because I don't have that running on my Mac, but I hope to in the future. Therefore, I can't follow the instructions literally, as given on one of your pages.
> However, let me guess, and try using LMSO, and a calculator.
> Let's take them one at a time.
> http://tinyurl.com/29zs84h
> Diaschismic
> I use 103.608 as a generator inside a modulus of 599.447 for 23 iterations, then take each of those cent values and add 599.447 cents to get all 46? Or do I add *600* cents?
Yes. I don't know LMSO, hopefully it makes this easy. You should add
599.447 cents.
> Rodan
> I use 234.48 inside a modulus of 1199.989 up to 46?
> Valentino
> I use 77.971 inside a mod of 1200.201 etc.?
Yes.
> Unidec
> I do 23 iterations of 183.315 inside 600.383, then add 600.383 for the remaining 23? Or do I add 600?
You add 600.383 but it won't make a great amount of difference if you add 600.
> Unidec one dimension higher
> 23 interations of 183.318 inside 600.4, then add 600.4 for the remaining 23? Or do I add 600?
It's the same as the other Unidec, really, but with a mapping for
intervals of 17.
> I'm sorry you have to be so literal and concrete, but that's my level.
That's exactly what you have to do, and what the readouts are telling
you to do, so I don't see anything to apologize for. You can also use
the mappings to get the fingering patterns. The one for 46 should
always be the same. There's another by generator that tells you which
intervals are in tune. You can also use this to work out how many
pure fifths you get.
Graham
From: Michael (2010-09-05)
Subject: Scales for maximum accuracy of Neutral intervals
In your opinion(s), what are the best scales/temperaments for getting both
strong major/minor 3rd,4th,5th,6th,7ths (ALA 31TET)...but also strong neutral
versions of those intervals (within about 8 cents or less accuracy in most
cases)?
If you could give the results in both estimated fractional (up to x/11
format) and exact cents format that would be much appreciated. The fractional
form would help me understand the kind of chords likely to be possible at a
quick glance.
From: caleb morgan (2010-09-05) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Amazing! I'm starting to get how this works. "so it seems to me rodan or diaschismic would be > the best choices. I could give 46 note MOS for those if you want them." I know that MOS stands for "moment of symmetry". But I don't know what these would be in practice, yet. So, yes, I'd be very curious in the MOS scales. Would a 46-note MOS be a subset of a larger EDO? Would these be substantially different from Rodan, Valentino, and Diaschismic? I didn't like Unidec, I think, because the 9/8 approximation was so high--I could be wrong. Same thing with Wizard, iirc, the 9/8 was too high. The other scale I really liked, but for slightly weird layout and/or 5ths, was GWS's "Cal Massacre"--which I renamed "Masaka", to make it sound, um, soulful. Ok, can we have something a little closer to JI in spirit, 11-limit, more unequal step-sizes (that is, both in terms of number of different sizes and relative proportion of sizes) a chain of 5ths at least 10 notes long, and 4ths 10 notes long, regular layout for 4ths and 5ths, and 36 to 46 pitches, with 9/8's pretty close? The result would only be really in tune or consistent in 8 to 12 keys, perhaps. It sounds sort of childishly demanding to put it that way. But you guys already know how to do this stuff without breaking a sweat. For those who are interested, I give the Scala files of the ones I liked. I'm still a long way from being able to tell these apart by ear. Caleb (Thanks--you guys really are amazing.) ! diachismic 46 (GB) 46-n diachismic 46 !0., 22.202, 59.205, 81.406, 103.608, 125.81, 162.813, 185.014, 207.216, 229.418, 266.421, 288.622, ! 310.824, 333.026, 370.029, 392.23, 414.432, 436.634, 473.637, 495.839, 518.04, 540.242, 577.245 599.447 ! ! 621.649 658.652 680.853 703.055 725.3 762.4 784.5 806.7 828.8 865.9 888.1 910.3 ! 932.5 969.7 991.8 1013.9 1036.1 1073.2 1095.3 1117.1 1139.7 1176.8 1198.89 ! cal46.scl 46-n 4 Cal by G.W.Smith "required" 46 ! 22.9251 56.2576 80.6369 104.0612 126.6171 160.4026 184.7357 208.1710 231.9308 263.2192 288.7711 ! 311.2289 336.7808 368.0692 391.8290 415.2643 439.5974 473.3829 495.9388 519.3631 543.7424 577.0749 600.0000 ! ! 622.9251 656.2576 680.6369 704.0612 726.6171 760.4026 784.7357 808.1710 831.9308 863.2192 888.7711 911.2289 ! 936.7808 968.0692 991.8290 1015.2643 1039.5974 1073.3829 1095.9388 1119.3631 1143.7424 1177.0749 1200.0000 ! Rodan 46 (GB) 46-n 234.48 generator ca. 28&14cent steps 46 !0., 27.586, 55.172, 82.758, 110.344, 124.137, 151.723, 179.309, 206.895, 234.481, 262.066, 289.652, ! 317.238, 344.824, 358.617, 386.203, 413.789, 441.375, 468.961, 496.547, 524.133, 551.719, 579.305, 593.098, ! ! 620.684, 648.27, 675.856, 703.442, 731.028, 758.613, 786.199, 813.785, 841.371, 855.164, 882.75, 910.336, ! 937.922, 965.508, 993.094, 1020.68, 1048.266, 1075.852, 1089.645, 1117.231, 1144.817, 1172.403 1199.989 ! Valentino 46 (GB) 46-n, 77.971 gen, 30.6 & 16.7-cents 46 !0., 30.636, 47.335, 77.971, 108.607, 125.306, 155.942, 186.578, 203.277, 233.913, 264.549, 281.248, ! 311.884, 342.52, 359.219, 389.855, 420.491, 437.19, 467.826, 498.462, 515.161, 545.797, 576.433, 593.132, ! ! 623.768, 654.404, 685.04, 701.739, 732.375, 763.011, 779.71, 810.346, 840.982, 857.681, 888.317, 918.953, ! 935.652, 966.288, 996.924, 1013.623, 1044.259, 1074.895, 1091.594, 1122.23, 1152.866, 1169.565 1200.201 On Sep 4, 2010, at 7:29 PM, Graham Breed wrote: > On 5 September 2010 06:24, genewardsmith <genewardsmith@...> wrote: > > > The most obvious way to do this is to use a 46 note MOS of an appropriate > > rank two temperament such as the 17-limit versions of wizard, valentine, > > rodan or diaschismic. Wizard would be excellent but for the fact that you want > > long chains of wide fifths, so it seems to me rodan or diaschismic would be > > the best choices. I could give 46 note MOS for those if you want them. > > Why 17? I don't see any mention of 17 in the thread above. Anyway, > I'll give URLs to the automatically generated pages, in the hope that > they'll be understood. This is diaschismic, which is an obvious > choice if you want the fifths: > > http://tinyurl.com/29zs84h > > Rodan: > > http://tinyurl.com/258ngvy > > Valentino, which must be the Valentine variant: > > http://tinyurl.com/23h89ye > > Wizard only comes up in the 17-limit search, so here's that: > > http://tinyurl.com/2bnlamt > > Unidec looks better, but may or may not be so in reality. > > 13-limit: > > http://tinyurl.com/23cno9d > > 17-limit: > > http://tinyurl.com/26oodsl > > You can take any rank 2 temperament and smooth the edges to get a well > temperament. > > Graham >
From: genewardsmith (2010-09-05) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > I know that MOS stands for "moment of symmetry". But I don't know what these would be in practice, yet. So, yes, I'd be very curious in the MOS scales. You seem to have them already. > Would a 46-note MOS be a subset of a larger EDO? If you used that tuning. Do you want it to be?
From: caleb morgan (2010-09-05) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? I apologize for being more greedy than competent. It's exciting to have tools for designing and hearing these scales, so I'm trying things so fast that many of my ideas are barely coherent. I also apologize if I sound like I'm treating you like Genie Ward Smith, Granter of Tuning Wishes. It's just that I don't yet have a clear sense of what I want to hear, and how to capture that in as few a set of notes as possible, with a consistent pattern of keys. Let's say we brought the limit down to 11. I certainly like to hear the difference between 11:10, 10:9, 9:8, 8:7, 7:6, and 5:4. It seems that to satisfy what I want to hear, the scale has to have something close to 182¢, 204¢, 231¢, 266¢, something to capture the sound of 6:5 and 5:4, something to get 11/8. So, what is close to the fewest notes that gives complete 7:8:9:10:11:12 on 8/7, 1/1, 16/9, 8/5, 16/11, 4/3, 8/7, 16/15 in EDO or JI? (Maybe I don't need a 13-limit, but I do really like the sound of that interval--13/2, 13/4, 13/8.) Supposing we left it out and used just 5/3 and 27/16, and also included a 15/8--that is, some OTs of 3. What EDOs come close? Also, I'm curious how to generate rank 3 and rank 4 temperaments when I stumble on them. For example, what to do with this: Portent one dimension higher Equal Temperament Mappings 2 3 5 7 11 13 [< 31 49 72 87 107 115 ] < 41 65 95 115 142 152 ] < 46 73 107 129 159 170 ]> Reduced Mapping 2 3 5 7 11 13 [< 1 1 0 3 5 7 ] < 0 3 0 -1 4 -5 ] < 0 0 1 0 -1 -1 ]> Generator Tunings (cents) [1200.067, 234.186, 2786.754> Step Tunings (cents) [5.660, 11.068, 12.409> Tuning Map (cents) <1200.067, 1902.624, 2786.754, 3366.014, 4150.323, 4442.783] a generator of 234.186 repeated 41 times makes step sizes of 29.07 and 30.696 if the modulus is 1200 cents. (This looks pretty good, actually: 0., 29.07, 58.14, 87.21, 116.28, 146.976, 176.046, 205.116, 234.186, 263.256, 292.326, 321.396, 350.466, 381.162, 410.232, 439.302, 468.372, 497.442, 526.512, 555.582, 584.652, 615.348, 644.418, 673.488, 702.558, 731.628, 760.698, 789.768, 818.838, 849.534, 878.604, 907.674, 936.744, 965.814, 994.884, 1023.954, 1053.024, 1083.72, 1112.79, 1141.86, 1170.93 But I don't understand what to do with the 2786 info (5th partial) that's included under Generator Tunings. This is ?Rank 2 because of 29 cent and 30.6 cent step-sizes? Caleb On Sep 5, 2010, at 2:44 PM, genewardsmith wrote: > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > I know that MOS stands for "moment of symmetry". But I don't know > what these would be in practice, yet. So, yes, I'd be very curious in > the MOS scales. > > You seem to have them already. > > > Would a 46-note MOS be a subset of a larger EDO? > > If you used that tuning. Do you want it to be? > >
From: Mike Battaglia (2010-09-06) Subject: Re: [tuning] Scales for maximum accuracy of Neutral intervals On Sat, Sep 4, 2010 at 11:34 PM, Michael <djtrancendance@...> wrote: > > In your opinion(s), what are the best scales/temperaments for getting both strong major/minor 3rd,4th,5th,6th,7ths (ALA 31TET)...but also strong neutral versions of those intervals (within about 8 cents or less accuracy in most cases)? > > If you could give the results in both estimated fractional (up to x/11 format) and exact cents format that would be much appreciated. The fractional form would help me understand the kind of chords likely to be possible at a quick glance. What are you judging the accuracy by? Is the ideal neutral third 11/9? Also, when you say "major/minor 4th and 5th," what do you mean exactly? And what would constitute a neutral 5th? -Mike
From: genewardsmith (2010-09-06) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > I certainly like to hear the difference between 11:10, 10:9, 9:8, 8:7, 7:6, and 5:4. See what you think of this: ! newts.scl ! 11-limit scale with boatload of neutral thirds 41 ! 32.91065 50.80017 83.50287 116.45974 149.89384 182.87269 199.63490 233.54070 266.22566 299.83415 316.84989 349.84324 383.18550 400.34913 449.39797 466.56160 499.90386 532.89721 549.91295 583.52144 616.20640 650.11220 666.87441 699.85326 733.28736 766.24423 798.94693 816.83645 849.74710 883.17168 899.88473 933.63277 966.38375 999.89157 1024.87355 1049.85553 1083.36335 1116.11433 1149.86237 1166.57542 1200.00000 > What EDOs come close? 46 or 58 don't do it? > Also, I'm curious how to generate rank 3 and rank 4 temperaments when I stumble on them. > > For example, what to do with this: > > Portent one dimension higher I have portent written up here: http://xenharmonic.wikispaces.com/Gamelismic+family but it probably won't make much sense. I'm trying to think of what a good introductory page on these writeups of rank 3 temperaments should look like. But one thing you might glean from it is that constructing scales by taking products of 8/7 and 12/11 and octave reducing, then tempering via a portent tuning map, would be a way of getting portent scales.
From: caleb morgan (2010-09-06) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Thank you! I'll listen today. Nah, I really like 41, 46, and 58EDO. I'm experimenting with different patterns (srutis) within those, to see if I can reduce the number of pitches and end up with any kind of keyboard mapping that is consistent, or at least propitious on a standard keyboard. You may already know that this is possible or impossible, but it's teaching me a lot. The holy grail for today would be some sruti pattern of 41, 46 or 58 EDO that contains the pitches I like, plus some kind of consistency in fingering. It might be possible, might not. I realized that any member (value in cents) of 41 can be a generator, because 41 is a prime number. Probably any *other* member of 46 or 58 can be a generator, because 23 and 39 are prime. I was sort of hoping that by finding the right generator within one of these three EDOs, that there would be a particularly effective pattern of srutis--or, pitches included or omitted. Failing that, I'm simply going to take inconsistent subsets of those EDOs with arbitrary patterns, and see what those are like to play with. As a result of these experiments and this list, I now have upwards of 30 different tunings/scales, ranging in # of pitches between 27 and 58, with 4 or 5 JI versions, 5 or 6 scales by Mr. Gene Ward Smith, the Wendy Carlos Gamma scale, and many variations on 46--Diaschismic, Rodan, Valentino. At some point soon, I'm going to switch to investigating dynamic retuning with Little Miss Scale Oven, and also, composing. Mustn't forget the composing part. Thanks again, Caleb On Sep 6, 2010, at 4:41 AM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > I certainly like to hear the difference between 11:10, 10:9, 9:8, 8:7, 7:6, and 5:4. > > See what you think of this: > > ! newts.scl > ! > 11-limit scale with boatload of neutral thirds > 41 > ! > 32.91065 > 50.80017 > 83.50287 > 116.45974 > 149.89384 > 182.87269 > 199.63490 > 233.54070 > 266.22566 > 299.83415 > 316.84989 > 349.84324 > 383.18550 > 400.34913 > 449.39797 > 466.56160 > 499.90386 > 532.89721 > 549.91295 > 583.52144 > 616.20640 > 650.11220 > 666.87441 > 699.85326 > 733.28736 > 766.24423 > 798.94693 > 816.83645 > 849.74710 > 883.17168 > 899.88473 > 933.63277 > 966.38375 > 999.89157 > 1024.87355 > 1049.85553 > 1083.36335 > 1116.11433 > 1149.86237 > 1166.57542 > 1200.00000 > > > What EDOs come close? > > 46 or 58 don't do it? > > > Also, I'm curious how to generate rank 3 and rank 4 temperaments when I stumble on them. > > > > For example, what to do with this: > > > > Portent one dimension higher > > I have portent written up here: > > http://xenharmonic.wikispaces.com/Gamelismic+family > > but it probably won't make much sense. I'm trying to think of what a good introductory page on these writeups of rank 3 temperaments should look like. But one thing you might glean from it is that constructing scales by taking products of 8/7 and 12/11 and octave reducing, then tempering via a portent tuning map, would be a way of getting portent scales. > >
From: caleb morgan (2010-09-06) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Newts is brilliant. On Sep 6, 2010, at 4:41 AM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > I certainly like to hear the difference between 11:10, 10:9, 9:8, 8:7, 7:6, and 5:4. > > See what you think of this: > > ! newts.scl > ! > 11-limit scale with boatload of neutral thirds > 41 > ! > 32.91065 > 50.80017 > 83.50287 > 116.45974 > 149.89384 > 182.87269 > 199.63490 > 233.54070 > 266.22566 > 299.83415 > 316.84989 > 349.84324 > 383.18550 > 400.34913 > 449.39797 > 466.56160 > 499.90386 > 532.89721 > 549.91295 > 583.52144 > 616.20640 > 650.11220 > 666.87441 > 699.85326 > 733.28736 > 766.24423 > 798.94693 > 816.83645 > 849.74710 > 883.17168 > 899.88473 > 933.63277 > 966.38375 > 999.89157 > 1024.87355 > 1049.85553 > 1083.36335 > 1116.11433 > 1149.86237 > 1166.57542 > 1200.00000 > > > What EDOs come close? > > 46 or 58 don't do it? > > > Also, I'm curious how to generate rank 3 and rank 4 temperaments when I stumble on them. > > > > For example, what to do with this: > > > > Portent one dimension higher > > I have portent written up here: > > http://xenharmonic.wikispaces.com/Gamelismic+family > > but it probably won't make much sense. I'm trying to think of what a good introductory page on these writeups of rank 3 temperaments should look like. But one thing you might glean from it is that constructing scales by taking products of 8/7 and 12/11 and octave reducing, then tempering via a portent tuning map, would be a way of getting portent scales. > >
From: Michael (2010-09-06)
Subject: Re: [tuning] Scales for maximum accuracy of Neutral intervals
MikeB>"What are you judging the accuracy by? Is the ideal neutral third 11/9?"
The lowest-limit version of that interval, so in the case of 11/9, yes (I
believe).
>"And what would constitute a neutral 5th?"
Hahaha...right, in literature so far as I can tell there is nothing formally
called a "neutral fifth". I'd leave it as 22/15....it's the first thing I find
below 3/2 which gets anywhere near sounding resolved (anything near it IE 16/11
or 40/27 sounds more less resolved to me). Maybe you could argue 13/9...but, at
least to me, that sounds much more like a very suspended 4th in mood.
From: Graham Breed (2010-09-06)
Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic?
On 6 September 2010 05:55, caleb morgan <calebmrgn@...> wrote:
> Let's say we brought the limit down to 11.
> I certainly like to hear the difference between 11:10, 10:9, 9:8, 8:7, 7:6, and 5:4.
Do you care about 12:11? If you want that distinct as well, what
you'd be looking for is 11-limit uniqueness. I think Miracle does it
first. It's not something the new code tells you because I left odd
limits behind. But I only unlinked the old code, I didn't delete it.
So this tells you Miracle is unique:
http://x31eq.com/cgi-bin/temperament.cgi?et1=31&et2=41&limit=11
This tells you Orwell isn't:
http://x31eq.com/cgi-bin/temperament.cgi?et1=31&et2=22&limit=11
> It seems that to satisfy what I want to hear, the scale has to have something close to 182¢, 204¢,
> 231¢, 266¢, something to capture the sound of 6:5 and 5:4, something to get 11/8.
> So, what is close to the fewest notes that gives complete 7:8:9:10:11:12 on 8/7, 1/1, 16/9, 8/5, 16/11, 4/3, 8/7, 16/15 in EDO or JI?
22 will give you it, from Orwell or Magic or other things. 31 notes
of Miracle will make it unique. Maybe 58 notes for a unique equal
temperament.
> Also, I'm curious how to generate rank 3 and rank 4 temperaments when I stumble on them.
> For example, what to do with this:
>
> Portent one dimension higher
Yeah, that's a pretty good question. It has something to do with why
the Scala files aren't magically produced on my website.
> Equal Temperament Mappings
> 23571113
> [<31497287107115]
> <416595115142152]
> <4673107129159170]>
What you can do is take two of those, to give a rank temperament
you're familiar with. Then use the other step to define a small
perturbation from it. Or you can generalize distributional evenness
so that the three different step sizes are evenly distributed. There
may be a simple formula for that.
> Reduced Mapping
> 23571113
> [<110357]
> <030-14-5]
> <0010-1-1]>
>
> Generator Tunings (cents)
> [1200.067, 234.186, 2786.754>
Or you can take this (which I believe to be Hermite normal form) and
note that one generator is a slightly detuned octave, and another is a
slightly detuned 5:1. So you can think of the 2-5 plane as just
intonation and use the other generator to give the 3:1. This approach
is probably more straightforward for temperaments where two generators
happen to give you the Pythagorean plane.
> Step Tunings (cents)
> [5.660, 11.068, 12.409>
>
> Tuning Map (cents)
> <1200.067, 1902.624, 2786.754, 3366.014, 4150.323, 4442.783]
The other thing is to design a scale in JI, and apply this tuning to it.
> a generator of 234.186 repeated 41 times makes step sizes of 29.07 and 30.696 if the modulus is 1200 cents.
> (This looks pretty good, actually: 0., 29.07, 58.14, 87.21, 116.28, 146.976, 176.046, 205.116, 234.186, 263.256, 292.326, 321.396, 350.466, 381.162, 410.232, 439.302, 468.372, 497.442, 526.512, 555.582, 584.652, 615.348, 644.418, 673.488, 702.558, 731.628, 760.698, 789.768, 818.838, 849.534, 878.604, 907.674, 936.744, 965.814, 994.884, 1023.954, 1053.024, 1083.72, 1112.79, 1141.86, 1170.93
You're only getting a rank 2 scale there. It may well be a good one
but I can't work out what temperament class it is offhand.
Note: this idea of iterating a generator within a period is called
MOS. Putting the detailed definitions aside, when people talk about
MOS, this is what they mean. Nothing more clever than that. Any MOS
can be interpreted as a rank 2 temperament (or rank 1 in the
degenerate case). Higher rank temperaments will lead to more
complicated scales.
> But I don't understand what to do with the 2786 info (5th partial) that's included under Generator Tunings.
> This is ?Rank 2 because of 29 cent and 30.6 cent step-sizes?
It's rank 2 because it's generated by two intervals, whichever two you take.
To make it rank 3, what you do is stop taking the 5:1 (or 5:4) from
this scale, and make it an independent interval. Maybe with two
keyboards a 5:4 apart.
Graham
From: Herman Miller (2010-09-06) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Graham Breed wrote: > On 6 September 2010 05:55, caleb morgan <calebmrgn@...> wrote: >> a generator of 234.186 repeated 41 times makes step sizes of 29.07 and 30.696 if the modulus is 1200 cents. >> (This looks pretty good, actually: 0., 29.07, 58.14, 87.21, 116.28, 146.976, 176.046, 205.116, 234.186, 263.256, 292.326, 321.396, 350.466, 381.162, 410.232, 439.302, 468.372, 497.442, 526.512, 555.582, 584.652, 615.348, 644.418, 673.488, 702.558, 731.628, 760.698, 789.768, 818.838, 849.534, 878.604, 907.674, 936.744, 965.814, 994.884, 1023.954, 1053.024, 1083.72, 1112.79, 1141.86, 1170.93 > > You're only getting a rank 2 scale there. It may well be a good one > but I can't work out what temperament class it is offhand. Looks like rodan <1, 1, -1, 3, 6], <0, 3, 17, -1, -13]>.
From: caleb morgan (2010-09-07) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Slightly tangential, but I'm trying to put together the idea of consistently-fingered chains of 4ths and 5ths and epimorphism from Gene; with reducing the number of notes a little; and hybrid-ism in which the adjacent-note intervals are inconsistent. This proved trickier than I thought. But it seems one way to do it is to take and EDO with a fairly accurate 5th, and then substitute a chain of 5ths and 4ths with consistent spacing, up to the point where the new 5ths and 4ths diverge too much from the EDO to make any sense. Then substitute freely with pitches that fall between the given locations of 5ths and 4ths, starting with a 5-limit, and adding more when possible. Also, simply leaving the remaining EDO pitches if nothing better strikes one. ! hybrid 27 hybrid 27EDO&5-lim just, with adjusted 4ths & 5ths 27 !0., 0 70.588 88.889, 2 16/15 111 177.778, 4 211.765 282.353 6/5 315 355.556, 8 5/4 389 423.529 494.118 533.333, 12 45/32 590 ! 64/45 609 635.294 705.882 776.471 8/5 813 844.444, 19 5/3 884 917.647 988.235 1022.222, 23 15/8 1088.3 1111.111, 25 1129.412 1200 27/0 On Sep 6, 2010, at 5:42 PM, Herman Miller wrote: > Graham Breed wrote: > > On 6 September 2010 05:55, caleb morgan <calebmrgn@...> wrote: > > >> a generator of 234.186 repeated 41 times makes step sizes of 29.07 and 30.696 if the modulus is 1200 cents. > >> (This looks pretty good, actually: 0., 29.07, 58.14, 87.21, 116.28, 146.976, 176.046, 205.116, 234.186, 263.256, 292.326, 321.396, 350.466, 381.162, 410.232, 439.302, 468.372, 497.442, 526.512, 555.582, 584.652, 615.348, 644.418, 673.488, 702.558, 731.628, 760.698, 789.768, 818.838, 849.534, 878.604, 907.674, 936.744, 965.814, 994.884, 1023.954, 1053.024, 1083.72, 1112.79, 1141.86, 1170.93 > > > > You're only getting a rank 2 scale there. It may well be a good one > > but I can't work out what temperament class it is offhand. > > Looks like rodan <1, 1, -1, 3, 6], <0, 3, 17, -1, -13]>. > >
From: caleb morgan (2010-09-07) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Oops. This is a little better. But I'm still missing a few conceptual bricks from my edifice. ! hybrid 27 hybrid 27EDO&5-lim just, with adjusted 4ths & 5ths 27 !0., !0 70.588 16/15 !2 133.333 177.778 !4 211.765 282.353 6/5 !315 355.556 !8 5/4 !389 423.529 494.118 533.333 !12 45/32 !590 !13 ! 64/45 !609 !14 666.667 !15 705.882 !16 755.556 !17 8/5 !813 !18 840.53 5/3 !884 917.647 988.235 1022.222 !23 15/8 !1088.3 1111.111 !25 1129.412 1200 !27/0 On Sep 7, 2010, at 10:16 AM, caleb morgan wrote: > > Slightly tangential, but I'm trying to put together the idea of consistently-fingered chains of 4ths and 5ths and epimorphism from Gene; with reducing the number of notes a little; and hybrid-ism in which the adjacent-note intervals are inconsistent. > > This proved trickier than I thought. > > But it seems one way to do it is to take and EDO with a fairly accurate 5th, and then > substitute a chain of 5ths and 4ths with consistent spacing, up to the point where the new > 5ths and 4ths diverge too much from the EDO to make any sense. > > Then substitute freely with pitches that fall between the given locations of 5ths and 4ths, starting with a 5-limit, and adding more when possible. Also, simply leaving the remaining EDO pitches if nothing better strikes one. > > ! hybrid 27 > hybrid 27EDO&5-lim just, with adjusted 4ths & 5ths > 27 > !0., 0 > 70.588 > 88.889, 2 > 16/15 111 > 177.778, 4 > 211.765 > 282.353 > 6/5 315 > 355.556, 8 > 5/4 389 > 423.529 > 494.118 > 533.333, 12 > 45/32 590 > ! > 64/45 609 > 635.294 > 705.882 > 776.471 > 8/5 813 > 844.444, 19 > 5/3 884 > 917.647 > 988.235 > 1022.222, 23 > 15/8 1088.3 > 1111.111, 25 > 1129.412 > 1200 27/0 > > On Sep 6, 2010, at 5:42 PM, Herman Miller wrote: > >> >> Graham Breed wrote: >> > On 6 September 2010 05:55, caleb morgan <calebmrgn@...> wrote: >> >> >> a generator of 234.186 repeated 41 times makes step sizes of 29.07 and 30.696 if the modulus is 1200 cents. >> >> (This looks pretty good, actually: 0., 29.07, 58.14, 87.21, 116.28, 146.976, 176.046, 205.116, 234.186, 263.256, 292.326, 321.396, 350.466, 381.162, 410.232, 439.302, 468.372, 497.442, 526.512, 555.582, 584.652, 615.348, 644.418, 673.488, 702.558, 731.628, 760.698, 789.768, 818.838, 849.534, 878.604, 907.674, 936.744, 965.814, 994.884, 1023.954, 1053.024, 1083.72, 1112.79, 1141.86, 1170.93 >> > >> > You're only getting a rank 2 scale there. It may well be a good one >> > but I can't work out what temperament class it is offhand. >> >> Looks like rodan <1, 1, -1, 3, 6], <0, 3, 17, -1, -13]>. >> > > >
From: genewardsmith (2010-09-07) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > Oops. > > This is a little better. > > But I'm still missing a few conceptual bricks from my edifice. Here's a 27-note scale with 24 slightly sharp fifths, coming in three groups of eight. ! hemifamity27.scl ! (3/2)^9 * (10/9)^3 hemifamity tempered 27 ! 24.81614 110.21232 180.72536 205.92493 230.32672 291.35517 316.19234 386.89900 411.35967 472.47399 496.93387 522.04780 592.41413 607.58587 677.95220 703.06613 727.52601 788.64033 813.10100 883.80766 908.64483 969.67328 994.07507 1019.27464 1089.78768 1175.18386 1200.00000
From: caleb morgan (2010-09-08) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Thanks, my last answer did'nt get through. That's a beautiful tuning/scale, imo. Is it mathematically impossible to have a tuning with 27 pitches with 5ths ca. 703, with completely consistent fingering? That is, 5ths all the same number of keys apart? I'm hoping to get more insight into when consistent fingering is possible and when it isn't--I don't have much understanding of that, yet. -c On Sep 7, 2010, at 4:52 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > > Oops. > > > > This is a little better. > > > > But I'm still missing a few conceptual bricks from my edifice. > > Here's a 27-note scale with 24 slightly sharp fifths, coming in three groups of eight. > > ! hemifamity27.scl > ! > (3/2)^9 * (10/9)^3 hemifamity tempered > 27 > ! > 24.81614 > 110.21232 > 180.72536 > 205.92493 > 230.32672 > 291.35517 > 316.19234 > 386.89900 > 411.35967 > 472.47399 > 496.93387 > 522.04780 > 592.41413 > 607.58587 > 677.95220 > 703.06613 > 727.52601 > 788.64033 > 813.10100 > 883.80766 > 908.64483 > 969.67328 > 994.07507 > 1019.27464 > 1089.78768 > 1175.18386 > 1200.00000 > >
From: genewardsmith (2010-09-08) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > Thanks, my last answer did'nt get through. > > That's a beautiful tuning/scale, imo. > > Is it mathematically impossible to have a tuning with 27 pitches with 5ths ca. 703, with completely consistent fingering? That is, 5ths all the same number of keys apart? > > I'm hoping to get more insight into when consistent fingering is possible and when it isn't--I don't have much understanding of that, yet. This tuning of octacot has fifths of exactly 704 cents if that's OK. You can tweak it some if you want a flatter fifth. ! octacot27.scl ! Octacot[27] in 88 cent (150et) tuning 27 ! 32.00000 88.00000 120.00000 176.00000 208.00000 264.00000 296.00000 352.00000 384.00000 440.00000 472.00000 528.00000 560.00000 616.00000 648.00000 704.00000 736.00000 792.00000 824.00000 880.00000 936.00000 968.00000 1024.00000 1056.00000 1112.00000 1144.00000 1200.00000
From: caleb morgan (2010-09-07) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Caleb's jaw drops. He picks it up off floor. That's beautiful. I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? Maybe some day, when I grow up, I'll understand. I never would have come up with that in a week of trial-and-error. Thank you, sir. -c On Sep 7, 2010, at 4:52 PM, genewardsmith wrote: > ! hemifamity27.scl > ! > (3/2)^9 * (10/9)^3 hemifamity tempered > 27 > ! > 24.81614 > 110.21232 > 180.72536 > 205.92493 > 230.32672 > 291.35517 > 316.19234 > 386.89900 > 411.35967 > 472.47399 > 496.93387 > 522.04780 > 592.41413 > 607.58587 > 677.95220 > 703.06613 > 727.52601 > 788.64033 > 813.10100 > 883.80766 > 908.64483 > 969.67328 > 994.07507 > 1019.27464 > 1089.78768 > 1175.18386 > 1200.00000
From: genewardsmith (2010-09-09) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. ! dwarf27_7tempered.scl ! Irregularly tempered Dwarf(<27 43 63 76|) 27 ! 8.50411 44.05819 94.02735 155.44995 204.62445 239.75461 275.21962 300.57603 386.44020 410.42948 471.11121 506.30767 541.94592 591.15701 616.87618 702.25982 737.66181 772.99566 797.33536 857.59196 907.39146 969.00623 977.50974 1003.78401 1088.74607 1113.63615 1200.00000
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Oh, there's interest! What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. Are there certain numbers of pitches per octave where consistency is impossible? (I'm sort of afraid that the answer will be over my head.) Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. But "Dwarf27" looks really good. In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. caleb On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? > > Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. > > ! dwarf27_7tempered.scl > ! > Irregularly tempered Dwarf(<27 43 63 76|) > 27 > ! > 8.50411 > 44.05819 > 94.02735 > 155.44995 > 204.62445 > 239.75461 > 275.21962 > 300.57603 > 386.44020 > 410.42948 > 471.11121 > 506.30767 > 541.94592 > 591.15701 > 616.87618 > 702.25982 > 737.66181 > 772.99566 > 797.33536 > 857.59196 > 907.39146 > 969.00623 > 977.50974 > 1003.78401 > 1088.74607 > 1113.63615 > 1200.00000 > >
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Caleb plays "27Dwarf" : Hmm: 5ths are all always 16 steps, but some are a long way from 3:2 702 cents. 4ths: 12 steps, except 16:9 to 32:27 approx is 11 steps, and the 4ths are charmingly different-sized-sounding. pattern of 12-12-11 steps on the 4ths? good 21/8 (7th par of 3) Those are my first impressions. caleb On Sep 9, 2010, at 5:36 AM, caleb morgan wrote: > > Oh, there's interest! > > What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. > > Are there certain numbers of pitches per octave where consistency is impossible? > > (I'm sort of afraid that the answer will be over my head.) > > Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. > > Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. > > But "Dwarf27" looks really good. > > In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. > > It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. > > caleb > > > > On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: > >> >> >> >> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >> >> > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? >> >> Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. >> >> ! dwarf27_7tempered.scl >> ! >> Irregularly tempered Dwarf(<27 43 63 76|) >> 27 >> ! >> 8.50411 >> 44.05819 >> 94.02735 >> 155.44995 >> 204.62445 >> 239.75461 >> 275.21962 >> 300.57603 >> 386.44020 >> 410.42948 >> 471.11121 >> 506.30767 >> 541.94592 >> 591.15701 >> 616.87618 >> 702.25982 >> 737.66181 >> 772.99566 >> 797.33536 >> 857.59196 >> 907.39146 >> 969.00623 >> 977.50974 >> 1003.78401 >> 1088.74607 >> 1113.63615 >> 1200.00000 >> > > >
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. Then that pattern is repeated at 400 and 800 cents. It's close to 11-limit JI in some ways, but has more symmetry and regularity. !Beast Augmentation by Caleb 5/4 in 23 parts, culled, repeated @ 400 and 800 42 !0., 33.592, 67.185, 100.777, 134.37, 151.166, 167.962, 184.759, 201.555, 235.147, 268.74, 302.332, 319.129, 386.315 ! 400 433.592 467.185 500.777 534.37 551.166 567.962 584.759 601.555 635.147 668.74 702.332 719.129 786.315 ! 800 833.592 867.185 900.777 934.37 951.166 967.962 984.759 1001.555 1035.147 1068.74 1102.332 1119.129 1186.315 ! 1200 On Sep 9, 2010, at 6:27 AM, caleb morgan wrote: > Caleb plays "27Dwarf" : > > > Hmm: 5ths are all always 16 steps, but some are a long way from 3:2 702 cents. > > 4ths: 12 steps, except 16:9 to 32:27 approx is 11 steps, and the 4ths are charmingly different-sized-sounding. > > pattern of 12-12-11 steps on the 4ths? > > good 21/8 (7th par of 3) > > Those are my first impressions. > > caleb > > > > > > On Sep 9, 2010, at 5:36 AM, caleb morgan wrote: > >> >> >> Oh, there's interest! >> >> What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. >> >> Are there certain numbers of pitches per octave where consistency is impossible? >> >> (I'm sort of afraid that the answer will be over my head.) >> >> Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. >> >> Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. >> >> But "Dwarf27" looks really good. >> >> In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. >> >> It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. >> >> caleb >> >> >> >> On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: >> >>> >>> >>> >>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>> >>> > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? >>> >>> Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. >>> >>> ! dwarf27_7tempered.scl >>> ! >>> Irregularly tempered Dwarf(<27 43 63 76|) >>> 27 >>> ! >>> 8.50411 >>> 44.05819 >>> 94.02735 >>> 155.44995 >>> 204.62445 >>> 239.75461 >>> 275.21962 >>> 300.57603 >>> 386.44020 >>> 410.42948 >>> 471.11121 >>> 506.30767 >>> 541.94592 >>> 591.15701 >>> 616.87618 >>> 702.25982 >>> 737.66181 >>> 772.99566 >>> 797.33536 >>> 857.59196 >>> 907.39146 >>> 969.00623 >>> 977.50974 >>> 1003.78401 >>> 1088.74607 >>> 1113.63615 >>> 1200.00000 >>> >> >> > > >
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Sorry, same thing cleaned up for better Scala format: !Beast Augmentation by Caleb 5/4 in 23 parts, culled, repeated @ 400 and 800 42 !0. 33.592 67.185 100.777 134.37 151.166 167.962 184.759 201.555 235.147 268.74 302.332 319.129 386.315 ! 400.000 433.592 467.185 500.777 534.37 551.166 567.962 584.759 601.555 635.147 668.74 702.332 719.129 786.315 ! 800.000 833.592 867.185 900.777 934.37 951.166 967.962 984.759 1001.555 1035.147 1068.74 1102.332 1119.129 1186.315 ! 1200.000 On Sep 9, 2010, at 9:05 AM, caleb morgan wrote: > > > Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". > > 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. > > Then that pattern is repeated at 400 and 800 cents. > > It's close to 11-limit JI in some ways, but has more symmetry and regularity. > > !Beast Augmentation by Caleb > 5/4 in 23 parts, culled, repeated @ 400 and 800 > 42 > !0., > 33.592, > 67.185, > 100.777, > 134.37, > 151.166, > 167.962, > 184.759, > 201.555, > 235.147, > 268.74, > 302.332, > 319.129, > 386.315 > ! > 400 > 433.592 > 467.185 > 500.777 > 534.37 > 551.166 > 567.962 > 584.759 > 601.555 > 635.147 > 668.74 > 702.332 > 719.129 > 786.315 > ! > 800 > 833.592 > 867.185 > 900.777 > 934.37 > 951.166 > 967.962 > 984.759 > 1001.555 > 1035.147 > 1068.74 > 1102.332 > 1119.129 > 1186.315 > ! > 1200 > > > > > > > > > > > On Sep 9, 2010, at 6:27 AM, caleb morgan wrote: > >> >> Caleb plays "27Dwarf" : >> >> >> Hmm: 5ths are all always 16 steps, but some are a long way from 3:2 702 cents. >> >> 4ths: 12 steps, except 16:9 to 32:27 approx is 11 steps, and the 4ths are charmingly different-sized-sounding. >> >> pattern of 12-12-11 steps on the 4ths? >> >> good 21/8 (7th par of 3) >> >> Those are my first impressions. >> >> caleb >> >> >> >> >> >> On Sep 9, 2010, at 5:36 AM, caleb morgan wrote: >> >>> >>> >>> Oh, there's interest! >>> >>> What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. >>> >>> Are there certain numbers of pitches per octave where consistency is impossible? >>> >>> (I'm sort of afraid that the answer will be over my head.) >>> >>> Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. >>> >>> Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. >>> >>> But "Dwarf27" looks really good. >>> >>> In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. >>> >>> It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. >>> >>> caleb >>> >>> >>> >>> On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: >>> >>>> >>>> >>>> >>>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>>> >>>> > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? >>>> >>>> Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. >>>> >>>> ! dwarf27_7tempered.scl >>>> ! >>>> Irregularly tempered Dwarf(<27 43 63 76|) >>>> 27 >>>> ! >>>> 8.50411 >>>> 44.05819 >>>> 94.02735 >>>> 155.44995 >>>> 204.62445 >>>> 239.75461 >>>> 275.21962 >>>> 300.57603 >>>> 386.44020 >>>> 410.42948 >>>> 471.11121 >>>> 506.30767 >>>> 541.94592 >>>> 591.15701 >>>> 616.87618 >>>> 702.25982 >>>> 737.66181 >>>> 772.99566 >>>> 797.33536 >>>> 857.59196 >>>> 907.39146 >>>> 969.00623 >>>> 977.50974 >>>> 1003.78401 >>>> 1088.74607 >>>> 1113.63615 >>>> 1200.00000 >>>> >>> >>> >> >> > > >
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Here's a 48-tone version of the same thing. This combines an attempt at epimorphism with 48-tone fingering with 11 and 13-limit JI with a concession to the standard keyboard pattern of 12 notes. It's pretty learnable on a standard keyboard, because of the 48-note pattern and consistent 5ths. It beats slightly differently than 72EDO or 48 EDO because of the slight stretch, making the major 3rd and 5th nearly perfect. The formula was, again, to divide 5/4 into 23 equal parts and repeat those pitches at 400 and 800 cents for something close to 69EDO, and then to throw away some pitches, keeping 4 pitches to every approximate 100 cents, repeating pitches starting at 702.33 so that they were accurate 5ths above the starting pitches. Caleb !Beast Augmentation by Caleb 5/4 in 23 parts, repeated @ 400 and 800 48 !0., 50.389 67.185 83.981 ! 117.574 151.166 167.962 184.759 ! 201.555 235.147 268.74 285.536 ! 302.332 319.129 352.721 386.315 ! 400 416.796 433.592 450.389 ! 500.777 551.166 567.962 584.759 ! 601.555 618.351 635.147 651.944 ! 702.332 752.721 769.517 786.315 ! 816.796 850.389 867.185 883.981 ! 900.777 934.37 967.962 984.759 ! 1001.555 1018.351 1051.944 1085.536 ! 1102.332 1119.129 1135.925 1152.721 ! 1200 On Sep 9, 2010, at 9:27 AM, caleb morgan wrote: > > Sorry, same thing cleaned up for better Scala format: > > !Beast Augmentation by Caleb > 5/4 in 23 parts, culled, repeated @ 400 and 800 > 42 > !0. > 33.592 > 67.185 > 100.777 > 134.37 > 151.166 > 167.962 > 184.759 > 201.555 > 235.147 > 268.74 > 302.332 > 319.129 > 386.315 > ! > 400.000 > 433.592 > 467.185 > 500.777 > 534.37 > 551.166 > 567.962 > 584.759 > 601.555 > 635.147 > 668.74 > 702.332 > 719.129 > 786.315 > ! > 800.000 > 833.592 > 867.185 > 900.777 > 934.37 > 951.166 > 967.962 > 984.759 > 1001.555 > 1035.147 > 1068.74 > 1102.332 > 1119.129 > 1186.315 > ! > 1200.000 > > > > > On Sep 9, 2010, at 9:05 AM, caleb morgan wrote: > >> >> >> >> Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". >> >> 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. >> >> Then that pattern is repeated at 400 and 800 cents. >> >> It's close to 11-limit JI in some ways, but has more symmetry and regularity. >> >> !Beast Augmentation by Caleb >> 5/4 in 23 parts, culled, repeated @ 400 and 800 >> 42 >> !0., >> 33.592, >> 67.185, >> 100.777, >> 134.37, >> 151.166, >> 167.962, >> 184.759, >> 201.555, >> 235.147, >> 268.74, >> 302.332, >> 319.129, >> 386.315 >> ! >> 400 >> 433.592 >> 467.185 >> 500.777 >> 534.37 >> 551.166 >> 567.962 >> 584.759 >> 601.555 >> 635.147 >> 668.74 >> 702.332 >> 719.129 >> 786.315 >> ! >> 800 >> 833.592 >> 867.185 >> 900.777 >> 934.37 >> 951.166 >> 967.962 >> 984.759 >> 1001.555 >> 1035.147 >> 1068.74 >> 1102.332 >> 1119.129 >> 1186.315 >> ! >> 1200 >> >> >> >> >> >> >> >> >> >> >> On Sep 9, 2010, at 6:27 AM, caleb morgan wrote: >> >>> >>> Caleb plays "27Dwarf" : >>> >>> >>> Hmm: 5ths are all always 16 steps, but some are a long way from 3:2 702 cents. >>> >>> 4ths: 12 steps, except 16:9 to 32:27 approx is 11 steps, and the 4ths are charmingly different-sized-sounding. >>> >>> pattern of 12-12-11 steps on the 4ths? >>> >>> good 21/8 (7th par of 3) >>> >>> Those are my first impressions. >>> >>> caleb >>> >>> >>> >>> >>> >>> On Sep 9, 2010, at 5:36 AM, caleb morgan wrote: >>> >>>> >>>> >>>> Oh, there's interest! >>>> >>>> What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. >>>> >>>> Are there certain numbers of pitches per octave where consistency is impossible? >>>> >>>> (I'm sort of afraid that the answer will be over my head.) >>>> >>>> Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. >>>> >>>> Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. >>>> >>>> But "Dwarf27" looks really good. >>>> >>>> In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. >>>> >>>> It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. >>>> >>>> caleb >>>> >>>> >>>> >>>> On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: >>>> >>>>> >>>>> >>>>> >>>>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>>>> >>>>> > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? >>>>> >>>>> Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. >>>>> >>>>> ! dwarf27_7tempered.scl >>>>> ! >>>>> Irregularly tempered Dwarf(<27 43 63 76|) >>>>> 27 >>>>> ! >>>>> 8.50411 >>>>> 44.05819 >>>>> 94.02735 >>>>> 155.44995 >>>>> 204.62445 >>>>> 239.75461 >>>>> 275.21962 >>>>> 300.57603 >>>>> 386.44020 >>>>> 410.42948 >>>>> 471.11121 >>>>> 506.30767 >>>>> 541.94592 >>>>> 591.15701 >>>>> 616.87618 >>>>> 702.25982 >>>>> 737.66181 >>>>> 772.99566 >>>>> 797.33536 >>>>> 857.59196 >>>>> 907.39146 >>>>> 969.00623 >>>>> 977.50974 >>>>> 1003.78401 >>>>> 1088.74607 >>>>> 1113.63615 >>>>> 1200.00000 >>>>> >>>> >>>> >>> >>> >> >> > > >
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? P.S. to Gene, or any one else who is interested, I'd be very grateful for 48-pitch systems that are compromises between JI and EDO, as I have attempted in my previous post. Probably Gene could do it better, with some clever temperings and additions. caleb On Sep 9, 2010, at 9:27 AM, caleb morgan wrote: > > Sorry, same thing cleaned up for better Scala format: > > !Beast Augmentation by Caleb > 5/4 in 23 parts, culled, repeated @ 400 and 800 > 42 > !0. > 33.592 > 67.185 > 100.777 > 134.37 > 151.166 > 167.962 > 184.759 > 201.555 > 235.147 > 268.74 > 302.332 > 319.129 > 386.315 > ! > 400.000 > 433.592 > 467.185 > 500.777 > 534.37 > 551.166 > 567.962 > 584.759 > 601.555 > 635.147 > 668.74 > 702.332 > 719.129 > 786.315 > ! > 800.000 > 833.592 > 867.185 > 900.777 > 934.37 > 951.166 > 967.962 > 984.759 > 1001.555 > 1035.147 > 1068.74 > 1102.332 > 1119.129 > 1186.315 > ! > 1200.000 > > > > > On Sep 9, 2010, at 9:05 AM, caleb morgan wrote: > >> >> >> >> Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". >> >> 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. >> >> Then that pattern is repeated at 400 and 800 cents. >> >> It's close to 11-limit JI in some ways, but has more symmetry and regularity. >> >> !Beast Augmentation by Caleb >> 5/4 in 23 parts, culled, repeated @ 400 and 800 >> 42 >> !0., >> 33.592, >> 67.185, >> 100.777, >> 134.37, >> 151.166, >> 167.962, >> 184.759, >> 201.555, >> 235.147, >> 268.74, >> 302.332, >> 319.129, >> 386.315 >> ! >> 400 >> 433.592 >> 467.185 >> 500.777 >> 534.37 >> 551.166 >> 567.962 >> 584.759 >> 601.555 >> 635.147 >> 668.74 >> 702.332 >> 719.129 >> 786.315 >> ! >> 800 >> 833.592 >> 867.185 >> 900.777 >> 934.37 >> 951.166 >> 967.962 >> 984.759 >> 1001.555 >> 1035.147 >> 1068.74 >> 1102.332 >> 1119.129 >> 1186.315 >> ! >> 1200 >> >> >> >> >> >> >> >> >> >> >> On Sep 9, 2010, at 6:27 AM, caleb morgan wrote: >> >>> >>> Caleb plays "27Dwarf" : >>> >>> >>> Hmm: 5ths are all always 16 steps, but some are a long way from 3:2 702 cents. >>> >>> 4ths: 12 steps, except 16:9 to 32:27 approx is 11 steps, and the 4ths are charmingly different-sized-sounding. >>> >>> pattern of 12-12-11 steps on the 4ths? >>> >>> good 21/8 (7th par of 3) >>> >>> Those are my first impressions. >>> >>> caleb >>> >>> >>> >>> >>> >>> On Sep 9, 2010, at 5:36 AM, caleb morgan wrote: >>> >>>> >>>> >>>> Oh, there's interest! >>>> >>>> What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. >>>> >>>> Are there certain numbers of pitches per octave where consistency is impossible? >>>> >>>> (I'm sort of afraid that the answer will be over my head.) >>>> >>>> Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. >>>> >>>> Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. >>>> >>>> But "Dwarf27" looks really good. >>>> >>>> In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. >>>> >>>> It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. >>>> >>>> caleb >>>> >>>> >>>> >>>> On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: >>>> >>>>> >>>>> >>>>> >>>>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>>>> >>>>> > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? >>>>> >>>>> Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. >>>>> >>>>> ! dwarf27_7tempered.scl >>>>> ! >>>>> Irregularly tempered Dwarf(<27 43 63 76|) >>>>> 27 >>>>> ! >>>>> 8.50411 >>>>> 44.05819 >>>>> 94.02735 >>>>> 155.44995 >>>>> 204.62445 >>>>> 239.75461 >>>>> 275.21962 >>>>> 300.57603 >>>>> 386.44020 >>>>> 410.42948 >>>>> 471.11121 >>>>> 506.30767 >>>>> 541.94592 >>>>> 591.15701 >>>>> 616.87618 >>>>> 702.25982 >>>>> 737.66181 >>>>> 772.99566 >>>>> 797.33536 >>>>> 857.59196 >>>>> 907.39146 >>>>> 969.00623 >>>>> 977.50974 >>>>> 1003.78401 >>>>> 1088.74607 >>>>> 1113.63615 >>>>> 1200.00000 >>>>> >>>> >>>> >>> >>> >> >> > > >
From: anton_pann (2010-09-09) Subject: I need your help! Hi, I'm new in this group. My name is Constantin. I saw you are familiar with the musical acoustic domain and i want to ask you if is possible give me some information regarding the antique musical ratio. If you have some books or article about this subject please send them to me. Or if you can explain me about Pytagora, Archytas, Arystoxenes, Dydimos and other please help me. Thenks and greetings, Constantin.
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Well, there's always this--though it didn't take much ingenuity: The 48 Boring & Pierce !Roaring, Boring, and Piercing 48 Boring & Pierce 48 !0. 33. 50. 66. ! 100. 133. 150. 167. ! 200. 233. 250. 267. ! 300. 333. 350. 367. ! 400. 433. 450. 467. ! 500. 533. 550. 567. ! 600. 633. 650. 667. ! 700. 733. 750. 767. ! 800. 833. 850. 867. ! 900. 933. 950. 967. ! 1000. 1033. 1050. 1067. ! 1100. 1133. 1150. 1167. ! 1200. On Sep 9, 2010, at 12:08 PM, caleb morgan wrote: > P.S. to Gene, or any one else who is interested, I'd be very grateful for 48-pitch systems that are compromises between JI and EDO, as I have attempted in my previous post. > > > Probably Gene could do it better, with some clever temperings and additions. > > caleb > > > > > > On Sep 9, 2010, at 9:27 AM, caleb morgan wrote: > >> >> >> Sorry, same thing cleaned up for better Scala format: >> >> !Beast Augmentation by Caleb >> 5/4 in 23 parts, culled, repeated @ 400 and 800 >> 42 >> !0. >> 33.592 >> 67.185 >> 100.777 >> 134.37 >> 151.166 >> 167.962 >> 184.759 >> 201.555 >> 235.147 >> 268.74 >> 302.332 >> 319.129 >> 386.315 >> ! >> 400.000 >> 433.592 >> 467.185 >> 500.777 >> 534.37 >> 551.166 >> 567.962 >> 584.759 >> 601.555 >> 635.147 >> 668.74 >> 702.332 >> 719.129 >> 786.315 >> ! >> 800.000 >> 833.592 >> 867.185 >> 900.777 >> 934.37 >> 951.166 >> 967.962 >> 984.759 >> 1001.555 >> 1035.147 >> 1068.74 >> 1102.332 >> 1119.129 >> 1186.315 >> ! >> 1200.000 >> >> >> >> >> On Sep 9, 2010, at 9:05 AM, caleb morgan wrote: >> >>> >>> >>> >>> Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". >>> >>> 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. >>> >>> Then that pattern is repeated at 400 and 800 cents. >>> >>> It's close to 11-limit JI in some ways, but has more symmetry and regularity. >>> >>> !Beast Augmentation by Caleb >>> 5/4 in 23 parts, culled, repeated @ 400 and 800 >>> 42 >>> !0., >>> 33.592, >>> 67.185, >>> 100.777, >>> 134.37, >>> 151.166, >>> 167.962, >>> 184.759, >>> 201.555, >>> 235.147, >>> 268.74, >>> 302.332, >>> 319.129, >>> 386.315 >>> ! >>> 400 >>> 433.592 >>> 467.185 >>> 500.777 >>> 534.37 >>> 551.166 >>> 567.962 >>> 584.759 >>> 601.555 >>> 635.147 >>> 668.74 >>> 702.332 >>> 719.129 >>> 786.315 >>> ! >>> 800 >>> 833.592 >>> 867.185 >>> 900.777 >>> 934.37 >>> 951.166 >>> 967.962 >>> 984.759 >>> 1001.555 >>> 1035.147 >>> 1068.74 >>> 1102.332 >>> 1119.129 >>> 1186.315 >>> ! >>> 1200 >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> On Sep 9, 2010, at 6:27 AM, caleb morgan wrote: >>> >>>> >>>> Caleb plays "27Dwarf" : >>>> >>>> >>>> Hmm: 5ths are all always 16 steps, but some are a long way from 3:2 702 cents. >>>> >>>> 4ths: 12 steps, except 16:9 to 32:27 approx is 11 steps, and the 4ths are charmingly different-sized-sounding. >>>> >>>> pattern of 12-12-11 steps on the 4ths? >>>> >>>> good 21/8 (7th par of 3) >>>> >>>> Those are my first impressions. >>>> >>>> caleb >>>> >>>> >>>> >>>> >>>> >>>> On Sep 9, 2010, at 5:36 AM, caleb morgan wrote: >>>> >>>>> >>>>> >>>>> Oh, there's interest! >>>>> >>>>> What I'm hoping to achieve, I guess, is to understand some rules of thumb about when it's possible and how to do it myself. >>>>> >>>>> Are there certain numbers of pitches per octave where consistency is impossible? >>>>> >>>>> (I'm sort of afraid that the answer will be over my head.) >>>>> >>>>> Meanwhile, the list of scales with which I hope to write pieces has grown to nearly 50, with some clear favorites--GWS 46-notes epimorphic 13-limit, GWS newts, 46EDO, 41 EDO, any some of my own JI scales. >>>>> >>>>> Plus, just to find out some stuff by trial-and-error myself, I'm looking into equal divisions of intervals other than the octave. >>>>> >>>>> But "Dwarf27" looks really good. >>>>> >>>>> In terms of my overall project, I was sort of hoping to accumulate a bunch of really good tunings, then switch to concentrating on composing with each one. >>>>> >>>>> It's fun to make new scales, but I can't hope to approach the kind of mastery that I see here from you and a few others, so I do intend to change my focus back to composing at some point. >>>>> >>>>> caleb >>>>> >>>>> >>>>> >>>>> On Sep 8, 2010, at 11:23 PM, genewardsmith wrote: >>>>> >>>>>> >>>>>> >>>>>> >>>>>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>>>>> >>>>>> > I suppose that a completely consistent fingering (5ths all the same number of steps) is mathematically impossible with a 5th at 703.06613 with 27 steps? >>>>>> >>>>>> Below is something a little closer to what you want, with fifths mostly in interval class 16 but some, including one good one, in 15. I'll return to this question if there is interest. >>>>>> >>>>>> ! dwarf27_7tempered.scl >>>>>> ! >>>>>> Irregularly tempered Dwarf(<27 43 63 76|) >>>>>> 27 >>>>>> ! >>>>>> 8.50411 >>>>>> 44.05819 >>>>>> 94.02735 >>>>>> 155.44995 >>>>>> 204.62445 >>>>>> 239.75461 >>>>>> 275.21962 >>>>>> 300.57603 >>>>>> 386.44020 >>>>>> 410.42948 >>>>>> 471.11121 >>>>>> 506.30767 >>>>>> 541.94592 >>>>>> 591.15701 >>>>>> 616.87618 >>>>>> 702.25982 >>>>>> 737.66181 >>>>>> 772.99566 >>>>>> 797.33536 >>>>>> 857.59196 >>>>>> 907.39146 >>>>>> 969.00623 >>>>>> 977.50974 >>>>>> 1003.78401 >>>>>> 1088.74607 >>>>>> 1113.63615 >>>>>> 1200.00000 >>>>>> >>>>> >>>>> >>>> >>>> >>> >>> >> >> > > >
From: Mike Battaglia (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? On Thu, Sep 9, 2010 at 9:05 AM, caleb morgan <calebmrgn@...> wrote: > > Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". Hahahaha! > 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. > Then that pattern is repeated at 400 and 800 cents. > It's close to 11-limit JI in some ways, but has more symmetry and regularity. > !Beast Augmentation by Caleb > 5/4 in 23 parts, culled, repeated @ 400 and 800 > 42 > !0., > 33.592, > 67.185, > 100.777, > 134.37, > 151.166, > 167.962, > 184.759, > 201.555, > 235.147, > 268.74, > 302.332, > 319.129, > 386.315 > ! > 400 > 433.592 > 467.185 > 500.777 > 534.37 > 551.166 > 567.962 > 584.759 > 601.555 > 635.147 > 668.74 > 702.332 > 719.129 > 786.315 > ! > 800 > 833.592 > 867.185 > 900.777 > 934.37 > 951.166 > 967.962 > 984.759 > 1001.555 > 1035.147 > 1068.74 > 1102.332 > 1119.129 > 1186.315 > ! > 1200 Looks like perhaps you're ready to take the plunge into 72-tet? Probably the easiest temperament to think in ever. -Mike
From: caleb morgan (2010-09-09) Subject: Re: [tuning] Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? Well, what I lack in tuning acumen I make up in ridiculous titles. Here's one that works in 36 or 48-notes, a generator of 352.721, stretched octave (modulus) of 1203.468. (That is, 352.721 is multiplied by every N Mod 1203.468 up to 36 or 48.) But I actually don't like it as much as Beast Aug. caleb !48 tones of 352.721 352.721x48 48 0., 21.083 41.028 62.111 83.194 124.222 145.305 166.388 186.333 207.416 228.499 269.527 290.61 311.693 331.638 352.721 373.804 414.832 435.915 476.943 498.026 519.109 539.054 560.137 581.22 622.248 643.331 664.414 684.359 705.442 726.525 767.553 788.636 829.664 850.747 871.83 891.775 912.858 933.941 974.969 996.052 1017.135 1037.08 1058.163 1079.246 1120.274 1141.357 1182.385 1203.468 On Sep 9, 2010, at 3:35 PM, Mike Battaglia wrote: > On Thu, Sep 9, 2010 at 9:05 AM, caleb morgan <calebmrgn@...> wrote: > > > > Here's a new 42-note scale (14x3) by me, called "Beast Augmentation". > > Hahahaha! > > > 5/4 (386.3315 cents) is divided into 23 parts, certain pretty tones are selected. > > Then that pattern is repeated at 400 and 800 cents. > > It's close to 11-limit JI in some ways, but has more symmetry and regularity. > > !Beast Augmentation by Caleb > > 5/4 in 23 parts, culled, repeated @ 400 and 800 > > 42 > > !0., > > 33.592, > > 67.185, > > 100.777, > > 134.37, > > 151.166, > > 167.962, > > 184.759, > > 201.555, > > 235.147, > > 268.74, > > 302.332, > > 319.129, > > 386.315 > > ! > > 400 > > 433.592 > > 467.185 > > 500.777 > > 534.37 > > 551.166 > > 567.962 > > 584.759 > > 601.555 > > 635.147 > > 668.74 > > 702.332 > > 719.129 > > 786.315 > > ! > > 800 > > 833.592 > > 867.185 > > 900.777 > > 934.37 > > 951.166 > > 967.962 > > 984.759 > > 1001.555 > > 1035.147 > > 1068.74 > > 1102.332 > > 1119.129 > > 1186.315 > > ! > > 1200 > > Looks like perhaps you're ready to take the plunge into 72-tet? > Probably the easiest temperament to think in ever. > > -Mike >
From: genewardsmith (2010-09-09) Subject: Re: Compromise between 46EDO & Gene Ward Smith's 46 Epimorphic? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > Here's a 48-tone version of the same thing. > > This combines an attempt at epimorphism with 48-tone fingering with 11 and 13-limit JI with a concession to the standard keyboard pattern of 12 notes. > > It's pretty learnable on a standard keyboard, because of the 48-note pattern and consistent 5ths. This should be easily learnable, and has a lot of nice 11-limit harmony: ! compton48.scl ! Compton[48] 11-limit tweaked 48 ! 50.02948 66.62693 83.40254 100.00000 150.02948 166.62693 183.40254 200.00000 250.02948 266.62693 283.40254 300.00000 350.02948 366.62693 383.40254 400.00000 450.02948 466.62693 483.40254 500.00000 550.02948 566.62693 583.40254 600.00000 650.02948 666.62693 683.40254 700.00000 750.02948 766.62693 783.40254 800.00000 850.02948 866.62693 883.40254 900.00000 950.02948 966.62693 983.40254 1000.00000 1050.02948 1066.62693 1083.40254 1100.00000 1150.02948 1166.62693 1183.40254 1200.00000
From: robert (2010-09-09) Subject: Re: I need your help! The Musical System of Archytas; http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html Divisions of the Tetrachord by John H. Chalmers: http://tinyurl.com/355fkw Converting Ratios to Cents etc: http://www.sengpielaudio.com/calculator-centsratio.htm Musical Mathematics by Cris Forster: http://www.chrysalis-foundation.org/musical_mathematics.htm More Links on the Links Page at: http://groups.google.com/group/microtonal --- In tuning@yahoogroups.com, "anton_pann" <anton_pann@...> wrote: > > Hi, > I'm new in this group. My name is Constantin. > I saw you are familiar with the musical acoustic domain and i want to ask you if is possible give me some information regarding the antique musical ratio. If you have some books or article about this subject please send them to me. Or if you can explain me about Pytagora, Archytas, Arystoxenes, Dydimos and other please help me. > > Thenks and greetings, > > Constantin. >
From: caleb morgan (2010-09-10) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 I'm sorry for excessive posting if this has been the case. I'm in a scale-design phase, which I hope to wrap up shortly. It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. A standard keyboard is a given. So, bear with me if I change my specs slightly one more time. The "perfect" scale would be: Size: 43 notes Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. 5ths: wide but no wider than 704.35 5/4's: wide by no more than 6 cents or dead on 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents octave: within 4 cents, preferably wide, say 1204. Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. But some "keys" could um, suck, to put it bluntly. So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. I think this is do-able. I think it's important, even. *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! It may already exist. It might look like a slight tempering of Partch's scale. This is my current thinking. I'm quite serious. It would be great to find one scale that is better than all the rest for a standard keyboard, allowing some modulation, giving good 7 and 11-limit harmony, with chains of 4ths and 5ths around 7-10 notes long on either side. They don't have to be the same size, but they do have to finger the same, and be acceptable, not wolves or voles. It would be great to be able to settle down with one "best" scale. This is as close as I can get. This is the best I can do to be serious, accessible, educational, respectful, and blunt, yet speak in the closest equivalent to ordinary language, free of jargon. Caleb On Sep 9, 2010, at 4:14 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > > Here's a 48-tone version of the same thing. > > > > This combines an attempt at epimorphism with 48-tone fingering with 11 and 13-limit JI with a concession to the standard keyboard pattern of 12 notes. > > > > It's pretty learnable on a standard keyboard, because of the 48-note pattern and consistent 5ths. > > This should be easily learnable, and has a lot of nice 11-limit harmony: > > ! compton48.scl > ! > Compton[48] 11-limit tweaked > 48 > ! > 50.02948 > 66.62693 > 83.40254 > 100.00000 > 150.02948 > 166.62693 > 183.40254 > 200.00000 > 250.02948 > 266.62693 > 283.40254 > 300.00000 > 350.02948 > 366.62693 > 383.40254 > 400.00000 > 450.02948 > 466.62693 > 483.40254 > 500.00000 > 550.02948 > 566.62693 > 583.40254 > 600.00000 > 650.02948 > 666.62693 > 683.40254 > 700.00000 > 750.02948 > 766.62693 > 783.40254 > 800.00000 > 850.02948 > 866.62693 > 883.40254 > 900.00000 > 950.02948 > 966.62693 > 983.40254 > 1000.00000 > 1050.02948 > 1066.62693 > 1083.40254 > 1100.00000 > 1150.02948 > 1166.62693 > 1183.40254 > 1200.00000 > >
From: caleb morgan (2010-09-10) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 In (what I hope is) the end, the best I can do is the scale by Gene Ward Smith, minus the two notes nearest 1/1 on the bottom, and near 2/1 on the top. I'll just learn to love the inconsistent fingering, and if I need other tonal relationships, I'll "modulate" by pitch-bending the whole tuning down to some other level. We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time. Through the unknown, unremembered gate When the last of earth left to discover Is that which was the beginning; At the source of the longest river The voice of the hidden waterfall And the children in the apple-tree Not known, because not looked for But heard, half-heard, in the stillness Between two waves of the sea. Quick now, here, now, always— A condition of complete simplicity (Costing not less than everything) And all shall be well and All manner of thing shall be well When the tongues of flames are in-folded Into the crowned knot of fire And the fire and the rose are one. ! cal42.scl 42-n 4 Cal by G.W.Smith "required" 42 ! 80.6369 104.0612 126.6171 160.4026 184.7357 208.1710 231.9308 263.2192 288.7711 ! 311.2289 336.7808 368.0692 391.8290 415.2643 439.5974 473.3829 495.9388 519.3631 543.7424 577.0749 600.0000 ! ! 622.9251 656.2576 680.6369 704.0612 726.6171 760.4026 784.7357 808.1710 831.9308 863.2192 888.7711 911.2289 ! 936.7808 968.0692 991.8290 1015.2643 1039.5974 1073.3829 1095.9388 1119.3631 1200.0000 Just for yucks: We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time. Through the unknown, unremembered gate When the last of earth left to discover Is that which was the beginning; At the source of the longest river The voice of the hidden waterfall And the children in the apple-tree Not known, because not looked for But heard, half-heard, in the stillness Between two waves of the sea. Quick now, here, now, always— A condition of complete simplicity (Costing not less than everything) And all shall be well and All manner of thing shall be well When the tongues of flames are in-folded Into the crowned knot of fire And the fire and the rose are one. On Sep 10, 2010, at 9:12 AM, caleb morgan wrote: > > I'm sorry for excessive posting if this has been the case. > > I'm in a scale-design phase, which I hope to wrap up shortly. > > It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. > > I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. > > 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. > > A standard keyboard is a given. > > So, bear with me if I change my specs slightly one more time. > > The "perfect" scale would be: > > Size: 43 notes > > Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. > > 5ths: wide but no wider than 704.35 > > 5/4's: wide by no more than 6 cents or dead on > > 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents > > octave: within 4 cents, preferably wide, say 1204. > > Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. > > There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. > > There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. > > The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. > > So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. > > But some "keys" could um, suck, to put it bluntly. > > So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. > > I think this is do-able. I think it's important, even. > > *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! > > It may already exist. > > It might look like a slight tempering of Partch's scale. > > This is my current thinking. > > I'm quite serious. > > It would be great to find one scale that is better than all the rest for a standard keyboard, allowing some modulation, giving good 7 and 11-limit harmony, with chains of 4ths and 5ths around 7-10 notes long on either side. They don't have to be the same size, but they do have to finger the same, and be acceptable, not wolves or voles. > > It would be great to be able to settle down with one "best" scale. This is as close as I can get. > > This is the best I can do to be serious, accessible, educational, respectful, and blunt, yet speak in the closest equivalent to ordinary language, free of jargon. > > Caleb > > > > > > > > > > > > > On Sep 9, 2010, at 4:14 PM, genewardsmith wrote: > >> >> >> >> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >> > >> > Here's a 48-tone version of the same thing. >> > >> > This combines an attempt at epimorphism with 48-tone fingering with 11 and 13-limit JI with a concession to the standard keyboard pattern of 12 notes. >> > >> > It's pretty learnable on a standard keyboard, because of the 48-note pattern and consistent 5ths. >> >> This should be easily learnable, and has a lot of nice 11-limit harmony: >> >> ! compton48.scl >> ! >> Compton[48] 11-limit tweaked >> 48 >> ! >> 50.02948 >> 66.62693 >> 83.40254 >> 100.00000 >> 150.02948 >> 166.62693 >> 183.40254 >> 200.00000 >> 250.02948 >> 266.62693 >> 283.40254 >> 300.00000 >> 350.02948 >> 366.62693 >> 383.40254 >> 400.00000 >> 450.02948 >> 466.62693 >> 483.40254 >> 500.00000 >> 550.02948 >> 566.62693 >> 583.40254 >> 600.00000 >> 650.02948 >> 666.62693 >> 683.40254 >> 700.00000 >> 750.02948 >> 766.62693 >> 783.40254 >> 800.00000 >> 850.02948 >> 866.62693 >> 883.40254 >> 900.00000 >> 950.02948 >> 966.62693 >> 983.40254 >> 1000.00000 >> 1050.02948 >> 1066.62693 >> 1083.40254 >> 1100.00000 >> 1150.02948 >> 1166.62693 >> 1183.40254 >> 1200.00000 >> > > >
From: genewardsmith (2010-09-10) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > The "perfect" scale would be: > > Size: 43 notes That's not a particularly good staring point for scales with wide fifths, though stretching the octave could change that. You could just take 43 equal and stretch the octave to 1204 cents and see if you like that, I suppose. An alternative would be to take Meantone[43] and stretch it. Stick 81/80 and 126/125, or 81/80, 126/125 and 99/98 in Graham's magic box, and use those numbers. The octave stretch is less than a cent, which I personally think is a good thing. Putting in 126/125 and 176/175 leads to thrush temperament, which is considerably more accurate and does tend to wide major thirds, but not wide fifths or octaves. > octave: within 4 cents, preferably wide, say 1204. Four cents is a hell of a wide octave considering the tolerances you are talking about. I'm not sure what to do now, as I'm not really sure you want octaves so wide. I wasn't aware wide octaves was a consideration; I've been leaving them pure. > I think this is do-able. I think it's important, even. Why is it important? I don't see what is special about 43. > > ! compton48.scl > > ! > > Compton[48] 11-limit tweaked > > 48 What do you think of Compton[48]?
From: Andy (2010-09-10) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: Hi Caleb, consider http://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale > It would be great to find one scale that is better than all the > rest for a standard keyboard, How about http://groups.yahoo.com/group/tuning/photos/album/515941611/pic/1703995626/view?picmode=&mode=tn&order=ordinal&start=1&count=20&dir=asc http://www.synthtopia.com/content/2007/10/18/the-mysterious-terpstra-midi-keyboard/ or it's historically forerunner model the Bosanquet keyboard http://sites.google.com/site/commator/flukes " In the early 70's the 19 th century, this aggregate was tuned as a 53EDO system and each octave of its seven-row keyboard with many unison doubled tones counts in 84 keys. " > allowing some modulation, > giving good 7 and 11-limit harmony, > with chains of 4ths and 5ths around 7-10 notes long on either > side. Why not empolying all the 53 times 4ths and 5ths? alike in my recent rational 53-tone: http://launch.groups.yahoo.com/group/tuning/message/92003 > They don't have to be the same size, but they do have to finger the > same, and be acceptable, not wolves or voles. Fully agreed! !Sp53rat.scl Sparschuh's [2010] rational 53-tone with some epimoric biased 5ths 53 ! 65/64 ! A +01 D/ 33/32 ! B +02 D+ 26/25 ! C +03 EB 20/19 ! D +04 Eb 16/15 ! E +05 D# 13/12 ! F +06 D& 11/10 ! G +07 E+ 10/9 ! H +08 E\ 9/8 ! I +09 E. 8/7 ! J +10 E/ 52/45 ! K +11 E+ = F- 7/6 ! L +12 F\ 32/27 ! M +13 F. 6/5 ! N +14 F/ 11/9 ! O +15 F+ 16/13 ! P +16 GB 5/4 ! Q +17 Gb 81/64 ! R +18 F# 9/7 ! S +19 F& 57/44 ! T +20 G- 21/16 ! U +21 G\ 4/3 ! V +22 G. 23/17 ! W +23 G/ 11/8 ! X +24 G+ 18/13 ! Y +25 AB 7/5 ! Z +26 Ab 10/7 ! z' -26 G# 13/9 ! y' -25 G& 16/11 ! x' -24 A- 34/23 ! w' -23 A\ 3/2 ! v' -22 A. 32/21 ! u' -21 A/ 88/57 ! t' -20 A+ 14/9 ! s' -19 BB 128/81 ! r' -18 Bb 8/5 ! q' -17 A# 13/8 ! p' -16 A& 18/11 ! o' -15 B- 5/3 ! n' -14 B\ 27/16 ! m' -13 B. 12/7 ! l' -12 B/ 45/26 ! k' -11 B+ = C- 7/4 ! j' -10 C\ 16/9 ! i' -09 C. 9/5 ! h' -08 C/ 20/11 ! g' -07 C+ 24/13 ! f' -06 DB 15/8 ! e' -05 Db 19/10 ! d' -04 C# 25/13 ! c' -03 C& 64/33 ! b' -02 D- 128/65 ! a' -01 D\ 2/1 ! @' +-0 D. ! ! ![eof] that satisfies and even exceeds all yours mentioned criterions. bye Andy
From: caleb morgan (2010-09-10) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Hi Gene, I'll try what you've suggested. The only thing special about 43 (or 42) is that I can fit 2 octaves into a standard Midi controller with 7 octaves plus 3 keys = 87 keys. I've got two of them. Of course you're right that 43 doesn't work so well. So, either it's back to something consistent with 41, or something that fingers inconsistently, or something with less that 2 octaves, or buying some new keyboards. My latest, plan (see previous post) is to use one of your 46-note scales with 4 notes removed. Alas, I insist on something very much like what Andy is proposing, but I want to throw out a few notes, or have my keyboard grow another octave. Caught between horn and hardart. Hey Andy, this looks good, but I didn't make it clear that I really want to fit two octaves--this has only become obvious to me recently. !Sp53rat.scl Sparschuh's [2010] rational 53-tone with some epimoric biased 5ths 53 ! 65/64 ! A +01 D/ 33/32 ! B +02 D+ 26/25 ! C +03 EB 20/19 ! D +04 Eb 16/15 ! E +05 D# 13/12 ! F +06 D& 11/10 ! G +07 E+ 10/9 ! H +08 E\ 9/8 ! I +09 E. 8/7 ! J +10 E/ 52/45 ! K +11 E+ = F- 7/6 ! L +12 F\ 32/27 ! M +13 F. 6/5 ! N +14 F/ 11/9 ! O +15 F+ 16/13 ! P +16 GB 5/4 ! Q +17 Gb 81/64 ! R +18 F# 9/7 ! S +19 F& 57/44 ! T +20 G- 21/16 ! U +21 G\ 4/3 ! V +22 G. 23/17 ! W +23 G/ 11/8 ! X +24 G+ 18/13 ! Y +25 AB 7/5 ! Z +26 Ab 10/7 ! z' -26 G# 13/9 ! y' -25 G& 16/11 ! x' -24 A- 34/23 ! w' -23 A\ 3/2 ! v' -22 A. 32/21 ! u' -21 A/ 88/57 ! t' -20 A+ 14/9 ! s' -19 BB 128/81 ! r' -18 Bb 8/5 ! q' -17 A# 13/8 ! p' -16 A& 18/11 ! o' -15 B- 5/3 ! n' -14 B\ 27/16 ! m' -13 B. 12/7 ! l' -12 B/ 45/26 ! k' -11 B+ = C- 7/4 ! j' -10 C\ 16/9 ! i' -09 C. 9/5 ! h' -08 C/ 20/11 ! g' -07 C+ 24/13 ! f' -06 DB 15/8 ! e' -05 Db 19/10 ! d' -04 C# 25/13 ! c' -03 C& 64/33 ! b' -02 D- 128/65 ! a' -01 D\ 2/1 ! @' +-0 D. ! ! ![eof] On Sep 10, 2010, at 2:19 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > The "perfect" scale would be: > > > > Size: 43 notes > > That's not a particularly good staring point for scales with wide fifths, though stretching the octave could change that. You could just take 43 equal and stretch the octave to 1204 cents and see if you like that, I suppose. An alternative would be to take Meantone[43] and stretch it. Stick 81/80 and 126/125, or 81/80, 126/125 and 99/98 in Graham's magic box, and use those numbers. The octave stretch is less than a cent, which I personally think is a good thing. Putting in 126/125 and 176/175 leads to thrush temperament, which is considerably more accurate and does tend to wide major thirds, but not wide fifths or octaves. > > > octave: within 4 cents, preferably wide, say 1204. > > Four cents is a hell of a wide octave considering the tolerances you are talking about. I'm not sure what to do now, as I'm not really sure you want octaves so wide. I wasn't aware wide octaves was a consideration; I've been leaving them pure. > > > I think this is do-able. I think it's important, even. > > Why is it important? I don't see what is special about 43. > > > > ! compton48.scl > > > ! > > > Compton[48] 11-limit tweaked > > > 48 > > What do you think of Compton[48]? > >
From: Carl Lumma (2010-09-10) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > Hi Gene, I'll try what you've suggested. > > The only thing special about 43 (or 42) is that I can fit > 2 octaves into a standard Midi controller with 7 octaves > plus 3 keys = 87 keys. I've got two of them. Have you tried 41-ET? You'll get two octaves plus a few spare notes, and completely consistent fingering. -Carl
From: genewardsmith (2010-09-10) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote: > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@> wrote: > > > > Hi Gene, I'll try what you've suggested. > > > > The only thing special about 43 (or 42) is that I can fit > > 2 octaves into a standard Midi controller with 7 octaves > > plus 3 keys = 87 keys. I've got two of them. > > Have you tried 41-ET? You'll get two octaves plus a few > spare notes, and completely consistent fingering. Studloco (Miracle[41]) is another interesting possibility; a slightly sharp octave would make sense.
From: genewardsmith (2010-09-10) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote: > > Have you tried 41-ET? You'll get two octaves plus a few > > spare notes, and completely consistent fingering. > > Studloco (Miracle[41]) is another interesting possibility; a slightly sharp octave would make sense. > It occurs to me that 87 is exactly divisible by 3, so that a 29 note scale would lead to three octaves exactly. 29 would tend towards slight sharpness of the fifth. Leapday[29], Garibaldi[29] and Grackle[29] are MOS with 29 notes.
From: Carl Lumma (2010-09-10) Subject: Re: Compromise between 43EDO & Partch's 43 Gene wrote: > > Have you tried 41-ET? You'll get two octaves plus a few > > spare notes, and completely consistent fingering. > > Studloco (Miracle[41]) is another interesting possibility; > a slightly sharp octave would make sense. Sure. Though I generally feel rank 2 shines, in musical applications involving instruments like keyboards, at low complexity. At high complexity like 41, ET accuracy is getting good enough. -Carl
From: caleb morgan (2010-09-10) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Ok, once again I apologize for changing my mind. If any reader is grumpy, just ignore this message, I'm obsessed and tired. What are some variations on 43EDO that play with the octave size a little and have any reasonable-size 5ths, large or small? I'm obsessed with getting 8:7 and 7:6 in tune, for some reason. caleb Oh, on another note, since 43 is a prime, any number mod 43 multiplied repeatedly by any N will give you all 43 numbers. So, any member of something approximating 43EDO *could* be a generator. for example, 12 steps in mod43 generates all 43 steps eventually. k = 1 2 3 4 5 6 7 8 9 10 12*k= 12 24 36 5 17 29 41 10 22 34 And, I notice that changing the octave size (basically, the modulus, in a way) has a HUGE impact on the results. Now, I find that I'm quite *unfussy* about the octave. So, it doesn't need to be that accurate. Plus, I don't mind quite uneven step-sizes. It doesn't really have to be an EDO. That's the wiggle room, if I could only grok it. Some slightly off-EDO generator and some slightly off-1200 foldover might give me a good result. Somehow, there's a generator/modulus combination that will give me 43 good notes. This is a weird way to approach the problem, but it kind of makes sense for me. I still don't understand how to use Graham's scripts, partly because I don't have Scala yet to plug the numbers into, and partly because I'm missing some theory about what the names mean and the results should be. I suspect the understanding gap would be solved by getting Scala, much as LMSO has changed my thinking already. 2 3 5 7 [< 43 68 100 121 ]> Tuning Map (cents) <1199.495, 1896.875, 2789.522, 3375.322] Is this telling me that my 5ths will be a little flat, along with the octave? Why not have less accurate octaves and 5ths, and more accurate 7ths, somehow, and less even steps...?? Sorry for weird format. caleb On Sep 10, 2010, at 4:37 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote: > > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@> wrote: > > > > > > Hi Gene, I'll try what you've suggested. > > > > > > The only thing special about 43 (or 42) is that I can fit > > > 2 octaves into a standard Midi controller with 7 octaves > > > plus 3 keys = 87 keys. I've got two of them. > > > > Have you tried 41-ET? You'll get two octaves plus a few > > spare notes, and completely consistent fingering. > > Studloco (Miracle[41]) is another interesting possibility; a slightly sharp octave would make sense. > >
From: Mike Battaglia (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 On Fri, Sep 10, 2010 at 7:57 PM, caleb morgan <calebmrgn@...> wrote: > > Ok, once again I apologize for changing my mind. > > If any reader is grumpy, just ignore this message, I'm obsessed and tired. And how grumpy I am. I demand you stop talking about this tuning, so that I can maintain the sanctity of My Inbox without having to learn how to use the "filter" function that comes standard on every modern email client. Feel bad? You should feel bad. >:( > What are some variations on 43EDO that play with the octave size a little and have any reasonable-size 5ths, large or small? > > I'm obsessed with getting 8:7 and 7:6 in tune, for some reason. > caleb What are your thoughts on Miracle[41], as Gene suggested? Or 41-equal, as Carl suggested? Perhaps you could then create a circulating temperament that's midway between those if you like the sound. And then there's always 31-equal for almost perfect septimal harmonies as well, with mostly passable 11-limit harmonies and not quite as good 13-limit harmonies. The fifth is a little bit flat as you no doubt know. Perhaps some circulating 31-note temperament might be good to think about as well. Just out of curiosity, and I just went back through the email chain and couldn't find an answer - what don't you like about 46-tet? Your discussion about it kickstarted some playing around with it on my end too... seems like not a bad tuning. -Mike
From: caleb morgan (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 (My favorite tunings--including many by the people who post here--O. Yarman, GWS, G. Secor, etc. can be found here: http://www.box.net/shared/m37jhti1og#/shared/m37jhti1og/1/50561828 Feel free to download or use any. Some are mine. Some are from the list. Some are from the Scala archives.) No, I love 46EDO. But it has 3 too many notes to fit 2 octaves onto my Midi controller. So, I could remove a few notes, but that would create the inconsistent-fingering problem. For some reason, I'm fixated on using nearly my whole keyboard. So, 41 would be a good choice. I've got a lot of 41-tunings. I was just hoping somehow that if I searched long enough, that I could do better somehow. It's not even clear to me right now if this is just compulsion or if I'm after something rational and real. I don't understand what Miracle 41 is. I'd love to know how to generate it, or at least get a Scala file. I'm not clear at all on the Miracle concept. I'd like to know how to use LMSO (or any glorified calculator), or the steps to using these scripts, such as the one below. Say, for instance, this one: 8 & 19 & 43 Equal Temperament Mappings 2 3 5 7 11 13 [< 43 68 100 121 149 159 ] < 19 30 44 53 65 70 ] < 8 13 19 23 28 30 ]> Reduced Mapping 2 3 5 7 11 13 [< 1 0 0 -1 -1 1 ] < 0 1 1 1 0 1 ] < 0 0 2 6 12 3 ]> Generator Tunings (cents) [1200.462, 1899.336, 445.662> Step Tunings (cents) [19.833, 16.261, 4.836> Tuning Map (cents) <1200.462, 1899.336, 2790.660, 3372.844, 4147.478, 4436.784] Maybe I'm looking for a compromise between JI and 41 EDO or JI and 46 EDO, The thing I don't like about 43 EDO is the 8:7 and 7:6 isn't very close. Caleb On Sep 10, 2010, at 8:31 PM, Mike Battaglia wrote: > On Fri, Sep 10, 2010 at 7:57 PM, caleb morgan <calebmrgn@yahoo.com> wrote: > > > > Ok, once again I apologize for changing my mind. > > > > If any reader is grumpy, just ignore this message, I'm obsessed and tired. > > And how grumpy I am. I demand you stop talking about this tuning, so > that I can maintain the sanctity of My Inbox without having to learn > how to use the "filter" function that comes standard on every modern > email client. > > Feel bad? You should feel bad. >:( > > > What are some variations on 43EDO that play with the octave size a little and have any reasonable-size 5ths, large or small? > > > > I'm obsessed with getting 8:7 and 7:6 in tune, for some reason. > > caleb > > What are your thoughts on Miracle[41], as Gene suggested? Or 41-equal, > as Carl suggested? Perhaps you could then create a circulating > temperament that's midway between those if you like the sound. > > And then there's always 31-equal for almost perfect septimal harmonies > as well, with mostly passable 11-limit harmonies and not quite as good > 13-limit harmonies. The fifth is a little bit flat as you no doubt > know. Perhaps some circulating 31-note temperament might be good to > think about as well. > > Just out of curiosity, and I just went back through the email chain > and couldn't find an answer - what don't you like about 46-tet? Your > discussion about it kickstarted some playing around with it on my end > too... seems like not a bad tuning. > > -Mike >
From: Mike Battaglia (2010-09-11)
Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43
On Fri, Sep 10, 2010 at 8:47 PM, caleb morgan <calebmrgn@...> wrote:
>
> I don't understand what Miracle 41 is. I'd love to know how to generate it, or at least get a Scala file.
> I'm not clear at all on the Miracle concept.
> I'd like to know how to use LMSO (or any glorified calculator), or the steps to using these scripts, such as the one below.
> Say, for instance, this one:
Miracle is something I just started delving into recently, so you
might find the thread happening simultaneously about that to be
helpful. I am again explaining this both to make sure I have it right
and to try and recommunicate what I have learned.
Miracle is generated by an interval called the "secor." The secor is
defined as 1/6 of a perfect fifth - that is, it splits the fifth into
6 parts. 12-tet (or any chromatic scale of any meantone), on the other
hand, splits the fifth into 7 parts, which is a more familiar way of
thinking about the fifth being split up. This diverges with that
tradition.
As the secor makes its way through the fifth and beyond, it hits a
bunch of interesting intervals. The first is the secor itself, which
is right between 16/15 and 15/14 (and functions as both, hence
225/224, which is the difference between them, is tempered out). Two
secors makes a wide second, which turns out to be an almost perfect
8/7. Three is a neutral third, which turns out to be an almost perfect
11/9. Four is a wide fourth, which turns out to be an almost perfect
21/16. Five pretty much nails 7/5, and 6 gives you an almost perfect
3/2. Seven gives you 8/5, eight gives you 12/7, and 9 gives you 11/6.
Some common miracle tunings are 31 (which has its problems) and 41
(which also has its problems). Combine them and you get 72, which is
also a miracle, because of top secret witchcraft pagan voodoo. 72 is
more accurate than 31 or 41 for 11-limit harmony. The secor for
miracle in 72-tet is 7 steps of 72, which you can think of as one
12-tet half step with one little 72-tet step added (1/6 of a semitone)
added on top of it.
(Seriously, if you haven't played around with 72, you need to get
started. Get scala installed and fire away. I didn't understand
11-limit harmony at all until I started messing with it. A 12-tet
major third, minus 1 little 72-tet "step," is a "just" 5/4. A 12-tet
minor 7th, minus 2 little 72-tet "steps," is a "just" 7/4. A 12-tet
minor 7th plus one little 72-tet step is a "just" 9/5. A 12-tet
tritone minus 3 little 72-tet steps is a "just" 11/8. It's really,
really easy.)
Anyways, so the secor is 7/72. This generates a 10 note MOS with 1
large step at the end and 9 smaller steps leading into it, so
sssssssssL. Until recently, I didn't understand what the hell the
point of this scale was, since there's not a 4:5:6:7 tetrad in it. Go
to the next MOS, though (21 notes), and the picture becomes much more
clear:
! blackjack.scl
!
21 note MOS of "MIRACLE" temperament, Erlich & Keenan, miracle1.scl,TL 2-5-2001
21
! G
83.33333 ! G#v
116.66667 ! Ab^
200.00000 ! A
233.33333 ! A>
316.66667 ! Bb^
350.00000 ! B[
383.33333 ! Bv
466.66667 ! C<
500.00000 ! C
583.33333 ! C#v
616.66667 ! Db^
700.00000 ! D
733.33333 ! D>
816.66667 ! Eb^
850.00000 ! E[
933.33333 ! E>
966.66667 ! F<
1050.00000 ! F]
1083.33333 ! F#v
1166.66667 ! G<
2/1 ! G
This is the famous "blackjack" miracle scale, so named because it has
21 notes, and blackjack is if you have 21, and you get it. Anyway,
load this up in Scala (get Scala installed) and go to the Chromatic
Clavier and set the notation system to B72, which is Graham's decimal
system. You will quickly see what the point of this scale is, which is
that all of the intervals lying adjacent to this 10-note decimal set
are extremely useful. One "diatonic" step to the right of the neutral
third is now 5/4, one diatonic step left is 6/5, and all sorts of
useful intervals are all over the place. Near the narrow fourth is
4/3, and near the wide second is 9/8, and so on.
The next mos is 31 notes ("canasta"), which gives even more intervals,
and then you have 41 notes ("stud loco"). It should also ring a bell
that 31-tet and 41-tet both support miracle temperament. Either way,
Gene is suggesting you mess around with stud loco, and perhaps if it's
a bit too "rough" for you, you can average it with 41-equal and come
up with some circulating temperament or something like that.
Here's the stud loco one:
! miracle3.scl
!
41 out of 72-tET Pythagorean scale "Miracle/Studloco", Erlich/Keenan 2001
41
!
33.33330
66.66660
83.33337
116.66667
149.99997
183.33327
200.00004
233.33334
266.66664
299.99994
316.66671
350.00001
383.33331
416.66661
433.33338
466.66668
499.99998
533.33328
550.00005
583.33335
616.66665
649.99995
666.66672
700.00002
733.33332
766.66662
783.33339
816.66669
849.99999
883.33329
900.00006
933.33336
966.66666
999.99996
1016.66673
1050.00003
1083.33333
1116.66663
1133.33340
1166.66670
2/1
See how you like it. One caveat: there is apparently a better
generator for 13-limit stuff that's like a few fractions of a cent
away. I don't remember what it is. Hopefully someone here will
remember. I remember there was more than one comma that could be
tempered out to get to the 13-limit, and just did a search, and
couldn't find it. But this should get you started.
-Mike
From: Mike Battaglia (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 I wrote: > Four is a wide fourth, which turns out to be an almost perfect > 21/16. Whoops, sorry, that should be "narrow fourth." -Mike
From: Mike Battaglia (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 One more tuning I just found, and that's meanpop[31]: ! meanpop_31.scl ! 31 note MOS of "meanpop" temperament 45.50500 73.54600 119.05100 147.09200 192.59700 238.10200 266.14300 311.64800 357.15300 385.19400 430.69900 458.74000 504.24500 549.75000 577.79100 623.29600 651.33700 696.84200 742.34700 770.38800 815.89300 843.93400 889.43900 934.94400 962.98500 1008.49000 1053.99500 1082.03600 1127.54100 1155.58200 1201.08700 5, 11, and 13 are really good, but 3 and 7 are flat. Perhaps this would be a good start for a well-temperament though. -Mike On Fri, Sep 10, 2010 at 9:36 PM, Mike Battaglia <battaglia01@...> wrote: > I wrote: >> Four is a wide fourth, which turns out to be an almost perfect >> 21/16. > > Whoops, sorry, that should be "narrow fourth." > > -Mike >
From: Herman Miller (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 caleb morgan wrote: > I'm sorry for excessive posting if this has been the case. > > I'm in a scale-design phase, which I hope to wrap up shortly. > > It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. > > I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. > > 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. > > A standard keyboard is a given. > > So, bear with me if I change my specs slightly one more time. > > The "perfect" scale would be: > > Size: 43 notes > > Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. > > 5ths: wide but no wider than 704.35 > > 5/4's: wide by no more than 6 cents or dead on > > 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents > > octave: within 4 cents, preferably wide, say 1204. > > Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. > > There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. > > There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. > > The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. > > So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. > > But some "keys" could um, suck, to put it bluntly. > > So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. > > I think this is do-able. I think it's important, even. > > *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! > > It may already exist. > > It might look like a slight tempering of Partch's scale. > > This is my current thinking. > Here's one that looks interesting. 3/2 is 701.96 cents. 5/4 is 4.78 cents sharp. 8/7, 7/6, 12/7, and 7/4 are all less than half a cent off. The scale is strictly proper, distributional even, and Constant Structure. Generators: 2/1, 391.095 ! C:\music\scales\43-46.scl ! 43 notes of 43&46 regular temperament 43 ! 26.71500 53.43000 80.14500 106.86000 133.57500 160.29000 187.00500 230.80500 257.52000 284.23500 310.95000 337.66500 364.38000 391.09500 417.81000 444.52500 471.24000 497.95500 524.67000 551.38500 578.10000 621.90000 648.61500 675.33000 702.04500 728.76000 755.47500 782.19000 808.90500 835.62000 862.33500 889.05000 915.76500 942.48000 969.19500 1012.99500 1039.71000 1066.42500 1093.14000 1119.85500 1146.57000 1173.28500 2/1
From: Mike Battaglia (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 On Fri, Sep 10, 2010 at 10:54 PM, Herman Miller <hmiller@...> wrote: > Here's one that looks interesting. > > 3/2 is 701.96 cents. > 5/4 is 4.78 cents sharp. > 8/7, 7/6, 12/7, and 7/4 are all less than half a cent off. > The scale is strictly proper, distributional even, and Constant Structure. Now that's not bad. The only problem I see is that there's only two 6:7:9 triads in the whole set, which makes this bad for 9-limit stuff. Perhaps some kind of near-MOS variant of this would be desirable. -Mike
From: jonszanto (2010-09-11) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > It might look like a slight tempering of Partch's scale. > > This is my current thinking. > > I'm quite serious. Compromise is for pussies. In your heart, you know it's true.
From: Daniel Forró (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 On 11 Sep 2010, at 10:34 AM, Mike Battaglia wrote: > > > Some common miracle tunings are 31 (which has its problems) and 41 > (which also has its problems). Combine them and you get 72, .... 31 and 41 have different size of steps, and by ? combining ? them (how?) for sure you can't get 72 steps which have even smaller size. Or do you know some miracle how to do it? So what do you mean by "combining" here? Just adding those two numbers wihout any relation to tuning, step sizes or so? Daniel Forro
From: Mike Battaglia (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 On Sat, Sep 11, 2010 at 2:28 AM, Daniel Forró <dan.for@...> wrote: > > On 11 Sep 2010, at 10:34 AM, Mike Battaglia wrote: > > Some common miracle tunings are 31 (which has its problems) and 41 > (which also has its problems). Combine them and you get 72, .... > > 31 and 41 have different size of steps, and by ? combining ? them (how?) for sure you can't get 72 steps which have even smaller size. Or do you know some miracle how to do it? > So what do you mean by "combining" here? Just adding those two numbers wihout any relation to tuning, step sizes or so? > Daniel Forro Yes, sorry, should have been more clear. I mean that 31-tet is a miracle temperament, and 41-tet is a miracle temperament, and if you add 31 and 41 you get the number 72, and 72-tet is also a miracle temperament. This is for the same reason that 7-tet is a meantone (sort of), and 12-tet is a meantone, and 12+7=19 which is a meantone, and 19+12=31 which is also a meantone, and 31+12=43 which is a meantone, and 31+19=50 which is a meantone, and so on. -Mike
From: Daniel Forró (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Thanks for explanation, now it's clear :-) Daniel Forro On 11 Sep 2010, at 3:32 PM, Mike Battaglia wrote: > On Sat, Sep 11, 2010 at 2:28 AM, Daniel Forró <dan.for@...> > wrote: >> >> On 11 Sep 2010, at 10:34 AM, Mike Battaglia wrote: >> >> Some common miracle tunings are 31 (which has its problems) and 41 >> (which also has its problems). Combine them and you get 72, .... >> >> 31 and 41 have different size of steps, and by ? combining ? them >> (how?) for sure you can't get 72 steps which have even smaller >> size. Or do you know some miracle how to do it? >> So what do you mean by "combining" here? Just adding those two >> numbers wihout any relation to tuning, step sizes or so? >> Daniel Forro > > Yes, sorry, should have been more clear. I mean that 31-tet is a > miracle temperament, and 41-tet is a miracle temperament, and if you > add 31 and 41 you get the number 72, and 72-tet is also a miracle > temperament. This is for the same reason that 7-tet is a meantone > (sort of), and 12-tet is a meantone, and 12+7=19 which is a meantone, > and 19+12=31 which is also a meantone, and 31+12=43 which is a > meantone, and 31+19=50 which is a meantone, and so on. > > -Mike
From: genewardsmith (2010-09-11) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote: > > > On 11 Sep 2010, at 10:34 AM, Mike Battaglia wrote: > > > > > > Some common miracle tunings are 31 (which has its problems) and 41 > > (which also has its problems). Combine them and you get 72, .... > > 31 and 41 have different size of steps, and by ? combining ? them > (how?) for sure you can't get 72 steps which have even smaller size. > Or do you know some miracle how to do it? > > So what do you mean by "combining" here? Just adding those two > numbers wihout any relation to tuning, step sizes or so? You can combine them through the miracle of the mediant; the 3/31 generator of 31et and the 4/41 generator of 41et "combine" as the (3+4)/(31+41) = 7/72 generator of 72et.
From: Daniel Forró (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 That's even more interesting numerology, I should start to study all this. Daniel Forro On 11 Sep 2010, at 4:07 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote: >> >> >> On 11 Sep 2010, at 10:34 AM, Mike Battaglia wrote: >>> >>> >>> Some common miracle tunings are 31 (which has its problems) and 41 >>> (which also has its problems). Combine them and you get 72, .... >> >> 31 and 41 have different size of steps, and by ? combining ? them >> (how?) for sure you can't get 72 steps which have even smaller size. >> Or do you know some miracle how to do it? >> >> So what do you mean by "combining" here? Just adding those two >> numbers wihout any relation to tuning, step sizes or so? > > You can combine them through the miracle of the mediant; the 3/31 > generator of 31et and the 4/41 generator of 41et "combine" as the (3 > +4)/(31+41) = 7/72 generator of 72et.
From: caleb morgan (2010-09-11)
Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43
Outstanding Mike!
I think this should be included with the explanations on the Wiki and on the Xenharmony pages.
Really, really I do.
It makes sense to me in a way that more terse explanations don't.
It's going in my 'microtonal wisdom' file--which is just a file of copies of posts I found particularly helpful.
Thanks, I'll even play around with these scales. Some look like 36 EDO at first, but then I see some 76EDO in there.
Caleb
On Sep 10, 2010, at 9:34 PM, Mike Battaglia wrote:
> On Fri, Sep 10, 2010 at 8:47 PM, caleb morgan <calebmrgn@...> wrote:
> >
> > I don't understand what Miracle 41 is. I'd love to know how to generate it, or at least get a Scala file.
> > I'm not clear at all on the Miracle concept.
> > I'd like to know how to use LMSO (or any glorified calculator), or the steps to using these scripts, such as the one below.
> > Say, for instance, this one:
>
> Miracle is something I just started delving into recently, so you
> might find the thread happening simultaneously about that to be
> helpful. I am again explaining this both to make sure I have it right
> and to try and recommunicate what I have learned.
>
> Miracle is generated by an interval called the "secor." The secor is
> defined as 1/6 of a perfect fifth - that is, it splits the fifth into
> 6 parts. 12-tet (or any chromatic scale of any meantone), on the other
> hand, splits the fifth into 7 parts, which is a more familiar way of
> thinking about the fifth being split up. This diverges with that
> tradition.
>
> As the secor makes its way through the fifth and beyond, it hits a
> bunch of interesting intervals. The first is the secor itself, which
> is right between 16/15 and 15/14 (and functions as both, hence
> 225/224, which is the difference between them, is tempered out). Two
> secors makes a wide second, which turns out to be an almost perfect
> 8/7. Three is a neutral third, which turns out to be an almost perfect
> 11/9. Four is a wide fourth, which turns out to be an almost perfect
> 21/16. Five pretty much nails 7/5, and 6 gives you an almost perfect
> 3/2. Seven gives you 8/5, eight gives you 12/7, and 9 gives you 11/6.
>
> Some common miracle tunings are 31 (which has its problems) and 41
> (which also has its problems). Combine them and you get 72, which is
> also a miracle, because of top secret witchcraft pagan voodoo. 72 is
> more accurate than 31 or 41 for 11-limit harmony. The secor for
> miracle in 72-tet is 7 steps of 72, which you can think of as one
> 12-tet half step with one little 72-tet step added (1/6 of a semitone)
> added on top of it.
>
> (Seriously, if you haven't played around with 72, you need to get
> started. Get scala installed and fire away. I didn't understand
> 11-limit harmony at all until I started messing with it. A 12-tet
> major third, minus 1 little 72-tet "step," is a "just" 5/4. A 12-tet
> minor 7th, minus 2 little 72-tet "steps," is a "just" 7/4. A 12-tet
> minor 7th plus one little 72-tet step is a "just" 9/5. A 12-tet
> tritone minus 3 little 72-tet steps is a "just" 11/8. It's really,
> really easy.)
>
> Anyways, so the secor is 7/72. This generates a 10 note MOS with 1
> large step at the end and 9 smaller steps leading into it, so
> sssssssssL. Until recently, I didn't understand what the hell the
> point of this scale was, since there's not a 4:5:6:7 tetrad in it. Go
> to the next MOS, though (21 notes), and the picture becomes much more
> clear:
>
> ! blackjack.scl
> !
> 21 note MOS of "MIRACLE" temperament, Erlich & Keenan, miracle1.scl,TL 2-5-2001
> 21
> ! G
> 83.33333 ! G#v
> 116.66667 ! Ab^
> 200.00000 ! A
> 233.33333 ! A>
> 316.66667 ! Bb^
> 350.00000 ! B[
> 383.33333 ! Bv
> 466.66667 ! C<
> 500.00000 ! C
> 583.33333 ! C#v
> 616.66667 ! Db^
> 700.00000 ! D
> 733.33333 ! D>
> 816.66667 ! Eb^
> 850.00000 ! E[
> 933.33333 ! E>
> 966.66667 ! F<
> 1050.00000 ! F]
> 1083.33333 ! F#v
> 1166.66667 ! G<
> 2/1 ! G
>
> This is the famous "blackjack" miracle scale, so named because it has
> 21 notes, and blackjack is if you have 21, and you get it. Anyway,
> load this up in Scala (get Scala installed) and go to the Chromatic
> Clavier and set the notation system to B72, which is Graham's decimal
> system. You will quickly see what the point of this scale is, which is
> that all of the intervals lying adjacent to this 10-note decimal set
> are extremely useful. One "diatonic" step to the right of the neutral
> third is now 5/4, one diatonic step left is 6/5, and all sorts of
> useful intervals are all over the place. Near the narrow fourth is
> 4/3, and near the wide second is 9/8, and so on.
>
> The next mos is 31 notes ("canasta"), which gives even more intervals,
> and then you have 41 notes ("stud loco"). It should also ring a bell
> that 31-tet and 41-tet both support miracle temperament. Either way,
> Gene is suggesting you mess around with stud loco, and perhaps if it's
> a bit too "rough" for you, you can average it with 41-equal and come
> up with some circulating temperament or something like that.
>
> Here's the stud loco one:
>
> ! miracle3.scl
> !
> 41 out of 72-tET Pythagorean scale "Miracle/Studloco", Erlich/Keenan 2001
> 41
> !
> 33.33330
> 66.66660
> 83.33337
> 116.66667
> 149.99997
> 183.33327
> 200.00004
> 233.33334
> 266.66664
> 299.99994
> 316.66671
> 350.00001
> 383.33331
> 416.66661
> 433.33338
> 466.66668
> 499.99998
> 533.33328
> 550.00005
> 583.33335
> 616.66665
> 649.99995
> 666.66672
> 700.00002
> 733.33332
> 766.66662
> 783.33339
> 816.66669
> 849.99999
> 883.33329
> 900.00006
> 933.33336
> 966.66666
> 999.99996
> 1016.66673
> 1050.00003
> 1083.33333
> 1116.66663
> 1133.33340
> 1166.66670
> 2/1
>
> See how you like it. One caveat: there is apparently a better
> generator for 13-limit stuff that's like a few fractions of a cent
> away. I don't remember what it is. Hopefully someone here will
> remember. I remember there was more than one comma that could be
> tempered out to get to the 13-limit, and just did a search, and
> couldn't find it. But this should get you started.
>
> -Mike
>
From: caleb morgan (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Damn, Herman, that's good! That's what I was looking for when I posted this. I might have found it myself, (Caleb says this with slight disappointment but real appreciation.) I wish I knew the thought process that lead you there. Maybe I will, soon. Thanks a lot, that's going in the favorite scales folder. Caleb On Sep 10, 2010, at 10:54 PM, Herman Miller wrote: > caleb morgan wrote: >> I'm sorry for excessive posting if this has been the case. >> >> I'm in a scale-design phase, which I hope to wrap up shortly. >> >> It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. >> >> I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. >> >> 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. >> >> A standard keyboard is a given. >> >> So, bear with me if I change my specs slightly one more time. >> >> The "perfect" scale would be: >> >> Size: 43 notes >> >> Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. >> >> 5ths: wide but no wider than 704.35 >> >> 5/4's: wide by no more than 6 cents or dead on >> >> 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents >> >> octave: within 4 cents, preferably wide, say 1204. >> >> Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. >> >> There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. >> >> There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. >> >> The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. >> >> So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. >> >> But some "keys" could um, suck, to put it bluntly. >> >> So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. >> >> I think this is do-able. I think it's important, even. >> >> *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! >> >> It may already exist. >> >> It might look like a slight tempering of Partch's scale. >> >> This is my current thinking. >> > > Here's one that looks interesting. > > 3/2 is 701.96 cents. > 5/4 is 4.78 cents sharp. > 8/7, 7/6, 12/7, and 7/4 are all less than half a cent off. > The scale is strictly proper, distributional even, and Constant Structure. > > Generators: 2/1, 391.095 > > ! C:\music\scales\43-46.scl > ! > 43 notes of 43&46 regular temperament > 43 > ! > 26.71500 > 53.43000 > 80.14500 > 106.86000 > 133.57500 > 160.29000 > 187.00500 > 230.80500 > 257.52000 > 284.23500 > 310.95000 > 337.66500 > 364.38000 > 391.09500 > 417.81000 > 444.52500 > 471.24000 > 497.95500 > 524.67000 > 551.38500 > 578.10000 > 621.90000 > 648.61500 > 675.33000 > 702.04500 > 728.76000 > 755.47500 > 782.19000 > 808.90500 > 835.62000 > 862.33500 > 889.05000 > 915.76500 > 942.48000 > 969.19500 > 1012.99500 > 1039.71000 > 1066.42500 > 1093.14000 > 1119.85500 > 1146.57000 > 1173.28500 > 2/1 > > > > > ------------------------------------ > > 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: caleb morgan (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Caleb plays scale. Oops, 230.805 is doing double duty as 9/8 and 8/7! Jon Szanto was right: Compromise is for domestic felines. Not *this* feral cat. Caleb On Sep 11, 2010, at 4:59 AM, caleb morgan wrote: > Damn, Herman, that's good! That's what I was looking for when I posted this. I might have found it myself, (Caleb says this with slight disappointment but real appreciation.) > > I wish I knew the thought process that lead you there. > > Maybe I will, soon. > > Thanks a lot, that's going in the favorite scales folder. > > Caleb > > On Sep 10, 2010, at 10:54 PM, Herman Miller wrote: > > > caleb morgan wrote: > >> I'm sorry for excessive posting if this has been the case. > >> > >> I'm in a scale-design phase, which I hope to wrap up shortly. > >> > >> It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. > >> > >> I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. > >> > >> 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. > >> > >> A standard keyboard is a given. > >> > >> So, bear with me if I change my specs slightly one more time. > >> > >> The "perfect" scale would be: > >> > >> Size: 43 notes > >> > >> Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. > >> > >> 5ths: wide but no wider than 704.35 > >> > >> 5/4's: wide by no more than 6 cents or dead on > >> > >> 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents > >> > >> octave: within 4 cents, preferably wide, say 1204. > >> > >> Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. > >> > >> There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. > >> > >> There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. > >> > >> The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. > >> > >> So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. > >> > >> But some "keys" could um, suck, to put it bluntly. > >> > >> So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. > >> > >> I think this is do-able. I think it's important, even. > >> > >> *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! > >> > >> It may already exist. > >> > >> It might look like a slight tempering of Partch's scale. > >> > >> This is my current thinking. > >> > > > > Here's one that looks interesting. > > > > 3/2 is 701.96 cents. > > 5/4 is 4.78 cents sharp. > > 8/7, 7/6, 12/7, and 7/4 are all less than half a cent off. > > The scale is strictly proper, distributional even, and Constant Structure. > > > > Generators: 2/1, 391.095 > > > > ! C:\music\scales\43-46.scl > > ! > > 43 notes of 43&46 regular temperament > > 43 > > ! > > 26.71500 > > 53.43000 > > 80.14500 > > 106.86000 > > 133.57500 > > 160.29000 > > 187.00500 > > 230.80500 > > 257.52000 > > 284.23500 > > 310.95000 > > 337.66500 > > 364.38000 > > 391.09500 > > 417.81000 > > 444.52500 > > 471.24000 > > 497.95500 > > 524.67000 > > 551.38500 > > 578.10000 > > 621.90000 > > 648.61500 > > 675.33000 > > 702.04500 > > 728.76000 > > 755.47500 > > 782.19000 > > 808.90500 > > 835.62000 > > 862.33500 > > 889.05000 > > 915.76500 > > 942.48000 > > 969.19500 > > 1012.99500 > > 1039.71000 > > 1066.42500 > > 1093.14000 > > 1119.85500 > > 1146.57000 > > 1173.28500 > > 2/1 > > > > > > > > > > ------------------------------------ > > > > 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: caleb morgan (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Awright, building on the idea of a 13-limit tonality diamond in 72 EDO: 1/1 0. 200. 383.333 550 700 833.333 966.667 1083.333 8:9 1000. 0., 183.333 350 500 633.333 766.667 883.333 4:5 816.667 1016.667 0 166.667 316.667 450. 583.333 700 8:11 650. 850. 1033.333 0 150. 283.333 416.667 533.333 4:3 500. 700. 883.333 1050 0 133.333 266.667 383.333 16:13 366.667 566.667, 750. 916.667 1066.667 0 133.333 250. 8:7 233.333, 433.333 616.667 783.333 933.333 1066.667 0 116.667 8:15 116.667 316.667 500. 666.667 816.667 950. 1083.333, 0 arranged as a scale it gives us 45: !0. 116.667 133.333 150.0 166.667 183.333 ! 200.0 233.333 250.0 266.667 283.333 316.667 ! 350.0 366.667 383.333 416.667 433.333 450.0 ! 500.0 533.333 550.0 566.667 583.333 616.667 ! 633.333 650.0 666.667 700. 750. 766.667 ! 783.333 816.667 833.333 850.0 883.333 916.667 ! 933.333 950.0 966.667 1000. 1016.667 1033.333 ! 1050.0 1066.667 1083.333 ! 1200 from which I snip 2 tones to give 43: !43Government Work 43-pitch near-complete 13-limit in 72EDO 43 !0. 116.667 133.333 150.0 166.667 183.333 ! 200.0 233.333 250.0 266.667 283.333 316.667 ! 350.0 366.667 383.333 416.667 433.333 450.0 ! 500.0 550.0 566.667 583.333 616.667 ! 633.333 650.0 666.667 700. 750. 766.667 ! 783.333 816.667 833.333 850.0 883.333 916.667 ! 933.333 966.667 1000. 1016.667 1033.333 ! 1050.0 1066.667 1083.333 ! 1200 On Sep 11, 2010, at 5:36 AM, caleb morgan wrote: > Caleb plays scale. > > > Oops, 230.805 is doing double duty as 9/8 and 8/7! > > Jon Szanto was right: Compromise is for domestic felines. > > Not *this* feral cat. > > Caleb > > > > On Sep 11, 2010, at 4:59 AM, caleb morgan wrote: > >> >> Damn, Herman, that's good! That's what I was looking for when I posted this. I might have found it myself, (Caleb says this with slight disappointment but real appreciation.) >> >> I wish I knew the thought process that lead you there. >> >> Maybe I will, soon. >> >> Thanks a lot, that's going in the favorite scales folder. >> >> Caleb >> >> On Sep 10, 2010, at 10:54 PM, Herman Miller wrote: >> >> > caleb morgan wrote: >> >> I'm sorry for excessive posting if this has been the case. >> >> >> >> I'm in a scale-design phase, which I hope to wrap up shortly. >> >> >> >> It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. >> >> >> >> I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. >> >> >> >> 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. >> >> >> >> A standard keyboard is a given. >> >> >> >> So, bear with me if I change my specs slightly one more time. >> >> >> >> The "perfect" scale would be: >> >> >> >> Size: 43 notes >> >> >> >> Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. >> >> >> >> 5ths: wide but no wider than 704.35 >> >> >> >> 5/4's: wide by no more than 6 cents or dead on >> >> >> >> 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents >> >> >> >> octave: within 4 cents, preferably wide, say 1204. >> >> >> >> Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. >> >> >> >> There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. >> >> >> >> There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. >> >> >> >> The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. >> >> >> >> So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. >> >> >> >> But some "keys" could um, suck, to put it bluntly. >> >> >> >> So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. >> >> >> >> I think this is do-able. I think it's important, even. >> >> >> >> *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! >> >> >> >> It may already exist. >> >> >> >> It might look like a slight tempering of Partch's scale. >> >> >> >> This is my current thinking. >> >> >> > >> > Here's one that looks interesting. >> > >> > 3/2 is 701.96 cents. >> > 5/4 is 4.78 cents sharp. >> > 8/7, 7/6, 12/7, and 7/4 are all less than half a cent off. >> > The scale is strictly proper, distributional even, and Constant Structure. >> > >> > Generators: 2/1, 391.095 >> > >> > ! C:\music\scales\43-46.scl >> > ! >> > 43 notes of 43&46 regular temperament >> > 43 >> > ! >> > 26.71500 >> > 53.43000 >> > 80.14500 >> > 106.86000 >> > 133.57500 >> > 160.29000 >> > 187.00500 >> > 230.80500 >> > 257.52000 >> > 284.23500 >> > 310.95000 >> > 337.66500 >> > 364.38000 >> > 391.09500 >> > 417.81000 >> > 444.52500 >> > 471.24000 >> > 497.95500 >> > 524.67000 >> > 551.38500 >> > 578.10000 >> > 621.90000 >> > 648.61500 >> > 675.33000 >> > 702.04500 >> > 728.76000 >> > 755.47500 >> > 782.19000 >> > 808.90500 >> > 835.62000 >> > 862.33500 >> > 889.05000 >> > 915.76500 >> > 942.48000 >> > 969.19500 >> > 1012.99500 >> > 1039.71000 >> > 1066.42500 >> > 1093.14000 >> > 1119.85500 >> > 1146.57000 >> > 1173.28500 >> > 2/1 >> > >> > >> > >> > >> > ------------------------------------ >> > >> > 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: Michael (2010-09-11)
Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43
MikeB,
Indeed, this explains the nature of Miracle Tunings very clearly.
Specifically the idea of the Secor adding up to create various low-limit
intervals, many of which can be considered individual generators of the scale
(if I have it correctly). It all seems to lend itself to a "low-limit intervals
adding up to larger low-limit intervals" framework. Now if you could explain
how this fits on, say, a periodicity block (perhaps on a side thread) in this
kind of well-thought pattern-oriented detail...I think I could actually follow
it and perhaps even "get it" 100% on the first try.
From: caleb morgan (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 as if to prove GWS right yet again, I'm posting, for your edification, a new kind of scale, the MOI? (Moment of Incompetence) scale. !43-tone Moment of Incompetence (MOI) scale MOI? 43 !0. 28. 43.7 70. 92.5 165. 182.4 203. 232.2 266.9 295.5 308. 315.64 386.3 406. 417.5 454.2 498.5 499. 536.9 551.3 591. ! 609. 648.7 663. 701.5 745.7 772. 794. 813.686 867. 884. 904.5 935.1 969.8 997. 1008. 1049.4 1088.27 1107.5 1119. 1155. 1176. 1202. On Sep 11, 2010, at 7:29 AM, caleb morgan wrote: > > > Awright, building on the idea of a 13-limit tonality diamond in 72 EDO: > > 1/1 0. 200. 383.333 550 700 833.333 966.667 1083.333 > > 8:9 1000. 0., 183.333 350 500 633.333 766.667 883.333 > > 4:5 816.667 1016.667 0 166.667 316.667 450. 583.333 700 > > 8:11 650. 850. 1033.333 0 150. 283.333 416.667 533.333 > > 4:3 500. 700. 883.333 1050 0 133.333 266.667 383.333 > > 16:13 366.667 566.667, 750. 916.667 1066.667 0 133.333 250. > > 8:7 233.333, 433.333 616.667 783.333 933.333 1066.667 0 116.667 > > 8:15 116.667 316.667 500. 666.667 816.667 950. 1083.333, 0 > > > arranged as a scale it gives us 45: > > > !0. > 116.667 > 133.333 > 150.0 > 166.667 > 183.333 > ! > 200.0 > 233.333 > 250.0 > 266.667 > 283.333 > 316.667 > ! > 350.0 > 366.667 > 383.333 > 416.667 > 433.333 > 450.0 > ! > 500.0 > 533.333 > 550.0 > 566.667 > 583.333 > 616.667 > ! > 633.333 > 650.0 > 666.667 > 700. > 750. > 766.667 > ! > 783.333 > 816.667 > 833.333 > 850.0 > 883.333 > 916.667 > ! > 933.333 > 950.0 > 966.667 > 1000. > 1016.667 > 1033.333 > ! > 1050.0 > 1066.667 > 1083.333 > ! > 1200 > > > from which I snip 2 tones to give 43: > > !43Government Work > 43-pitch near-complete 13-limit in 72EDO > 43 > !0. > 116.667 > 133.333 > 150.0 > 166.667 > 183.333 > ! > 200.0 > 233.333 > 250.0 > 266.667 > 283.333 > 316.667 > ! > 350.0 > 366.667 > 383.333 > 416.667 > 433.333 > 450.0 > ! > 500.0 > 550.0 > 566.667 > 583.333 > 616.667 > ! > 633.333 > 650.0 > 666.667 > 700. > 750. > 766.667 > ! > 783.333 > 816.667 > 833.333 > 850.0 > 883.333 > 916.667 > ! > 933.333 > 966.667 > 1000. > 1016.667 > 1033.333 > ! > 1050.0 > 1066.667 > 1083.333 > ! > 1200 > > > > > > On Sep 11, 2010, at 5:36 AM, caleb morgan wrote: > >> >> Caleb plays scale. >> >> >> Oops, 230.805 is doing double duty as 9/8 and 8/7! >> >> Jon Szanto was right: Compromise is for domestic felines. >> >> Not *this* feral cat. >> >> Caleb >> >> >> >> On Sep 11, 2010, at 4:59 AM, caleb morgan wrote: >> >>> >>> Damn, Herman, that's good! That's what I was looking for when I posted this. I might have found it myself, (Caleb says this with slight disappointment but real appreciation.) >>> >>> I wish I knew the thought process that lead you there. >>> >>> Maybe I will, soon. >>> >>> Thanks a lot, that's going in the favorite scales folder. >>> >>> Caleb >>> >>> On Sep 10, 2010, at 10:54 PM, Herman Miller wrote: >>> >>> > caleb morgan wrote: >>> >> I'm sorry for excessive posting if this has been the case. >>> >> >>> >> I'm in a scale-design phase, which I hope to wrap up shortly. >>> >> >>> >> It's been a process of learning what's possible, what's desirable, what's convenient, and what's easily learnable. >>> >> >>> >> I've been circling 'round something. It involves JI/EDO hybrids of between 36 and 48 pitches. >>> >> >>> >> 43 pitches turns out to fit two "octaves" perfectly, so it seems optimal for a number of reasons. >>> >> >>> >> A standard keyboard is a given. >>> >> >>> >> So, bear with me if I change my specs slightly one more time. >>> >> >>> >> The "perfect" scale would be: >>> >> >>> >> Size: 43 notes >>> >> >>> >> Consistency: Not *entirely* consistent in smallest-step sizes, but fingering of closest equivalents to 3/2, 4/3, 9/8, 16/9, 5/4, 8/5, etc. would always be the *same* number of key-steps. >>> >> >>> >> 5ths: wide but no wider than 704.35 >>> >> >>> >> 5/4's: wide by no more than 6 cents or dead on >>> >> >>> >> 8/7, 7/6, 12/7, 7/4 off by no more than 6 cents >>> >> >>> >> octave: within 4 cents, preferably wide, say 1204. >>> >> >>> >> Consistency in every "key"*: *not* necessary. However, every "key" that has 1/1 as a member must be fairly in-tune, that is, have a good 3:4:5 triad. >>> >> >>> >> There can be a number of "bad" keys, such as the one on the "second" degree of scale of 43. >>> >> >>> >> There can be a very few "filler" notes for the sole purpose of making the fingering consistent. You might never use them. >>> >> >>> >> The "error in the system" should be greatest around the keys that you wouldn't use as being harmonically-related to 1/1. So, /8, /9 etc to /11, perhaps even /13 would be accurate enough. >>> >> >>> >> So would the "strange" tonalities on 9/8, and 5/4, and 27/16 and 5/3, even. >>> >> >>> >> But some "keys" could um, suck, to put it bluntly. >>> >> >>> >> So, it's possible to play this scale with good consonant 5:6:7:8:9:10:11 in at least 7 keys, with many more good but non OT scales available on other keys. >>> >> >>> >> I think this is do-able. I think it's important, even. >>> >> >>> >> *Some* beating in the 5's, 9's, 11's 13's, and 15's is even desirable, but not too much! >>> >> >>> >> It may already exist. >>> >> >>> >> It might look like a slight tempering of Partch's scale. >>> >> >>> >> This is my current thinking. >>> >> >>> > >>> > Here's one that looks interesting. >>> > >>> > 3/2 is 701.96 cents. >>> > 5/4 is 4.78 cents sharp. >>> > 8/7, 7/6, 12/7, and 7/4 are all less than half a cent off. >>> > The scale is strictly proper, distributional even, and Constant Structure. >>> > >>> > Generators: 2/1, 391.095 >>> > >>> > ! C:\music\scales\43-46.scl >>> > ! >>> > 43 notes of 43&46 regular temperament >>> > 43 >>> > ! >>> > 26.71500 >>> > 53.43000 >>> > 80.14500 >>> > 106.86000 >>> > 133.57500 >>> > 160.29000 >>> > 187.00500 >>> > 230.80500 >>> > 257.52000 >>> > 284.23500 >>> > 310.95000 >>> > 337.66500 >>> > 364.38000 >>> > 391.09500 >>> > 417.81000 >>> > 444.52500 >>> > 471.24000 >>> > 497.95500 >>> > 524.67000 >>> > 551.38500 >>> > 578.10000 >>> > 621.90000 >>> > 648.61500 >>> > 675.33000 >>> > 702.04500 >>> > 728.76000 >>> > 755.47500 >>> > 782.19000 >>> > 808.90500 >>> > 835.62000 >>> > 862.33500 >>> > 889.05000 >>> > 915.76500 >>> > 942.48000 >>> > 969.19500 >>> > 1012.99500 >>> > 1039.71000 >>> > 1066.42500 >>> > 1093.14000 >>> > 1119.85500 >>> > 1146.57000 >>> > 1173.28500 >>> > 2/1 >>> > >>> > >>> > >>> > >>> > ------------------------------------ >>> > >>> > 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: genewardsmith (2010-09-11) Subject: Re: Compromise between 43EDO & Partch's 43 --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > !43-tone Moment of Incompetence (MOI) scale > 498.5 > 499. Is this the actual Moment of Incompetence?
From: Mike Battaglia (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 On Sat, Sep 11, 2010 at 1:48 PM, genewardsmith <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > !43-tone Moment of Incompetence (MOI) scale > > > 498.5 > > 499. > > Is this the actual Moment of Incompetence? Hahaha! And then there were 42... Although if that were something like 478.5 it would fit the pattern better. -Mike
From: caleb morgan (2010-09-11) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43 Here's something somewhere between serious and not serious. The cent-values of 44EDO were generated, it was observed that most the odd-numbered pitches from 0 cents (27.27, 81.818, etc.) would generate 44EDO. Then values slightly off from those were tried. 190.909 was adjusted to be 190.3, then this was multiplied by n's up to 44. These values were repeated at the octave, removing the next-to last pitch to give a 4:1 on the highest of 88 keys. It *does* hit some good pitches and have some regularity. Otherwise, it's kind of wacka-diddly. So, in the spirit of "Flanders", I give you: HiDiddlyHonegger. !190.3 Gen 44 pitches, with top oct HiDiddlyHonegger 88 !0., 15.7, 58.2, 73.9, 116.4, 132.1, 174.6, 190.3, 206., 248.5, 264.2, 306.7, 322.4, 364.9, 380.6, 396.3, 438.8, 454.5, 497., 512.7, 555.2, 570.9, 586.6, 629.1, 644.8, 687.3, 703., 745.5, 761.2, 803.7, 819.4, 835.1, 877.6, 893.3, 935.8, 951.5, 994., 1009.7, 1025.4, 1067.9, 1083.6, 1126.1, 1141.8, 1184.3 1200 1215.7, 1258.2, 1273.9, 1316.4, 1332.1, 1374.6, 1390.3, 1406., 1448.5, 1464.2, 1506.7, 1522.4, 1564.9, 1580.6, 1596.3, 1638.8, 1654.5, 1697., 1712.7, 1755.2, 1770.9, 1786.6, 1829.1, 1844.8, 1887.3, 1903., 1945.5, 1961.2, 2003.7, 2019.4, 2035.1, 2077.6, 2093.3, 2135.8, 2151.5, 2194., 2209.7, 2225.4, 2267.9, 2283.6, 2326.1, 2341.8, 2400 2415.7 On Sep 11, 2010, at 2:02 PM, Mike Battaglia wrote: > On Sat, Sep 11, 2010 at 1:48 PM, genewardsmith > <genewardsmith@...> wrote: > > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > > > !43-tone Moment of Incompetence (MOI) scale > > > > > 498.5 > > > 499. > > > > Is this the actual Moment of Incompetence? > > Hahaha! And then there were 42... > > Although if that were something like 478.5 it would fit the pattern better. > > -Mike >
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz I've gone back and forth a lot, and hopefully I've learned something. Tuning takes a mix of factors into account, from the mathematical to the contingent. 41 pitches per 2/1 seems to be the best framework for my future work. With a consistent keyboard pattern, I don't have to learn a dozen new "languages"--I only have to learn one. 41 fits two "octaves" into an 88-note keyboard. I have 2 keyboards for 4 octaves--about the range of an electric guitar. Any member of 41 can serve as a generator for any of the others, since 41 is prime. With a program like LMSO or Scala, it's easy to generate variations on 41 quickly. Each generator--if the value is changed slightly--can produce different patterns of slight distortion or perturbation of the 41EDO scale. Some will come closer to JI in some "keys", as I think the one below does. These can be explored within the same fingering patterns. So one is not starting from scratch each time. I still like a slightly wide 3/2 plus a few cents, and a slightly wide octave. Different variations sound different in different keys, and have different beatings. I don't like too severe a beating, but a little feels good. (Cue Percy Grainger jokes.) 41 feels like the best framework to settle on. The version below gets 16/15, 8/7, 7/6, 11/8 pretty darn close. The octave stretch doesn't bother me at all. (It even sounds good.) The title is a reference to that great piece of cinema by Mr. Ed Wood--Plan 9 from Outer Space. Caleb !234.92 gen in 1202.595 octave 41 near-EDO, (28 cents and 39 cents) 41 0., 27.995, 55.99, 83.985, 111.98, 150.935, 178.93, 206.925, 234.92, 262.915, 290.91, 318.905, 346.9, 385.855, 413.85, 441.845, 469.84, 497.835, 525.83, 553.825, 581.82, ! 620.775, 648.77, 676.765, 704.76, 732.755, 760.75, 788.745, 816.74, 855.695, 883.69, 911.685, 939.68, 967.675, 995.67, 1023.665, 1051.66, 1090.615, 1118.61, 1146.605, 1174.6 1202.595 On Sep 11, 2010, at 2:02 PM, Mike Battaglia wrote: > On Sat, Sep 11, 2010 at 1:48 PM, genewardsmith > <genewardsmith@...> wrote: > > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > > > !43-tone Moment of Incompetence (MOI) scale > > > > > 498.5 > > > 499. > > > > Is this the actual Moment of Incompetence? > > Hahaha! And then there were 42... > > Although if that were something like 478.5 it would fit the pattern better. > > -Mike >
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Fixed for Scala. -c On Sep 12, 2010, at 8:15 AM, caleb morgan wrote: > !234.92 gen in 1202.595 octave > 41 near-EDO, (28 cents and 39 cents) > 41 > !0., > 27.995 > 55.99 > 83.985 > 111.98 > 150.935 > 178.93 > 206.925 > 234.92 > 262.915 > 290.91 > 318.905 > 346.9 > 385.855 > 413.85 > 441.845 > 469.84 > 497.835 > 525.83 > 553.825 > 581.82 > ! > 620.775 > 648.77 > 676.765 > 704.76 > 732.755 > 760.75 > 788.745 > 816.74 > 855.695 > 883.69 > 911.685 > 939.68 > 967.675 > 995.67 > 1023.665 > 1051.66 > 1090.615 > 1118.61 > 1146.605 > 1174.6 > 1202.595 >
From: genewardsmith (2010-09-12) Subject: Re: Plan 41 from Utter Spaz --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > !234.92 gen in 1202.595 octave > 41 near-EDO, (28 cents and 39 cents) This is rodan, I temperament I've been working with lately.
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz That's interesting! I was looking here, but I didn't see 8/7-ish generators or Rodan, or 41EDO: http://xenharmonic.wikispaces.com/Regular+Temperaments What defines Rodan? On Sep 12, 2010, at 1:30 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > !234.92 gen in 1202.595 octave > > 41 near-EDO, (28 cents and 39 cents) > > This is rodan, I temperament I've been working with lately. > >
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Ah, here it is: http://xenharmonic.wikispaces.com/Gamelismic+clan+ Lemme chew on this for a while. -c On Sep 12, 2010, at 1:46 PM, caleb morgan wrote: > That's interesting! > > > I was looking here, but I didn't see 8/7-ish generators or Rodan, or 41EDO: > > > http://xenharmonic.wikispaces.com/Regular+Temperaments > > > What defines Rodan? > > > On Sep 12, 2010, at 1:30 PM, genewardsmith wrote: > >> >> >> >> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >> >> > !234.92 gen in 1202.595 octave >> > 41 near-EDO, (28 cents and 39 cents) >> >> This is rodan, I temperament I've been working with lately. >> > > >
From: genewardsmith (2010-09-12) Subject: Re: Plan 41 from Utter Spaz --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote: > > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@> wrote: > > > !234.92 gen in 1202.595 octave > > 41 near-EDO, (28 cents and 39 cents) > > This is rodan, I temperament I've been working with lately. > I don't get why you want these extreme (relative to the accuracy of the temperament) octave stretches; octave stretching to that extent introduces tuning problems that weren't there originally. Of course maybe you want to sound like a gamelan orchestra, and rodan is a gamelismic temperament. If you stick 41 and 87 into Graham's magic box http://x31eq.com/temper/net.html for various limits, you will see it doesn't suggest there is much payoff to tweaking the octave in rodan.
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz 243 is 3.3.3.3.3, and 245 is 5.7.7-- these are "tempered out". Rodan makes 3 8:7 intervals equal 1 3:2 in 41EDO, this translates into 6 4-note steps, which more or less hit: 1/1, 16/15, 8/7, ?, 21/16, 4/3, ?, 3/2 On Sep 12, 2010, at 1:53 PM, caleb morgan wrote: > Ah, here it is: > > > http://xenharmonic.wikispaces.com/Gamelismic+clan+ > > Lemme chew on this for a while. > > -c > > > > > On Sep 12, 2010, at 1:46 PM, caleb morgan wrote: > >> >> That's interesting! >> >> >> I was looking here, but I didn't see 8/7-ish generators or Rodan, or 41EDO: >> >> >> http://xenharmonic.wikispaces.com/Regular+Temperaments >> >> >> What defines Rodan? >> >> >> On Sep 12, 2010, at 1:30 PM, genewardsmith wrote: >> >>> >>> >>> >>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>> >>> > !234.92 gen in 1202.595 octave >>> > 41 near-EDO, (28 cents and 39 cents) >>> >>> This is rodan, I temperament I've been working with lately. >>> >> >> > > >
From: genewardsmith (2010-09-12) Subject: Re: Plan 41 from Utter Spaz --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > What defines Rodan? Rodan is the 41&87 temperament, and 87edo provides a good tuning for it. Compared to miracle, which is also gamelismic, it has exactly half the complexity for 3 and 7, and hence 7/6 and 9/7; and the complexity of 6/5, 14, is not much worse than the 13 of miracle. But it takes 17 generators to get to the major third, compared to 7 for miracle. 11 has a complexity of 13 compared to the 15 for miracle, but it doesn't work well with the 5 as it's in the opposite direction. 13 has a complexity of 22 and you get plenty of it in a span of 41 notes, whereas miracle isn't as good in the 13 limit as in 11. Miracle is a bit more tuning accurate than rodan, in case that matters to you which I'm beginning to doubt, but miracle tends flat rather than sharp. You can get an idea of how they compare simply by comparing the tunings for 72et (miracle) with those of 87et (rodan.) For instance, 72 has a fifth two cents flat, the same as 12et, whereas 87 has a fifth a cent and a half sharp, the same as 29et. Stick 41 and 87 into Graham's box, and you should see what defines rodan.
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Oh, I don't know what I'm doing at your level. I was just doing trial-and-error deviations from any of the 41 possible generators in 41EDO--basically every pitch and near-miss. Then I was trying to stretch the octave a little either way to see what would happen. The idea with the tuning I posted was that it had a pretty good 9/8, 8/7, 7/6 in near-41EDO. The stretched octave doesn't sound bad to me at all. Thinking about this, I simply lack a theory of accuracy--some beating sounds good, but with 7's 11's, I like to hear them really close. I'm not sure how to think about that. Here's the map for Rodan. I'll mess around with it. Rodan Equal Temperament Mappings 2 3 5 7 11 [< 41 65 95 115 142 ] < 87 138 202 244 301 ]> Reduced Mapping 2 3 5 7 11 [< 1 1 -1 3 6 ] < 0 3 17 -1 -13 ]> Generator Tunings (cents) [1200.057, 234.470> Step Tunings (cents) [2.091, 12.809> On Sep 12, 2010, at 1:56 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote: > > > > > > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@> wrote: > > > > > !234.92 gen in 1202.595 octave > > > 41 near-EDO, (28 cents and 39 cents) > > > > This is rodan, I temperament I've been working with lately. > > > > I don't get why you want these extreme (relative to the accuracy of the temperament) octave stretches; octave stretching to that extent introduces tuning problems that weren't there originally. Of course maybe you want to sound like a gamelan orchestra, and rodan is a gamelismic temperament. If you stick 41 and 87 into Graham's magic box > > http://x31eq.com/temper/net.html > > for various limits, you will see it doesn't suggest there is much payoff to tweaking the octave in rodan. > >
From: genewardsmith (2010-09-12) Subject: Re: Plan 41 from Utter Spaz --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote: > 11 has a complexity of 13 compared to the 15 for miracle, but it doesn't work well with the 5 as it's in the opposite direction. It's in the opposite direction in miracle as well, and what I was trying very badly to say is that since it has a less complex 5, the 5-11 stuff is overall less complex in miracle.
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Here's Rodan that someone else generated, which I had overlooked. Probably you, GWS, did this one. I like it. It's very close to what I posted except toward the top, where my pitches trend about 5 cents sharper. ! rodan41.scl Rodan[41] in 128-tET tuning 41 !0. 28.125 56.250 84.375 112.500 150.000 178.125 206.250 234.375 262.500 290.625 318.750 346.875 384.375 412.500 440.625 468.750 496.875 525.000 553.125 581.250 ! 618.750 646.875 675.000 703.125 731.250 759.375 787.500 815.625 853.125 881.250 909.375 937.500 965.625 993.750 1021.875 1050.000 1087.500 1115.625 1143.750 1171.875 2/1 On Sep 12, 2010, at 2:18 PM, caleb morgan wrote: > Oh, I don't know what I'm doing at your level. > > > I was just doing trial-and-error deviations from any of the 41 possible generators in 41EDO--basically every pitch and near-miss. > > Then I was trying to stretch the octave a little either way to see what would happen. > > The idea with the tuning I posted was that it had a pretty good 9/8, 8/7, 7/6 in near-41EDO. > > The stretched octave doesn't sound bad to me at all. > > Thinking about this, I simply lack a theory of accuracy--some beating sounds good, but with 7's 11's, I like to hear them really close. > > I'm not sure how to think about that. > > Here's the map for Rodan. > > I'll mess around with it. > > Rodan > > Equal Temperament Mappings > 2 3 5 7 11 > [< 41 65 95 115 142 ] > < 87 138 202 244 301 ]> > > Reduced Mapping > 2 3 5 7 11 > [< 1 1 -1 3 6 ] > < 0 3 17 -1 -13 ]> > > Generator Tunings (cents) > [1200.057, 234.470> > > Step Tunings (cents) > [2.091, 12.809> > > > > On Sep 12, 2010, at 1:56 PM, genewardsmith wrote: > >> >> >> >> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote: >> > >> > >> > >> > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@> wrote: >> > >> > > !234.92 gen in 1202.595 octave >> > > 41 near-EDO, (28 cents and 39 cents) >> > >> > This is rodan, I temperament I've been working with lately. >> > >> >> I don't get why you want these extreme (relative to the accuracy of the temperament) octave stretches; octave stretching to that extent introduces tuning problems that weren't there originally. Of course maybe you want to sound like a gamelan orchestra, and rodan is a gamelismic temperament. If you stick 41 and 87 into Graham's magic box >> >> http://x31eq.com/temper/net.html >> >> for various limits, you will see it doesn't suggest there is much payoff to tweaking the octave in rodan. >> > > >
From: caleb morgan (2010-09-12) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Ok, I've been happily typing 41 & Some Big N into the magic box, with 11 and 13-limits, and I note that the generators all fall close to some member of 41EDO, and the octaves are a little big or a little small. Three questions: Where do the names come from? (not a very important question) How does this program arrive at optimums? (slightly more interesting question, but not too important) Most important: What are some slightly more radical things to try typing in, if any--that is, as you said, *less* accuracy, for the experience of seeing what happens? (I'm thinking in terms of radically uneven 41EDO) -c On Sep 12, 2010, at 2:25 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote: > > 11 has a complexity of 13 compared to the 15 for miracle, but it doesn't work well with the 5 as it's in the opposite direction. > > It's in the opposite direction in miracle as well, and what I was trying very badly to say is that since it has a less complex 5, the 5-11 stuff is overall less complex in miracle. > >
From: Graham Breed (2010-09-13)
Subject: Re: [tuning] Re: Plan 41 from Utter Spaz
On 13 September 2010 03:32, caleb morgan <calebmrgn@...> wrote:
>
>
> Ok, I've been happily typing 41 & Some Big N into the magic box, with 11
> and 13-limits, and I note that the generators all fall close to some member
> of 41EDO, and the octaves are a little big or a little small.
>
They'll be close to 41 EDO because the aim is to get close to JI, and 41 EDO
is close to JI.
> Three questions:
>
> Where do the names come from? (not a very important question)
>
I collect them. Most came from the tuning lists at some point. Some are
from Paul Erlich's key paper, some from Gene's old website, some from the
wiki, and some I made up myself.
> How does this program arrive at optimums? (slightly more interesting
> question, but not too important)
>
It does a Tenney-weighted least squares optimization, using a pure Python
linear algebra library.
> Most important: What are some slightly more radical things to try typing
> in, if any--that is, as you said, *less* accuracy, for the experience of
> seeing what happens?
>
You can choose the accuracy you want from the searches.
> (I'm thinking in terms of radically uneven 41EDO)
>
If you want uneven 41 note scales you can pair 41 with your favourite
nowhere-near-JI octave divisions. (If it's uneven, it isn't an EDO.)
Graham
From: caleb morgan (2010-09-13) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Thank you! -c On Sep 12, 2010, at 8:38 PM, Graham Breed wrote: > > On 13 September 2010 03:32, caleb morgan <calebmrgn@...> wrote: > > > Ok, I've been happily typing 41 & Some Big N into the magic box, with 11 and 13-limits, and I note that the generators all fall close to some member of 41EDO, and the octaves are a little big or a little small. > > They'll be close to 41 EDO because the aim is to get close to JI, and 41 EDO is close to JI. > > Three questions: > > Where do the names come from? (not a very important question) > > I collect them. Most came from the tuning lists at some point. Some are from Paul Erlich's key paper, some from Gene's old website, some from the wiki, and some I made up myself. > > How does this program arrive at optimums? (slightly more interesting question, but not too important) > > It does a Tenney-weighted least squares optimization, using a pure Python linear algebra library. > > Most important: What are some slightly more radical things to try typing in, if any--that is, as you said, *less* accuracy, for the experience of seeing what happens? > > You can choose the accuracy you want from the searches. > > (I'm thinking in terms of radically uneven 41EDO) > > If you want uneven 41 note scales you can pair 41 with your favourite nowhere-near-JI octave divisions. (If it's uneven, it isn't an EDO.) > > > Graham > > >
From: caleb morgan (2010-09-13) Subject: Re: [tuning] Re: Plan 41 from Utter Spaz Graham wrote: > If you want uneven 41 note scales you can pair 41 with your favourite nowhere-near-JI octave divisions. (If it's uneven, it isn't an EDO.) I think I'm exploring 41-ism, rather than only 41EDO. 41-ism just means having 41 pitches ranked from lower to higher, usually--but not exclusively--within an octave. I'm also going to check out 41 within 3:1, etc. There could be a 41 which contains approximations of all the far-from-JI EDOs, as you suggest. There could also be a 41-pitch scale not too far from 41EDO where certain tonalities are very much in tune, others are not usable at all. But one wouldn't have to learn an entirely new geography--just as people bend a 12-pitch scale without having to learn a whole new geography. With practice, 41-ism will become a framework for hand-habits. So 41-ism is a framework just as 12-ism is a framework for a lot of people, including the makers of Logic. caleb On Sep 12, 2010, at 8:38 PM, Graham Breed wrote: > > On 13 September 2010 03:32, caleb morgan <calebmrgn@yahoo.com> wrote: > > > Ok, I've been happily typing 41 & Some Big N into the magic box, with 11 and 13-limits, and I note that the generators all fall close to some member of 41EDO, and the octaves are a little big or a little small. > > They'll be close to 41 EDO because the aim is to get close to JI, and 41 EDO is close to JI. > > Three questions: > > Where do the names come from? (not a very important question) > > I collect them. Most came from the tuning lists at some point. Some are from Paul Erlich's key paper, some from Gene's old website, some from the wiki, and some I made up myself. > > How does this program arrive at optimums? (slightly more interesting question, but not too important) > > It does a Tenney-weighted least squares optimization, using a pure Python linear algebra library. > > Most important: What are some slightly more radical things to try typing in, if any--that is, as you said, *less* accuracy, for the experience of seeing what happens? > > You can choose the accuracy you want from the searches. > > (I'm thinking in terms of radically uneven 41EDO) > > If you want uneven 41 note scales you can pair 41 with your favourite nowhere-near-JI octave divisions. (If it's uneven, it isn't an EDO.) > > > Graham > > >
From: caleb morgan (2010-09-13) Subject: Re: [tuning] Re: Plan 41 with Lil' Miss Scale Oven I really should read the LMSO manual, because it was only *today* that I discovered the Interactive Scale Quantize feature, that lets you gradually or partly bend or morph any JI scale to any EDO and vice-versa. So, this is more fun than a barrel of monkeys. I can take my 41-tone JI scale and gradually smooth off the rough edges. Can take any 41 MOS scale like Rodan, etc. and make it a little more JI. Can take any other EDO and make a 41-note scale have some of its flavor, in an extremely radical or subtle way as I choose. Just when I thought my experimentations was drawing to a close. What fun. caleb On Sep 13, 2010, at 6:40 AM, caleb morgan wrote: > > Graham wrote: > >> If you want uneven 41 note scales you can pair 41 with your favourite nowhere-near-JI octave divisions. (If it's uneven, it isn't an EDO.) > > > I think I'm exploring 41-ism, rather than only 41EDO. 41-ism just means having 41 pitches ranked from lower to higher, usually--but not exclusively--within an octave. > > I'm also going to check out 41 within 3:1, etc. > > There could be a 41 which contains approximations of all the far-from-JI EDOs, as you suggest. > > There could also be a 41-pitch scale not too far from 41EDO where certain tonalities are very much in tune, others are not usable at all. But one wouldn't have to learn an entirely new geography--just as people bend a 12-pitch scale without having to learn a whole new geography. > > With practice, 41-ism will become a framework for hand-habits. > > So 41-ism is a framework just as 12-ism is a framework for a lot of people, including the makers of Logic. > > caleb > > > > > > On Sep 12, 2010, at 8:38 PM, Graham Breed wrote: > >> >> >> On 13 September 2010 03:32, caleb morgan <calebmrgn@...> wrote: >> >> >> Ok, I've been happily typing 41 & Some Big N into the magic box, with 11 and 13-limits, and I note that the generators all fall close to some member of 41EDO, and the octaves are a little big or a little small. >> >> They'll be close to 41 EDO because the aim is to get close to JI, and 41 EDO is close to JI. >> >> Three questions: >> >> Where do the names come from? (not a very important question) >> >> I collect them. Most came from the tuning lists at some point. Some are from Paul Erlich's key paper, some from Gene's old website, some from the wiki, and some I made up myself. >> >> How does this program arrive at optimums? (slightly more interesting question, but not too important) >> >> It does a Tenney-weighted least squares optimization, using a pure Python linear algebra library. >> >> Most important: What are some slightly more radical things to try typing in, if any--that is, as you said, *less* accuracy, for the experience of seeing what happens? >> >> You can choose the accuracy you want from the searches. >> >> (I'm thinking in terms of radically uneven 41EDO) >> >> If you want uneven 41 note scales you can pair 41 with your favourite nowhere-near-JI octave divisions. (If it's uneven, it isn't an EDO.) >> >> >> Graham >> >> > > >
From: caleb morgan (2010-09-14) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? Heh. Thing is, you're right that I haven't been easily satisfied. That's why my plans keep changing. Now, I think I'm settling for uneven fingering and a design much closer to JI, which fits 4 octaves on two 88-key keyboards. It's very close to the Rube Goldberg scales I came up with, which are basically JI with an attempt at tempering out the difference between 32/27 and 13/11. At the same time, I discovered that Lil' Miss Scale Oven will let me do compromise tunings between a given scale and some EDO. My scale is printed below. I tried morphing it 50% if the way to 76EDO, just to see what would happen. The results aren't bad. What might be some other EDOs to try to "quantize" it, all or part of the way to? Caleb 43-pitch 13 Rube Goldberg 43 !cents PC Approximate ratio !0. 0 1/1 84.5 1 [4/3 below 7/5, or 21/20] 117.0 2 16/15-ish 135.0 3 13/12 was 138.6 150.6 4 12/11 ! 165.0 5 11/10 179.1 6 10/9 was 182.4 207.2 7 9/8 wide with 3/2 231.2 8 8/7 247.74 9 15/13 265.2 10 7/6 lowered for low 4/3 ! 289.2 11 13/11 and tempered 32/27 313.6 0 6/5 344.1 1 11/9 tempered 359.47 2 16/13 385.0 3 5/4 414.5 4 14/11 low to go with 22/13 ! 435.1 5 9/7 496.4 6 4/3 low 551.3 7 11/8 563.4 8 18/13 582.5 9 7/5 ! 617.5 10 10/7 648.7 11 16/11 703.6 0 3/2 wide 745.8 1 20/13 ! 764.9 2 14/9 782.5 3 11/7 819.0 4 8/5 high, originally 813.78 840.53 5 13/8 852.6 6 18/11 882.7 7 5/3 lowered with 4/3 ! 910.79 8 22/13 933.1 9 12/7 968.8 10 7/4 992.8 11 16/9 low with 4/3 1013.6 0 9/5 ! 1035.0 1 20/11 1049.4 2 11/6 1061.4 3 24/13 1071.7 4 13/7 1085.0 5 15/8 1115.5 6 [4/3 above 10/7, or 40/21] ! 1200.0 0 2/1 Attempt to quantize to nearest 72EDO by 50% percent 0., 83.917, 116.833, 134.167, 150.3, 165.833, 181.217, 203.6, 232.267, 248.87, 265.933, 286.267, 315.133, 347.051, 363.068, 384.167, 415.583, 434.217, 498.2, 550.65, 565.033, 582.917, 617.083, 649.35, 701.8, 747.9, 765.783, 782.917, 817.833, 836.932, 851.3, 883.017, 913.728, 933.217, 967.733, 996.401, 1015.133, 1034.167, 1049.7, 1064.033, 1069.183, 1084.167, 1116.083 On Sep 11, 2010, at 2:13 AM, jonszanto wrote: > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > It might look like a slight tempering of Partch's scale. > > > > This is my current thinking. > > > > I'm quite serious. > > Compromise is for pussies. In your heart, you know it's true. > >
From: caleb morgan (2010-09-14) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? oops, meant 72EDO, not 76. -c On Sep 14, 2010, at 11:27 AM, caleb morgan wrote: > > Heh. > > Thing is, you're right that I haven't been easily satisfied. > > That's why my plans keep changing. > > Now, I think I'm settling for uneven fingering and a design much closer to JI, which fits 4 octaves on two 88-key keyboards. > > It's very close to the Rube Goldberg scales I came up with, which are basically JI with an attempt at tempering out the difference between 32/27 and 13/11. > > At the same time, I discovered that Lil' Miss Scale Oven will let me do compromise tunings between a given scale and some EDO. > > My scale is printed below. I tried morphing it 50% if the way to 76EDO, just to see what would happen. The results aren't bad. > > What might be some other EDOs to try to "quantize" it, all or part of the way to? > > Caleb > > 43-pitch 13 Rube Goldberg > 43 > !cents PC Approximate ratio > !0. 0 1/1 > 84.5 1 [4/3 below 7/5, or 21/20] > 117.0 2 16/15-ish > 135.0 3 13/12 was 138.6 > 150.6 4 12/11 > ! > 165.0 5 11/10 > 179.1 6 10/9 was 182.4 > 207.2 7 9/8 wide with 3/2 > 231.2 8 8/7 > 247.74 9 15/13 > 265.2 10 7/6 lowered for low 4/3 > ! > 289.2 11 13/11 and tempered 32/27 > 313.6 0 6/5 > 344.1 1 11/9 tempered > 359.47 2 16/13 > 385.0 3 5/4 > 414.5 4 14/11 low to go with 22/13 > ! > 435.1 5 9/7 > 496.4 6 4/3 low > 551.3 7 11/8 > 563.4 8 18/13 > 582.5 9 7/5 > ! > 617.5 10 10/7 > 648.7 11 16/11 > 703.6 0 3/2 wide > 745.8 1 20/13 > ! > 764.9 2 14/9 > 782.5 3 11/7 > 819.0 4 8/5 high, originally 813.78 > 840.53 5 13/8 > 852.6 6 18/11 > 882.7 7 5/3 lowered with 4/3 > ! > 910.79 8 22/13 > 933.1 9 12/7 > 968.8 10 7/4 > 992.8 11 16/9 low with 4/3 > 1013.6 0 9/5 > ! > 1035.0 1 20/11 > 1049.4 2 11/6 > 1061.4 3 24/13 > 1071.7 4 13/7 > 1085.0 5 15/8 > 1115.5 6 [4/3 above 10/7, or 40/21] > ! > 1200.0 0 2/1 > > > Attempt to quantize to nearest 72EDO by 50% percent > > 0., 83.917, 116.833, 134.167, 150.3, 165.833, 181.217, 203.6, 232.267, 248.87, 265.933, 286.267, 315.133, 347.051, 363.068, 384.167, 415.583, 434.217, 498.2, 550.65, 565.033, 582.917, 617.083, 649.35, 701.8, 747.9, 765.783, 782.917, 817.833, 836.932, 851.3, 883.017, 913.728, 933.217, 967.733, 996.401, 1015.133, 1034.167, 1049.7, 1064.033, 1069.183, 1084.167, 1116.083 > > > > > On Sep 11, 2010, at 2:13 AM, jonszanto wrote: > >> >> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >> > It might look like a slight tempering of Partch's scale. >> > >> > This is my current thinking. >> > >> > I'm quite serious. >> >> Compromise is for pussies. In your heart, you know it's true. >> > > >
From: caleb morgan (2010-09-14) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? Here I looked up EDOs on the Xenharmony page and chose 87EDO to quantize to: 0., 82.759, 110.345, 137.931, 151.724, 165.517, 179.31, 206.897, 234.483, 248.276, 262.069, 289.655, 317.241, 344.828, 358.621, 386.207, 413.793, 441.379, 496.552, 551.724, 565.517, 579.31, 620.69, 648.276, 703.448, 744.828, 758.621, 786.207, 813.793, 841.379, 855.172, 882.759, 910.345, 937.931, 965.517, 993.103, 1006.897, 1034.483, 1048.276, 1062.069, 1075.862, 1089.655, 1117.241 looks pretty good! I'm not sure about advantages or disadvantages, yet. It makes all the step sizes multiples of 13.793 cents, with a "sruti" pattern of: 6, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 4, 4, 1, 1, 3, 2, 4, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 6 -c On Sep 14, 2010, at 11:34 AM, caleb morgan wrote: > oops, meant 72EDO, not 76. > > > -c > > > On Sep 14, 2010, at 11:27 AM, caleb morgan wrote: > >> >> >> Heh. >> >> Thing is, you're right that I haven't been easily satisfied. >> >> That's why my plans keep changing. >> >> Now, I think I'm settling for uneven fingering and a design much closer to JI, which fits 4 octaves on two 88-key keyboards. >> >> It's very close to the Rube Goldberg scales I came up with, which are basically JI with an attempt at tempering out the difference between 32/27 and 13/11. >> >> At the same time, I discovered that Lil' Miss Scale Oven will let me do compromise tunings between a given scale and some EDO. >> >> My scale is printed below. I tried morphing it 50% if the way to 76EDO, just to see what would happen. The results aren't bad. >> >> What might be some other EDOs to try to "quantize" it, all or part of the way to? >> >> Caleb >> >> 43-pitch 13 Rube Goldberg >> 43 >> !cents PC Approximate ratio >> !0. 0 1/1 >> 84.5 1 [4/3 below 7/5, or 21/20] >> 117.0 2 16/15-ish >> 135.0 3 13/12 was 138.6 >> 150.6 4 12/11 >> ! >> 165.0 5 11/10 >> 179.1 6 10/9 was 182.4 >> 207.2 7 9/8 wide with 3/2 >> 231.2 8 8/7 >> 247.74 9 15/13 >> 265.2 10 7/6 lowered for low 4/3 >> ! >> 289.2 11 13/11 and tempered 32/27 >> 313.6 0 6/5 >> 344.1 1 11/9 tempered >> 359.47 2 16/13 >> 385.0 3 5/4 >> 414.5 4 14/11 low to go with 22/13 >> ! >> 435.1 5 9/7 >> 496.4 6 4/3 low >> 551.3 7 11/8 >> 563.4 8 18/13 >> 582.5 9 7/5 >> ! >> 617.5 10 10/7 >> 648.7 11 16/11 >> 703.6 0 3/2 wide >> 745.8 1 20/13 >> ! >> 764.9 2 14/9 >> 782.5 3 11/7 >> 819.0 4 8/5 high, originally 813.78 >> 840.53 5 13/8 >> 852.6 6 18/11 >> 882.7 7 5/3 lowered with 4/3 >> ! >> 910.79 8 22/13 >> 933.1 9 12/7 >> 968.8 10 7/4 >> 992.8 11 16/9 low with 4/3 >> 1013.6 0 9/5 >> ! >> 1035.0 1 20/11 >> 1049.4 2 11/6 >> 1061.4 3 24/13 >> 1071.7 4 13/7 >> 1085.0 5 15/8 >> 1115.5 6 [4/3 above 10/7, or 40/21] >> ! >> 1200.0 0 2/1 >> >> >> Attempt to quantize to nearest 72EDO by 50% percent >> >> 0., 83.917, 116.833, 134.167, 150.3, 165.833, 181.217, 203.6, 232.267, 248.87, 265.933, 286.267, 315.133, 347.051, 363.068, 384.167, 415.583, 434.217, 498.2, 550.65, 565.033, 582.917, 617.083, 649.35, 701.8, 747.9, 765.783, 782.917, 817.833, 836.932, 851.3, 883.017, 913.728, 933.217, 967.733, 996.401, 1015.133, 1034.167, 1049.7, 1064.033, 1069.183, 1084.167, 1116.083 >> >> >> >> >> On Sep 11, 2010, at 2:13 AM, jonszanto wrote: >> >>> >>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>> > It might look like a slight tempering of Partch's scale. >>> > >>> > This is my current thinking. >>> > >>> > I'm quite serious. >>> >>> Compromise is for pussies. In your heart, you know it's true. >>> >> >> > > >
From: genewardsmith (2010-09-14) Subject: Re: Compromise between 43EDO & Partch's 43? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > What might be some other EDOs to try to "quantize" it, all or part of the way to? The most obvious choice is 43edo, where you could push it to the point where the scale becomes proper.
From: caleb morgan (2010-09-14) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? Just a brief summary of the method to my madness. Without being able, at the moment, to put my finger on exactly *what*, I've felt something missing from 41EDO and variations on it. I tried some crazy experiments with it, trying to stick pitches I wanted in spots in mod 41 where I would never use those pitches--scale degrees 2,3, 39, and 40. There were a few others, but those were the obvious candidates. The results were absurd at best. I like some aspects of 46 EDO, but I can't fit two octaves on a standard 88-note keyboard. I prefer the 10/9, 9/8, 8/7, 7/6 approximation in 41EDO anyway. Research into bigger standard keyboards produced zip, nada, bupkis. With only 88 keys, you get the feeling that you don't want to waste any of them, not even 4. I briefly considered a double (two-octave) scale of 46 EDO with 4 pitches lopped off the top, but that didn't cut it. So, I decided to accept inconsistent fingering and go for having enough pitches with enough accuracy. I can get more pitches by simply pitch-bending the whole tuning base--I'd already constructed the tables of values. Previous work has shown this to be a somewhat funky but reliable method. The idea--proposed by someone--that one could work with a subset of the pitches one needs in Logic--which is limited to 12 pitches--and then divide the composition into groups of 12 pitches used--is insupportable because I need to be able to hear the scales changing, and I need to be able to experiment, get the sound in my hands. It's about as impractical an approach as I can possibly imagine. I'm not ready at this time to tackle dynamic retuning with LMSO, and I'm not sure if it will meet my needs. I've worked more or less this way--in the past--with a 36-pitch JI scale, by pitch-bending the instruments when going to different tuning-bases. So I know this method will work. Only the scale remained to be worked out exactly. I was hoping to broaden my horizons a little over 36-pitch JI. Using Lil' Miss Scale Oven (LMSO), I designed a big JI tonality diamond with a 19-limit. Then I threw out pitches to bring it down first to 60, then 48, then 43 pitches. Sadly, the 19s and 17s had to go. Some of the 15s had to be cheated a little, and some other pitches had to be tempered out. 43 is the most I can really fit. Then using the Quantize feature of LMSO, I've made my scale conform to 72, 87, 94. and 104 EDO, because the brilliant folks here have already done the research and understand what EDOs have good conformation to JI. So, I at least have a framework, with a continuum from almost-pure JI to something with a little more of a tempered sound. It seems to work--for me at least. It's a little hard to explain why I can tolerate some beating in octaves, some very slight sharpness in the 5ths (3/2s), but want to hear many of the 7's 11's and 13's dead-on. It might be because of the larger "field of attraction" of the very simple ratios. 72, 87, 94, 104 EDOs produce small variations in the sound of the scale--different rates of beating, subtilely different colors. Caleb On Sep 14, 2010, at 12:57 PM, caleb morgan wrote: > > Here I looked up EDOs on the Xenharmony page and chose 87EDO to quantize to: > > 0., 82.759, 110.345, 137.931, 151.724, 165.517, 179.31, 206.897, 234.483, 248.276, 262.069, 289.655, 317.241, 344.828, 358.621, 386.207, 413.793, 441.379, 496.552, 551.724, 565.517, 579.31, 620.69, 648.276, 703.448, 744.828, 758.621, 786.207, 813.793, 841.379, 855.172, 882.759, 910.345, 937.931, 965.517, 993.103, 1006.897, 1034.483, 1048.276, 1062.069, 1075.862, 1089.655, 1117.241 > > looks pretty good! > > I'm not sure about advantages or disadvantages, yet. > > It makes all the step sizes multiples of 13.793 cents, with a "sruti" pattern of: > > 6, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 4, 4, 1, 1, 3, 2, 4, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 6 > > -c > > > > On Sep 14, 2010, at 11:34 AM, caleb morgan wrote: > >> >> oops, meant 72EDO, not 76. >> >> >> -c >> >> >> On Sep 14, 2010, at 11:27 AM, caleb morgan wrote: >> >>> >>> >>> Heh. >>> >>> Thing is, you're right that I haven't been easily satisfied. >>> >>> That's why my plans keep changing. >>> >>> Now, I think I'm settling for uneven fingering and a design much closer to JI, which fits 4 octaves on two 88-key keyboards. >>> >>> It's very close to the Rube Goldberg scales I came up with, which are basically JI with an attempt at tempering out the difference between 32/27 and 13/11. >>> >>> At the same time, I discovered that Lil' Miss Scale Oven will let me do compromise tunings between a given scale and some EDO. >>> >>> My scale is printed below. I tried morphing it 50% if the way to 76EDO, just to see what would happen. The results aren't bad. >>> >>> What might be some other EDOs to try to "quantize" it, all or part of the way to? >>> >>> Caleb >>> >>> 43-pitch 13 Rube Goldberg >>> 43 >>> !cents PC Approximate ratio >>> !0. 0 1/1 >>> 84.5 1 [4/3 below 7/5, or 21/20] >>> 117.0 2 16/15-ish >>> 135.0 3 13/12 was 138.6 >>> 150.6 4 12/11 >>> ! >>> 165.0 5 11/10 >>> 179.1 6 10/9 was 182.4 >>> 207.2 7 9/8 wide with 3/2 >>> 231.2 8 8/7 >>> 247.74 9 15/13 >>> 265.2 10 7/6 lowered for low 4/3 >>> ! >>> 289.2 11 13/11 and tempered 32/27 >>> 313.6 0 6/5 >>> 344.1 1 11/9 tempered >>> 359.47 2 16/13 >>> 385.0 3 5/4 >>> 414.5 4 14/11 low to go with 22/13 >>> ! >>> 435.1 5 9/7 >>> 496.4 6 4/3 low >>> 551.3 7 11/8 >>> 563.4 8 18/13 >>> 582.5 9 7/5 >>> ! >>> 617.5 10 10/7 >>> 648.7 11 16/11 >>> 703.6 0 3/2 wide >>> 745.8 1 20/13 >>> ! >>> 764.9 2 14/9 >>> 782.5 3 11/7 >>> 819.0 4 8/5 high, originally 813.78 >>> 840.53 5 13/8 >>> 852.6 6 18/11 >>> 882.7 7 5/3 lowered with 4/3 >>> ! >>> 910.79 8 22/13 >>> 933.1 9 12/7 >>> 968.8 10 7/4 >>> 992.8 11 16/9 low with 4/3 >>> 1013.6 0 9/5 >>> ! >>> 1035.0 1 20/11 >>> 1049.4 2 11/6 >>> 1061.4 3 24/13 >>> 1071.7 4 13/7 >>> 1085.0 5 15/8 >>> 1115.5 6 [4/3 above 10/7, or 40/21] >>> ! >>> 1200.0 0 2/1 >>> >>> >>> Attempt to quantize to nearest 72EDO by 50% percent >>> >>> 0., 83.917, 116.833, 134.167, 150.3, 165.833, 181.217, 203.6, 232.267, 248.87, 265.933, 286.267, 315.133, 347.051, 363.068, 384.167, 415.583, 434.217, 498.2, 550.65, 565.033, 582.917, 617.083, 649.35, 701.8, 747.9, 765.783, 782.917, 817.833, 836.932, 851.3, 883.017, 913.728, 933.217, 967.733, 996.401, 1015.133, 1034.167, 1049.7, 1064.033, 1069.183, 1084.167, 1116.083 >>> >>> >>> >>> >>> On Sep 11, 2010, at 2:13 AM, jonszanto wrote: >>> >>>> >>>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>>> > It might look like a slight tempering of Partch's scale. >>>> > >>>> > This is my current thinking. >>>> > >>>> > I'm quite serious. >>>> >>>> Compromise is for pussies. In your heart, you know it's true. >>>> >>> >>> >> >> > > >
From: caleb morgan (2010-09-15) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? http://www.box.net/shared/m37jhti1og#/shared/m37jhti1og/1/51261090 For those who want to check out my "all the pitch that fits" approach, I've posted the original 43-note Rube Goldberg (RG) file, plus 15 variations--two are more in tune with JI, and the other 13 or so are nearly or exactly in the following EDOs: 46, 53, 72, 94, 96, 104, 159, 166, 171, 185, 190, 205, I chose these, on the whole, to make the 3/2 and the 9/8, if anything, less sharp, and I chose EDOs that didn't eliminate any of the 43 pitches. Somewhat to my surprise, they actually sound different in some intervals. The idea for this EDOs came from the Xenharmonic page: http://xenharmonic.wikispaces.com/edo Which is incredibly helpful. So, I thank Graham Breed, Gene Ward Smith, Margo Schulter, Ozan Yarman, George Secor, for their work. (Even If I accomplish nothing, I'm still appreciative.) ah, heck, even Carl Lumma and Mike Battaglia. They, more than the Flying Spaghetti Monster, have really helped me. But they bear no responsibility for my folly. Caleb On Sep 14, 2010, at 3:08 PM, caleb morgan wrote: > > Just a brief summary of the method to my madness. > > Without being able, at the moment, to put my finger on exactly *what*, I've felt something missing from 41EDO and variations on it. > > I tried some crazy experiments with it, trying to stick pitches I wanted in spots in mod 41 where I would never use those pitches--scale degrees 2,3, 39, and 40. There were a few others, but those were the obvious candidates. The results were absurd at best. > > I like some aspects of 46 EDO, but I can't fit two octaves on a standard 88-note keyboard. I prefer the 10/9, 9/8, 8/7, 7/6 approximation in 41EDO anyway. > > Research into bigger standard keyboards produced zip, nada, bupkis. > > With only 88 keys, you get the feeling that you don't want to waste any of them, not even 4. > > I briefly considered a double (two-octave) scale of 46 EDO with 4 pitches lopped off the top, but that didn't cut it. > > So, I decided to accept inconsistent fingering and go for having enough pitches with enough accuracy. I can get more pitches by simply pitch-bending the whole tuning base--I'd already constructed the tables of values. Previous work has shown this to be a somewhat funky but reliable method. > > The idea--proposed by someone--that one could work with a subset of the pitches one needs in Logic--which is limited to 12 pitches--and then divide the composition into groups of 12 pitches used--is insupportable because I need to be able to hear the scales changing, and I need to be able to experiment, get the sound in my hands. It's about as impractical an approach as I can possibly imagine. > > I'm not ready at this time to tackle dynamic retuning with LMSO, and I'm not sure if it will meet my needs. > > I've worked more or less this way--in the past--with a 36-pitch JI scale, by pitch-bending the instruments when going to different tuning-bases. So I know this method will work. > > Only the scale remained to be worked out exactly. I was hoping to broaden my horizons a little over 36-pitch JI. > > Using Lil' Miss Scale Oven (LMSO), I designed a big JI tonality diamond with a 19-limit. Then I threw out pitches to bring it down first to 60, then 48, then 43 pitches. Sadly, the 19s and 17s had to go. Some of the 15s had to be cheated a little, and some other pitches had to be tempered out. > > 43 is the most I can really fit. > > Then using the Quantize feature of LMSO, I've made my scale conform to 72, 87, 94. and 104 EDO, because the brilliant folks here have already done the research and understand what EDOs have good conformation to JI. > > So, I at least have a framework, with a continuum from almost-pure JI to something with a little more of a tempered sound. > > It seems to work--for me at least. > > It's a little hard to explain why I can tolerate some beating in octaves, some very slight sharpness in the 5ths (3/2s), but want to hear many of the 7's 11's and 13's dead-on. It might be because of the larger "field of attraction" of the very simple ratios. > > 72, 87, 94, 104 EDOs produce small variations in the sound of the scale--different rates of beating, subtilely different colors. > > Caleb > > > > > > > > > > > > On Sep 14, 2010, at 12:57 PM, caleb morgan wrote: > >> >> >> Here I looked up EDOs on the Xenharmony page and chose 87EDO to quantize to: >> >> 0., 82.759, 110.345, 137.931, 151.724, 165.517, 179.31, 206.897, 234.483, 248.276, 262.069, 289.655, 317.241, 344.828, 358.621, 386.207, 413.793, 441.379, 496.552, 551.724, 565.517, 579.31, 620.69, 648.276, 703.448, 744.828, 758.621, 786.207, 813.793, 841.379, 855.172, 882.759, 910.345, 937.931, 965.517, 993.103, 1006.897, 1034.483, 1048.276, 1062.069, 1075.862, 1089.655, 1117.241 >> >> looks pretty good! >> >> I'm not sure about advantages or disadvantages, yet. >> >> It makes all the step sizes multiples of 13.793 cents, with a "sruti" pattern of: >> >> 6, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 4, 4, 1, 1, 3, 2, 4, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 6 >> >> -c >> >> >> >> On Sep 14, 2010, at 11:34 AM, caleb morgan wrote: >> >>> >>> oops, meant 72EDO, not 76. >>> >>> >>> -c >>> >>> >>> On Sep 14, 2010, at 11:27 AM, caleb morgan wrote: >>> >>>> >>>> >>>> Heh. >>>> >>>> Thing is, you're right that I haven't been easily satisfied. >>>> >>>> That's why my plans keep changing. >>>> >>>> Now, I think I'm settling for uneven fingering and a design much closer to JI, which fits 4 octaves on two 88-key keyboards. >>>> >>>> It's very close to the Rube Goldberg scales I came up with, which are basically JI with an attempt at tempering out the difference between 32/27 and 13/11. >>>> >>>> At the same time, I discovered that Lil' Miss Scale Oven will let me do compromise tunings between a given scale and some EDO. >>>> >>>> My scale is printed below. I tried morphing it 50% if the way to 76EDO, just to see what would happen. The results aren't bad. >>>> >>>> What might be some other EDOs to try to "quantize" it, all or part of the way to? >>>> >>>> Caleb >>>> >>>> 43-pitch 13 Rube Goldberg >>>> 43 >>>> !cents PC Approximate ratio >>>> !0. 0 1/1 >>>> 84.5 1 [4/3 below 7/5, or 21/20] >>>> 117.0 2 16/15-ish >>>> 135.0 3 13/12 was 138.6 >>>> 150.6 4 12/11 >>>> ! >>>> 165.0 5 11/10 >>>> 179.1 6 10/9 was 182.4 >>>> 207.2 7 9/8 wide with 3/2 >>>> 231.2 8 8/7 >>>> 247.74 9 15/13 >>>> 265.2 10 7/6 lowered for low 4/3 >>>> ! >>>> 289.2 11 13/11 and tempered 32/27 >>>> 313.6 0 6/5 >>>> 344.1 1 11/9 tempered >>>> 359.47 2 16/13 >>>> 385.0 3 5/4 >>>> 414.5 4 14/11 low to go with 22/13 >>>> ! >>>> 435.1 5 9/7 >>>> 496.4 6 4/3 low >>>> 551.3 7 11/8 >>>> 563.4 8 18/13 >>>> 582.5 9 7/5 >>>> ! >>>> 617.5 10 10/7 >>>> 648.7 11 16/11 >>>> 703.6 0 3/2 wide >>>> 745.8 1 20/13 >>>> ! >>>> 764.9 2 14/9 >>>> 782.5 3 11/7 >>>> 819.0 4 8/5 high, originally 813.78 >>>> 840.53 5 13/8 >>>> 852.6 6 18/11 >>>> 882.7 7 5/3 lowered with 4/3 >>>> ! >>>> 910.79 8 22/13 >>>> 933.1 9 12/7 >>>> 968.8 10 7/4 >>>> 992.8 11 16/9 low with 4/3 >>>> 1013.6 0 9/5 >>>> ! >>>> 1035.0 1 20/11 >>>> 1049.4 2 11/6 >>>> 1061.4 3 24/13 >>>> 1071.7 4 13/7 >>>> 1085.0 5 15/8 >>>> 1115.5 6 [4/3 above 10/7, or 40/21] >>>> ! >>>> 1200.0 0 2/1 >>>> >>>> >>>> Attempt to quantize to nearest 72EDO by 50% percent >>>> >>>> 0., 83.917, 116.833, 134.167, 150.3, 165.833, 181.217, 203.6, 232.267, 248.87, 265.933, 286.267, 315.133, 347.051, 363.068, 384.167, 415.583, 434.217, 498.2, 550.65, 565.033, 582.917, 617.083, 649.35, 701.8, 747.9, 765.783, 782.917, 817.833, 836.932, 851.3, 883.017, 913.728, 933.217, 967.733, 996.401, 1015.133, 1034.167, 1049.7, 1064.033, 1069.183, 1084.167, 1116.083 >>>> >>>> >>>> >>>> >>>> On Sep 11, 2010, at 2:13 AM, jonszanto wrote: >>>> >>>>> >>>>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >>>>> > It might look like a slight tempering of Partch's scale. >>>>> > >>>>> > This is my current thinking. >>>>> > >>>>> > I'm quite serious. >>>>> >>>>> Compromise is for pussies. In your heart, you know it's true. >>>>> >>>> >>>> >>> >>> >> >> > > >
From: caleb morgan (2010-09-15) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? I wanted to make this "something missing" point a little more substantial. Specifically, in 41EDO I miss: 13/12 @ 138.57 cents 11/10 @ 165 cents 15/13 @ 247.7 cents 11/9 @ 347.4 cents and so forth. So, a lot of 11 and 13 harmony. While this fact is hardly a secret, it bears repeating for people like me--rather than for the old hands and experts here. Also, the 5/4 feels slightly low, though not bad. The list continues, but I wanted to confirm to myself and anyone else interested in 11 and 13-ratio harmonic sounds that these aren't well-represented. Plus, it has, for my purposes, 4 pitches I would never use right next to 1/1 and 2/1: 29.26, 58.54, 1141.4, and 1170.7. So, as Mr. Lumma said, 41 is not bad for an EDO. It's darn good. I wonder, for my own scale design--before I attempt to "burn in" my current scale--whether I ought to attempt something like Mod43-consistent 5ths and 4ths. A helpful tool for consistent fingering is this modular multiplier: http://pages.central.edu/emp/LintonT/classes/spring01/cryptography/java/Multiples.html But I think that any scheme will have to cheat something, and I've chosen to cheat regular fingering, which I intend to get around by simply labelling my keyboard with the ratios, written on a long swatch of tape above the keys, just like mixing boards are labelled with the instruments. I've already done this, and it makes finding the pitches pretty easy. The scale I intend to practice is as evenly proportioned as the sensory-motor homunculus mapping in the cortex. (That is, it's a little screwy.) http://www.google.com/images?hl=en&expIds=17259,18168,25260,25900,26447,26515,26565&sugexp=ldymls&xhr=t&q=sensory-motor+homunculus&cp=14&um=1&ie=UTF-8&source=og&sa=N&tab=wi&biw=1065&bih=836 If anyone has any (non-abusive) thoughts, let me know. Perhaps there's a mass-produced 100+ key Midi controller. That might change everything. Caleb On Sep 14, 2010, at 3:08 PM, caleb morgan wrote: > > Just a brief summary of the method to my madness. > > Without being able, at the moment, to put my finger on exactly *what*, I've felt something missing from 41EDO and variations on it. >
From: Mike Battaglia (2010-09-15) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? On Wed, Sep 15, 2010 at 9:10 AM, caleb morgan <calebmrgn@...> wrote: > > ah, heck, even Carl Lumma and Mike Battaglia. > They, more than the Flying Spaghetti Monster, have really helped me. But they bear no responsibility for my folly. Well, I do. Carl, I dunno about. -Mike
From: Carl Lumma (2010-09-15) Subject: Re: Compromise between 43EDO & Partch's 43? Caleb wrote: > But they bear no responsibility for my folly. I wasn't aware of any folly. However I would like your reactions to 41-ET if you get around to it. -Carl
From: caleb morgan (2010-09-15) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? see post of 5:55 pm, I felt that it's a wonderful EDO but lacks some pitches I want "on hand." -c On Sep 15, 2010, at 7:05 PM, Carl Lumma wrote: > Caleb wrote: > > > But they bear no responsibility for my folly. > > I wasn't aware of any folly. However I would like your > reactions to 41-ET if you get around to it. -Carl > >
From: genewardsmith (2010-09-16)
Subject: Re: Compromise between 43EDO & Partch's 43?
--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
> I wanted to make this "something missing" point a little more substantial.
>
> Specifically, in 41EDO I miss:
Here is what is found in Miracle[41] ("Studloco")
> 13/12 @ 138.57 cents
9 13/12s
> 11/10 @ 165 cents
19 11/10s
> 15/13 @ 247.7 cents
10 15/13s
> 11/9 @ 347.4 cents
38 11/9s
> and so forth.
Vast amounts of and so forth.
Below I give a particular tuning from the Scala directory, which could be tweaked to emphasize the intervals you most want.
! miracle41s.scl
!
Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976
41
!
32.84406
51.02748
83.87154
116.71559
149.55965
10/9
200.58713
233.43119
266.27525
299.11931
317.30272
350.14678
382.99084
415.83490
434.01832
466.86238
499.70643
532.55049
550.73391
583.57797
616.42203
649.26609
667.44951
700.29357
733.13762
765.98168
784.16510
817.00916
849.85322
882.69728
900.88069
933.72475
966.56881
999.41287
9/5
1050.44035
1083.28441
1116.12847
1134.31188
1167.15594
2/1
From: caleb morgan (2010-09-16) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? Wow. This looks good. You're not making it easy for me to settle on something. I'll play this one for a while too, and if I have anything to say, later, I'll say it. Much of it comes very close to the scale I was going to practice, so I'm hoping some tweak/synthesis of the two might somehow be possible. A lot of this scale comes close to 72EDO, except this looks better. -c On Sep 15, 2010, at 8:54 PM, genewardsmith wrote: > ! miracle41s.scl > ! > Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976 > 41 > ! > 32.84406 > 51.02748 > 83.87154 > 116.71559 > 149.55965 > 10/9 > 200.58713 > 233.43119 > 266.27525 > 299.11931 > 317.30272 > 350.14678 > 382.99084 > 415.83490 > 434.01832 > 466.86238 > 499.70643 > 532.55049 > 550.73391 > 583.57797 > 616.42203 > 649.26609 > 667.44951 > 700.29357 > 733.13762 > 765.98168 > 784.16510 > 817.00916 > 849.85322 > 882.69728 > 900.88069 > 933.72475 > 966.56881 > 999.41287 > 9/5 > 1050.44035 > 1083.28441 > 1116.12847 > 1134.31188 > 1167.15594 > 2/1
From: caleb morgan (2010-09-16) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? This scale seems to be the clear winner. I have nothing to say, so I'm going to post some doggerel. Tuning and tuning in his widening gyre, The Fatso tries an EDO. Fifths move apart, the tritone cannot hold; The Fatso wears a Speedo. Sure, some tunings fit his hands. Sure some Miracle has hit the fan, Another tuning! The tuner's had enough, But he only sits and eats some Cheetos. The time to Shed has come again, his happy tinkering at an end, Patience, practice, is his credo, But the fatso lacks libido. (tuner, fatso = me, so no one should think this is about them.) caleb On Sep 16, 2010, at 5:30 AM, caleb morgan wrote: > Wow. This looks good. You're not making it easy for me to settle on something. I'll play this one for a while too, and if I have anything to say, later, I'll say it. Much of it comes very close to the scale I was going to practice, so I'm hoping some tweak/synthesis of the two might somehow be possible. > > > A lot of this scale comes close to 72EDO, except this looks better. > > -c > > > On Sep 15, 2010, at 8:54 PM, genewardsmith wrote: > >> ! miracle41s.scl >> ! >> Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976 >> 41 >> ! >> 32.84406 >> 51.02748 >> 83.87154 >> 116.71559 >> 149.55965 >> 10/9 >> 200.58713 >> 233.43119 >> 266.27525 >> 299.11931 >> 317.30272 >> 350.14678 >> 382.99084 >> 415.83490 >> 434.01832 >> 466.86238 >> 499.70643 >> 532.55049 >> 550.73391 >> 583.57797 >> 616.42203 >> 649.26609 >> 667.44951 >> 700.29357 >> 733.13762 >> 765.98168 >> 784.16510 >> 817.00916 >> 849.85322 >> 882.69728 >> 900.88069 >> 933.72475 >> 966.56881 >> 999.41287 >> 9/5 >> 1050.44035 >> 1083.28441 >> 1116.12847 >> 1134.31188 >> 1167.15594 >> 2/1 > > >
From: caleb morgan (2010-09-16) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? >all the pitches I want except 22/13 and 20/11? check >consistent fingering? check Darn your superior facts, logic and knowledge of scale theory. But...but...doesn't this here miracle41s scale lack some ineffable um, *soul*? Perhaps it's....*too* perfect. Yeah, that's the ticket. Do I care that the 5ths are a teeny-tiny bit low? -c On Sep 16, 2010, at 5:30 AM, caleb morgan wrote: > Wow. This looks good. You're not making it easy for me to settle on something. I'll play this one for a while too, and if I have anything to say, later, I'll say it. Much of it comes very close to the scale I was going to practice, so I'm hoping some tweak/synthesis of the two might somehow be possible. > > > A lot of this scale comes close to 72EDO, except this looks better. > > -c > > > On Sep 15, 2010, at 8:54 PM, genewardsmith wrote: > >> ! miracle41s.scl >> ! >> Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976 >> 41 >> ! >> 32.84406 >> 51.02748 >> 83.87154 >> 116.71559 >> 149.55965 >> 10/9 >> 200.58713 >> 233.43119 >> 266.27525 >> 299.11931 >> 317.30272 >> 350.14678 >> 382.99084 >> 415.83490 >> 434.01832 >> 466.86238 >> 499.70643 >> 532.55049 >> 550.73391 >> 583.57797 >> 616.42203 >> 649.26609 >> 667.44951 >> 700.29357 >> 733.13762 >> 765.98168 >> 784.16510 >> 817.00916 >> 849.85322 >> 882.69728 >> 900.88069 >> 933.72475 >> 966.56881 >> 999.41287 >> 9/5 >> 1050.44035 >> 1083.28441 >> 1116.12847 >> 1134.31188 >> 1167.15594 >> 2/1 > > >
From: caleb morgan (2010-09-16) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? Here are 4 micro-variations on miracle41 stud-loco, by quantizing to different EDOs, using Lil Miss Scale Oven. I just had to try it, I'm not sure if there are any advantages, yet. But they all do sound a little different. ! miracle 41 Stud Loco in 46EDO 41 ! 26.08700 52.17400 78.26100 104.34800 156.52200 182.60900 208.69600 234.78300 260.87000 286.95700 313.04300 339.13000 391.30400 417.39100 443.47800 469.56500 495.65200 521.73900 547.82600 573.91300 626.08700 652.17400 678.26100 704.34800 730.43500 756.52200 782.60900 808.69600 860.87000 886.95700 913.04300 939.13000 965.21700 991.30400 1017.39100 1043.47800 1095.65200 1121.73900 1147.82600 1173.91300 1200.00000 ! miracle41 SL in 94 EDO 41 ! 38.29787 51.06383 89.36170 114.89362 153.19149 178.72340 204.25532 229.78723 268.08511 293.61702 319.14894 344.68085 382.97872 421.27660 434.04255 472.34043 497.87234 536.17021 548.93617 587.23404 612.76596 651.06383 663.82979 702.12766 727.65957 765.95745 778.72340 817.02128 855.31915 880.85106 906.38298 931.91489 970.21277 995.74468 1021.27660 1046.80851 1085.10638 1110.63830 1136.17021 1161.70213 1200.00000 ! miracle 41 Stud Loco quantized to 159 EDO miracle41s in 159 EDO 41 ! 30.18900 52.83000 83.01900 113.20800 150.94300 181.13200 203.77400 233.96200 264.15100 301.88700 316.98100 347.17000 384.90600 415.09400 437.73600 467.92500 498.11300 535.84900 550.94300 581.13200 618.86800 649.05700 664.15100 701.88700 732.07500 762.26400 784.90600 815.09400 852.83000 883.01900 898.11300 935.84900 966.03800 996.22600 1018.86800 1049.05700 1086.79200 1116.98100 1132.07600 1169.81100 1200.00000 ! miracle41s in 171 EDO 41 ! 35.08800 49.12300 84.21100 119.29800 147.36800 182.45600 203.50900 231.57900 266.66700 301.75400 315.78900 350.87700 385.96500 414.03500 435.08800 470.17500 498.24600 533.33300 547.36800 582.45600 617.54400 652.63200 666.66700 701.75400 729.82500 764.91200 785.96500 814.03500 849.12300 884.21100 898.24600 933.33300 968.42100 996.49100 1017.54400 1052.63200 1080.70200 1115.78900 1136.84200 1164.91200 1200.00000 On Sep 16, 2010, at 6:21 AM, caleb morgan wrote: > >all the pitches I want except 22/13 and 20/11? check > > > >consistent fingering? check > > Darn your superior facts, logic and knowledge of scale theory. > > But...but...doesn't this here miracle41s scale lack some ineffable um, *soul*? Perhaps it's....*too* perfect. Yeah, that's the ticket. > > Do I care that the 5ths are a teeny-tiny bit low? > > -c > > > On Sep 16, 2010, at 5:30 AM, caleb morgan wrote: > >> >> Wow. This looks good. You're not making it easy for me to settle on something. I'll play this one for a while too, and if I have anything to say, later, I'll say it. Much of it comes very close to the scale I was going to practice, so I'm hoping some tweak/synthesis of the two might somehow be possible. >> >> >> A lot of this scale comes close to 72EDO, except this looks better. >> >> -c >> >> >> On Sep 15, 2010, at 8:54 PM, genewardsmith wrote: >> >>> ! miracle41s.scl >>> ! >>> Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976 >>> 41 >>> ! >>> 32.84406 >>> 51.02748 >>> 83.87154 >>> 116.71559 >>> 149.55965 >>> 10/9 >>> 200.58713 >>> 233.43119 >>> 266.27525 >>> 299.11931 >>> 317.30272 >>> 350.14678 >>> 382.99084 >>> 415.83490 >>> 434.01832 >>> 466.86238 >>> 499.70643 >>> 532.55049 >>> 550.73391 >>> 583.57797 >>> 616.42203 >>> 649.26609 >>> 667.44951 >>> 700.29357 >>> 733.13762 >>> 765.98168 >>> 784.16510 >>> 817.00916 >>> 849.85322 >>> 882.69728 >>> 900.88069 >>> 933.72475 >>> 966.56881 >>> 999.41287 >>> 9/5 >>> 1050.44035 >>> 1083.28441 >>> 1116.12847 >>> 1134.31188 >>> 1167.15594 >>> 2/1 >> >> > > >
From: genewardsmith (2010-09-16) Subject: Re: Compromise between 43EDO & Partch's 43? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > Here are 4 micro-variations on miracle41 stud-loco, > > by quantizing to different EDOs, using Lil Miss Scale Oven. > > I just had to try it, I'm not sure if there are any advantages, yet. > > But they all do sound a little different. Flying in the face of the ancient wisdom which says if it ain't broke, don't fix it, I'll take a stab at it: ! studwacko.scl Tweaked miracle41s.scl 41 ! 33.60446 50.12246 83.22129 116.66878 150.11628 183.21510 199.73311 233.33756 266.53967 300.89382 316.92405 349.73617 383.66091 417.32974 432.94139 466.78427 500.17066 533.68151 549.32740 583.23392 616.58329 650.76422 666.40459 699.58485 733.75271 766.93297 782.57334 816.75427 850.10364 884.01016 899.65606 933.16690 966.55329 1000.39617 1016.00782 1049.67666 1083.60139 1116.41351 1132.44374 1166.79790 1200.00000
From: caleb morgan (2010-09-17)
Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43?
Just to clear up one thing.
When I read the response below, I was persuaded that some variant of 41 had everything I wanted.
However, today I realize something that may or may not be important for my own music.
While 41Miracle Stud Loco may have 19 13/12's, etc. it doesn't have 13/12 *in relation to 1/1*. And the same all the way down the list.
So, there's always going to be a trade-off between consistent fingering, number of keys, and accuracy.
This is not hard to understand, but I keep hoping for a new solution.
Many times, I've read that such-and-such an EDO is a complete x-limit system. For instance, iirc, 58 EDO.
Today I'm going to see if somehow I can take a 44-note scale, and keep the epimorphism aspect so that all approximate 5ths (3/2s) are the same number of keys, same with all 4ths (4/3s) . So in Mod 44, it makes somewhat consistent patterns.
Then I'm going to design a two-octave version of the scale where the next-to-top note is removed to give a 4/1 on the very highest key.
The question that I don't know about is how much I can make the 3'2 in mod 44 not be too sharp before the result is ridiculous. That's the beauty of not having done this before.
I saw George Secor's In Defense of Inequality, and I've been a fan of Gene Ward Smith's epimorphic scales.
Perhaps there's something in 44 that is epimorphic and 4ths-5ths consistent or nearly so, and I only have to mutilate it slightly.
One of the advantages of being a relative newbie/ignoramous is that you don't quite know when something is impossible.
So you can tinker for *just one more day*...
hmm, here's 44, the 5th would sit at 709.091 and the 9th at 218.18, which is way too high:
0., 27.273, 54.545, 81.818, 109.091, 136.364, 163.636, 190.909, 218.182, 245.455, 272.727, 300., 327.273, 354.545, 381.818, 409.091, 436.364, 463.636, 490.909, 518.182, 545.455, 572.727, 600., 627.273, 654.545, 681.818, 709.091, 736.364, 763.636, 790.909, 818.182,
4ths want to be every 18 keys
5ths want to be every 26 keys
I only need a chain of good 5ths and 4ths moderately sharp, say 703.6, that lasts for 7 pitches in either direction.
That would mean that the following keyboard keys are spoken for:
chain of 4ths
k = 1 2 3 4 5 6 7
18*k= 18 36 10 28 2 20 38
chain of 5ths
k = 1 2 3 4 5 6 7
26*k= 26 8 34 16 42 24 6
Perhaps this chain could be extended a bit farther, as well, I don't know.
And everything else needs to fit between these, at least, if not more so.
It would be an ec-centric version of 22x2 notes, with fifths not so sharp, with one note lopped to allow for a 4/1 on top, on an 88-note controller.
Today's quixotic design adventure.
41 is probably better, though.
Hope springs eternal in the mind of the deluded one, but he recognizes reality, too.
-caleb
On Sep 15, 2010, at 8:54 PM, genewardsmith wrote:
>
>
> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> >
> > I wanted to make this "something missing" point a little more substantial.
> >
> > Specifically, in 41EDO I miss:
>
> Here is what is found in Miracle[41] ("Studloco")
>
> > 13/12 @ 138.57 cents
>
> 9 13/12s
>
> > 11/10 @ 165 cents
>
> 19 11/10s
>
> > 15/13 @ 247.7 cents
>
> 10 15/13s
>
> > 11/9 @ 347.4 cents
>
> 38 11/9s
>
> > and so forth.
>
> Vast amounts of and so forth.
>
> Below I give a particular tuning from the Scala directory, which could be tweaked to emphasize the intervals you most want.
>
> ! miracle41s.scl
> !
> Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976
> 41
> !
> 32.84406
> 51.02748
> 83.87154
> 116.71559
> 149.55965
> 10/9
> 200.58713
> 233.43119
> 266.27525
> 299.11931
> 317.30272
> 350.14678
> 382.99084
> 415.83490
> 434.01832
> 466.86238
> 499.70643
> 532.55049
> 550.73391
> 583.57797
> 616.42203
> 649.26609
> 667.44951
> 700.29357
> 733.13762
> 765.98168
> 784.16510
> 817.00916
> 849.85322
> 882.69728
> 900.88069
> 933.72475
> 966.56881
> 999.41287
> 9/5
> 1050.44035
> 1083.28441
> 1116.12847
> 1134.31188
> 1167.15594
> 2/1
>
>
From: caleb morgan (2010-09-17)
Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43?
Here would be the framework that is consistent, before I start trying to see what I can fit.
I'm not smart enough to see in advance whether this has advantages
0 1/1
1
2 pyth b2-4ths chain, low!
3
4
5
6
7
8 9/8wide
9 8/7 goes here
10 32/27low
11
12
13
14 16/13 here
15 5/4!
16 81/64 high
17
18 4/3 low
19
20 4ths-chain tritone, low
21
22
23
24 5ths-chain tritone, high
25
26 3/2 high @ 703.6
27
28 128/81 low!
29 8/5!
30 13/8 here
31
32
33
34 27/16wider
35 7/4 goes here
36 16/9 low
37
38
39
40
41 15/8 is here!
42 pyth major 7th, higher than high!
43 (this note will be removed on top octave, to make top note be 4/1)
44
On Sep 17, 2010, at 9:57 AM, caleb morgan wrote:
>
> Just to clear up one thing.
>
> When I read the response below, I was persuaded that some variant of 41 had everything I wanted.
>
> However, today I realize something that may or may not be important for my own music.
>
> While 41Miracle Stud Loco may have 19 13/12's, etc. it doesn't have 13/12 *in relation to 1/1*. And the same all the way down the list.
>
> So, there's always going to be a trade-off between consistent fingering, number of keys, and accuracy.
>
> This is not hard to understand, but I keep hoping for a new solution.
>
> Many times, I've read that such-and-such an EDO is a complete x-limit system. For instance, iirc, 58 EDO.
>
> Today I'm going to see if somehow I can take a 44-note scale, and keep the epimorphism aspect so that all approximate 5ths (3/2s) are the same number of keys, same with all 4ths (4/3s) . So in Mod 44, it makes somewhat consistent patterns.
>
> Then I'm going to design a two-octave version of the scale where the next-to-top note is removed to give a 4/1 on the very highest key.
>
> The question that I don't know about is how much I can make the 3'2 in mod 44 not be too sharp before the result is ridiculous. That's the beauty of not having done this before.
>
> I saw George Secor's In Defense of Inequality, and I've been a fan of Gene Ward Smith's epimorphic scales.
>
> Perhaps there's something in 44 that is epimorphic and 4ths-5ths consistent or nearly so, and I only have to mutilate it slightly.
>
> One of the advantages of being a relative newbie/ignoramous is that you don't quite know when something is impossible.
>
> So you can tinker for *just one more day*...
>
> hmm, here's 44, the 5th would sit at 709.091 and the 9th at 218.18, which is way too high:
>
> 0., 27.273, 54.545, 81.818, 109.091, 136.364, 163.636, 190.909, 218.182, 245.455, 272.727, 300., 327.273, 354.545, 381.818, 409.091, 436.364, 463.636, 490.909, 518.182, 545.455, 572.727, 600., 627.273, 654.545, 681.818, 709.091, 736.364, 763.636, 790.909, 818.182,
>
> 4ths want to be every 18 keys
>
> 5ths want to be every 26 keys
>
> I only need a chain of good 5ths and 4ths moderately sharp, say 703.6, that lasts for 7 pitches in either direction.
>
> That would mean that the following keyboard keys are spoken for:
>
> chain of 4ths
> k = 1 2 3 4 5 6 7
> 18*k= 18 36 10 28 2 20 38
>
> chain of 5ths
>
> k = 1 2 3 4 5 6 7
> 26*k= 26 8 34 16 42 24 6
>
> Perhaps this chain could be extended a bit farther, as well, I don't know.
>
>
> And everything else needs to fit between these, at least, if not more so.
>
> It would be an ec-centric version of 22x2 notes, with fifths not so sharp, with one note lopped to allow for a 4/1 on top, on an 88-note controller.
>
> Today's quixotic design adventure.
>
>
> 41 is probably better, though.
>
> Hope springs eternal in the mind of the deluded one, but he recognizes reality, too.
>
>
>
> -caleb
>
>
>
>
>
> On Sep 15, 2010, at 8:54 PM, genewardsmith wrote:
>
>>
>>
>>
>> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>> >
>> > I wanted to make this "something missing" point a little more substantial.
>> >
>> > Specifically, in 41EDO I miss:
>>
>> Here is what is found in Miracle[41] ("Studloco")
>>
>> > 13/12 @ 138.57 cents
>>
>> 9 13/12s
>>
>> > 11/10 @ 165 cents
>>
>> 19 11/10s
>>
>> > 15/13 @ 247.7 cents
>>
>> 10 15/13s
>>
>> > 11/9 @ 347.4 cents
>>
>> 38 11/9s
>>
>> > and so forth.
>>
>> Vast amounts of and so forth.
>>
>> Below I give a particular tuning from the Scala directory, which could be tweaked to emphasize the intervals you most want.
>>
>> ! miracle41s.scl
>> !
>> Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976
>> 41
>> !
>> 32.84406
>> 51.02748
>> 83.87154
>> 116.71559
>> 149.55965
>> 10/9
>> 200.58713
>> 233.43119
>> 266.27525
>> 299.11931
>> 317.30272
>> 350.14678
>> 382.99084
>> 415.83490
>> 434.01832
>> 466.86238
>> 499.70643
>> 532.55049
>> 550.73391
>> 583.57797
>> 616.42203
>> 649.26609
>> 667.44951
>> 700.29357
>> 733.13762
>> 765.98168
>> 784.16510
>> 817.00916
>> 849.85322
>> 882.69728
>> 900.88069
>> 933.72475
>> 966.56881
>> 999.41287
>> 9/5
>> 1050.44035
>> 1083.28441
>> 1116.12847
>> 1134.31188
>> 1167.15594
>> 2/1
>>
>
>
>
From: genewardsmith (2010-09-17) Subject: Re: Compromise between 43EDO & Partch's 43? --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > While 41Miracle Stud Loco may have 19 13/12's, etc. it doesn't have 13/12 *in relation to 1/1*. And the same all the way down the list. You can move the 1/1 wherever you like.
From: caleb morgan (2010-09-17) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? Heh. My obsession has led me to actually consider a non-standard keyboard. Are there any keyboards that are velocity-sensitive, have more than 120 or so keys, and are by companies that won't go out of business*, and don't cost over $1,000? [/Gripe mode] Why are there no companies that make standard keyboard with 97 keys (48x2 (+1)) [/Gripe mode] Otherwise, I might as well just settle down and learn 41 and variants. Its layout on a standard keyboard is actually sort of beautiful. And, I can use pitch-bend on the whole thing to move the 1/1 around with all the other pitches. -c *This is pretty important to me, as I've been burned before. On Sep 17, 2010, at 12:04 PM, genewardsmith wrote: > > > --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: > > > While 41Miracle Stud Loco may have 19 13/12's, etc. it doesn't have 13/12 *in relation to 1/1*. And the same all the way down the list. > > You can move the 1/1 wherever you like. > >
From: Carl Lumma (2010-09-17) Subject: Re: Compromise between 43EDO & Partch's 43? --- In tuning@yahoogroups.com, caleb morgan wrote: > > Heh. > > My obsession has led me to actually consider a non-standard > keyboard. That's crazy, Caleb. Why would you ever consider trying something other than the 7-white 5-black piano layout, which as we all know, is perfect for all tunings at all times? > Are there any keyboards that are velocity-sensitive, have more > than 120 or so keys, and are by companies that won't go out of > business*, and don't cost over $1,000? No. However, you can get a velocity-sensitive keyboard with 98 keys for about $500! http://www.c-thru-music.com/cgi/?page=prod_axis-49 And you should. -Carl
From: caleb morgan (2010-09-20) Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43? I've got a fever of 87. I'm both using 87EDO as a tuning, but I'm also thinking in terms of an 87-key +1 (top octave) system. By taking a scale of Gene Ward Smith that I had tweaked several times, and removing some notes so that it was down to 44, I was able to come up with a scale that has all the pitches I want, plus operates in a 87-unit or 174-unit 2-octave tuning. The top key on the keyboard is 4/1. The pattern of intervals and srutis: 4, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 4, 4, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 4 0, 4, 6, 8, 10, 11, 13, 15, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 62, 64, 66, 68, 70, 72, 74, 76, 77, 79, 81, 83, 87, 91, 93, 95, 97, 98, 100, 102, 104, 106, 108, 110, 112, 113, 115, 117, 119, 121, 123, 125, 127, 129, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 149, 151, 153, 155, 157, 159, 161, 163, 164, 166, 168, 170, 174 and the scale in cents: 0., 55.172, 82.759, 110.345, 137.931, 151.724, 179.31, 206.897, 234.483, 262.069, 289.655, 317.241, 344.828, 358.621, 386.207, 413.793, 441.379, 468.966, 496.552, 524.138, 551.724, 579.31, 593.103, 620.69, 648.276, 675.862, 703.448, 731.034, 758.621, 786.207, 813.793, 841.379, 855.172, 882.759, 910.345, 937.931, 965.517, 993.103, 1020.69, 1048.276, 1062.069, 1089.655, 1117.241, 1144.828, 1200., 1255.172, 1282.759, 1310.345, 1337.931, 1351.724, 1379.31, 1406.897, 1434.483, 1462.069, 1489.655, 1517.241, 1544.828, 1558.621, 1586.207, 1613.793, 1641.379, 1668.966, 1696.552, 1724.138, 1751.724, 1779.31, 1793.103, 1820.69, 1848.276, 1875.862, 1903.448, 1931.034, 1958.621, 1986.207, 2013.793, 2041.379, 2055.172, 2082.759, 2110.345, 2137.931, 2165.517, 2193.103, 2220.69, 2248.276, 2262.069, 2289.655, 2317.241, 2400. and the intervals in cents: 55.172, 27.587, 27.586, 27.586, 13.793, 27.586, 27.587, 27.586, 27.586, 27.586, 27.586, 27.587, 13.793, 27.586, 27.586, 27.586, 27.587, 27.586, 27.586, 27.586, 27.586, 13.793, 27.587, 27.586, 27.586, 27.586, 27.586, 27.587, 27.586, 27.586, 27.586, 13.793, 27.587, 27.586, 27.586, 27.586, 27.586, 27.587, 27.586, 13.793, 27.586, 27.586, 27.587, 55.172, 55.172, 27.587, 27.586, 27.586, 13.793, 27.586, 27.587, 27.586, 27.586, 27.586, 27.586, 27.587, 13.793, 27.586, 27.586, 27.586, 27.587, 27.586, 27.586, 27.586, 27.586, 13.793, 27.587, 27.586, 27.586, 27.586, 27.586, 27.587, 27.586, 27.586, 27.586, 13.793, 27.587, 27.586, 27.586, 27.586, 27.586, 27.587, 27.586, 13.793, 27.586, 27.586, 82.759, For some reason, thinking that 87 is 29x3, so this is a 400-cent symmetrical system, and seeing the pattern of srutis above, with the many stretches of 2's with a 1 every 7 or 8--this piques my combinatorial curiosity. I bet there are many strange common-tone situations to be explored. On Sep 17, 2010, at 12:40 PM, caleb morgan wrote: > > Heh. > > My obsession has led me to actually consider a non-standard keyboard. > > Are there any keyboards that are velocity-sensitive, have more than 120 or so keys, and are by companies that won't go out of business*, and don't cost over $1,000? > > [/Gripe mode] Why are there no companies that make standard keyboard with 97 keys (48x2 (+1)) [/Gripe mode] > > > Otherwise, I might as well just settle down and learn 41 and variants. > > Its layout on a standard keyboard is actually sort of beautiful. > > And, I can use pitch-bend on the whole thing to move the 1/1 around with all the other pitches. > > -c > > *This is pretty important to me, as I've been burned before. > > > > On Sep 17, 2010, at 12:04 PM, genewardsmith wrote: > >> >> >> >> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote: >> >> > While 41Miracle Stud Loco may have 19 13/12's, etc. it doesn't have 13/12 *in relation to 1/1*. And the same all the way down the list. >> >> You can move the 1/1 wherever you like. >> > > >
From: Graham Breed (2010-09-21)
Subject: Re: [tuning] Re: Compromise between 43EDO & Partch's 43?
On 20 September 2010 18:13, caleb morgan <calebmrgn@...> wrote:
> For some reason, thinking that 87 is 29x3, so this is a 400-cent
> symmetrical system, and seeing the pattern of srutis above, with the many
> stretches of 2's with a 1 every 7 or 8--this piques my combinatorial
> curiosity.
>
29x3 is Mystery:
http://x31eq.com/cgi-bin/rt.cgi?ets=29+87&limit=13
but that doesn't divide the octave into three parts. This does:
http://x31eq.com/cgi-bin/rt.cgi?ets=72+87&limit=13
Graham