Topic: reality of using tuning systems in fretted instruments
2 scales
| File | Description | Notes | Period (¢) | Limit |
|---|---|---|---|---|
| shahin | Mohajeri Shahin Iranian style scale tuning@yahoo April 9 2006 | 18 | 1200.0 | 89 |
| shahin118 | Shahin scale in 118-et | 18 | 1200.0 |
Thread (13 messages)
From: Mohajeri Shahin (2006-03-15) Subject: reality of using tuning systems in fretted instruments Hi all Nowadays , I'm thinking about the usage of theoretical concepts. All the systems of tuning can be used in non-acoustic musical instruments or in instruments such as paino and ..... but what about fretted-string instruments like tar <http://www.newtonmusichall.com/thetar.html> and setar <http://www.newtonmusichall.com/thesettar.html> ? Assume some points : 1- string-length of tar is for example about 66 cm ( 660 mm). 2- the accuracy of moving fretts is 1 mm. using scala for making 660-EDL (equal divisions of length) system , we see that : we have pure fifth and fourth but no major second of 9/8. now assume string-length of my setar which is 64 cm ( 640 mm). using scala for making 640-EDL system , we see that : we have pure fourth but no pure fifth of 3/2 and major second of 9/8. if I assume the accuracy of moving fretts in my setar is 0.3333(or 1/3) mm then have 1980-EDL and have : 4/3 , 3/2 , ..... but we cant have 16/9 and ..... now the conditions change : according to scale length compensation for fretted instruments , we know that the real places of frets on setar neck which depend on height of bridge and nut and fretts and , ..... are different from interval position on strings and are lesser( considering position of frett from nut) , so we must consider the real place of octave in the neck of instrument for new scale length . for length of 640 mm the octave is lesser than 320 mm ( from nut) so the EDL must have lesser than 320 degrees. for my setar due to an inaccurate measurement the first octave is fretted about 3 mm lesser than position of interval on string (317 mm) . an example :fretting my setar according to 19-edo results a system with errors between 1 and -1.5 cent : @@@@@@@@ 19-edo @@@ tuning scale after fretting @@ difference of 19-edo with the fretting scale (length of vibrating part from nut in my setar @@@@@@@@@@@@@@@@@@@@@@@@@@@@ with accuracy of 0.5 mm without compensation) 0 @@ 0 @@ 0 @@ 0 1 @@ 63.15789474 @@ 63.36169889 @@ -0.203804149 2 @@ 126.3157895 @@ 126.218684 @@ 0.097105443 3 @@ 189.4736842 @@ 189.9341026 @@ -0.460418435 4 @@ 252.6315789 @@ 252.9509096 @@ -0.319330636 5 @@ 315.7894737 @@ 316.7236466 @@ -0.93417287 6 @@ 378.9473684 @@ 379.5642548 @@ -0.616886411 7 @@ 442.1052632 @@ 441.2781414 @@ 0.827121757 8 @@ 505.2631579 @@ 505.2735443 @@ -0.010386393 9 @@ 568.4210526 @@ 567.9661853 @@ 0.454867282 10 @@ 631.5789474 @@ 631.0661833 @@ 0.512764099 11 @@ 694.7368421 @@ 694.5320409 @@ 0.204801175 12 @@ 757.8947368 @@ 758.3161482 @@ -0.421411319 13 @@ 821.0526316 @@ 822.3641692 @@ -1.311537634 14 @@ 884.2105263 @@ 884.358713 @@ -0.148186684 15 @@ 947.3684211 @@ 948.6559612 @@ -1.287540193 16 @@ 1010.526316 @@ 1010.577397 @@ -0.05108124 17 @@ 1073.684211 @@ 1074.796008 @@ -1.111797696 18 @@ 1136.842105 @@ 1136.266396 @@ 0.575709015 19 @@ 1200 @@ 1200 @@ 0 according to compensation to have octave of about 317 mm and actual length of 634 mm , the difference of these 2 pseudo-19-edo systems which are parts of 640-EDL and 634-EDL systems( or more accurate , with 0.5 mm accuracy , 1280-edl and 1268-edl ) are between 1.5 and -2.5 cent. In 1268-edl we have 4/3 but no 3/2 and if we consider a fifth we cant have second major of fifth - fourth so the system of temperament is irregular . it is obviously that the aquracy of moving fretts , the geometrical parameters of string and nut and compensation and other physical factors.... imposes the systems of tuning in fretted instruments. so I think the realistic tuning systems for fretted instruments ( and may be fretless ) are EDL systems according to real length of octave and string . Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak <file:///C:\Documents%20and%20Settings\shahinm.000\Desktop\www.geocities .com\acousticsoftombak> My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html <http://www.harmonytalk.com/archives/000296.html> www.harmonytalk.com/archives/000288.html <http://www.harmonytalk.com/archives/000288.html> My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm <http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>
From: Aaron Wolf (2006-03-15) Subject: Re: reality of using tuning systems in fretted instruments Shaahin, Your whole basis of calculation is fundamentally confused. Having 1mm accuracy at most for moving of frets doesn't mean that 640mm gets translated into 640 EDO. First off, 1mm of movement is a very different pitch change near the nut than near the bridge, so with 1mm accuracy, we have decreasing pitch accuracy the closer we get to the bridge. Secondly, 1mm accuracy simply means we must accept a 1mm range of offset, not that we are going to have perfectly exact 1mm movements. So we might be have a perfect 3/2 interval, but it could also end up off by as much as 1mm offset would be at that point in the scale, because we can't be perfect. But even still, exact fretting, from pressure towards the neck to pulling or pushing up or down towards or away from the fret has such a significant impact on tuning that we have much less perfect accuracy on top of that. A lot is up to the subtle control of the musician's careful playing and ear. There is a legitimate discussion about how much consistent accuracy can be possibly acheived on a fretted instrument, but your discussion of fretting compared to EDOs really is not applicable. -Aaron
From: Dave Keenan (2006-03-15) Subject: Re: reality of using tuning systems in fretted instruments --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote: > All the systems of tuning can be used in non-acoustic musical > instruments or in instruments such as paino and ..... but what about > fretted-string instruments like tar ... > so I think the realistic tuning systems for fretted instruments ( and > may be fretless ) are EDL systems according to real length of octave and > string . Hi Shaahin, You may find this article useful: "Optimising JI guitar designs using linear microtemperaments or If it aint Baroque don't waste your lute fixing it" http://users.bigpond.net.au/d.keenan/Music/MicroGuitar.pdf It shows how linear temperaments (non-equal) can be implemented on fretted instruments using only continuous frets, and it gives a number of linear temperaments that approach just intonation with errors less than typical fretting+playing errors. -- Dave Keenan
From: Carl Lumma (2006-03-15) Subject: Re: reality of using tuning systems in fretted instruments > Hi Shaahin, > > You may find this article useful: > "Optimising JI guitar designs using linear microtemperaments > or > If it aint Baroque don't waste your lute fixing it" > http://users.bigpond.net.au/d.keenan/Music/MicroGuitar.pdf > > It shows how linear temperaments (non-equal) can be implemented > on fretted instruments using only continuous frets, and it gives > a number of linear temperaments that approach just intonation > with errors less than typical fretting+playing errors. I always thought this was one of your coolest projects. I'm not a guitarist, but it seemed to be really good thinking, and the state transition diagrams were the bomb. I wish some more guitarists would take note of this paper (maybe they have and I haven't heard of it). -Carl
From: Mohajeri Shahin (2006-03-16) Subject: RE: [tuning] Re: reality of using tuning systems in fretted instruments Dear Aaron I know all the things you wrote , Please notice to EDL , it is not the same as EDO : EDL is equal divisions of length as discussed before in group in some mail , It is proposed by ozan instead of my EDS(equal divisions of string). Best for you Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html <http://www.harmonytalk.com/archives/000296.html> www.harmonytalk.com/archives/000288.html <http://www.harmonytalk.com/archives/000288.html> My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm <http://www.drumdojo.com/world/persia/tonbak_acoustics.htm> ________________________________ From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Aaron Wolf Sent: Wednesday, March 15, 2006 6:46 PM To: tuning@yahoogroups.com Subject: [tuning] Re: reality of using tuning systems in fretted instruments Shaahin, Your whole basis of calculation is fundamentally confused. Having 1mm accuracy at most for moving of frets doesn't mean that 640mm gets translated into 640 EDO. First off, 1mm of movement is a very different pitch change near the nut than near the bridge, so with 1mm accuracy, we have decreasing pitch accuracy the closer we get to the bridge. Secondly, 1mm accuracy simply means we must accept a 1mm range of offset, not that we are going to have perfectly exact 1mm movements. So we might be have a perfect 3/2 interval, but it could also end up off by as much as 1mm offset would be at that point in the scale, because we can't be perfect. But even still, exact fretting, from pressure towards the neck to pulling or pushing up or down towards or away from the fret has such a significant impact on tuning that we have much less perfect accuracy on top of that. A lot is up to the subtle control of the musician's careful playing and ear. There is a legitimate discussion about how much consistent accuracy can be possibly acheived on a fretted instrument, but your discussion of fretting compared to EDOs really is not applicable. -Aaron 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. SPONSORED LINKS Music education <http://groups.yahoo.com/gads?t=ms&k=Music+education&w1=Music+education& w2=Music+production+education&w3=Music+education+degree&w4=Degree+educat ion+music+online&w5=Music+business+education&w6=Music+education+online&c =6&s=174&.sig=zMNRfOOOdo7nVqxhYS_0Yg> Music production education <http://groups.yahoo.com/gads?t=ms&k=Music+production+education&w1=Music +education&w2=Music+production+education&w3=Music+education+degree&w4=De gree+education+music+online&w5=Music+business+education&w6=Music+educati on+online&c=6&s=174&.sig=xvNPUlceIGAdVcjAsHH8JA> Music education degree <http://groups.yahoo.com/gads?t=ms&k=Music+education+degree&w1=Music+edu cation&w2=Music+production+education&w3=Music+education+degree&w4=Degree +education+music+online&w5=Music+business+education&w6=Music+education+o nline&c=6&s=174&.sig=lrDYh_-yrdu524mpql-csg> Degree education music online <http://groups.yahoo.com/gads?t=ms&k=Degree+education+music+online&w1=Mu sic+education&w2=Music+production+education&w3=Music+education+degree&w4 =Degree+education+music+online&w5=Music+business+education&w6=Music+educ ation+online&c=6&s=174&.sig=SVm8lC0-Q2tryy6Hv14ihQ> Music business education <http://groups.yahoo.com/gads?t=ms&k=Music+business+education&w1=Music+e ducation&w2=Music+production+education&w3=Music+education+degree&w4=Degr ee+education+music+online&w5=Music+business+education&w6=Music+education +online&c=6&s=174&.sig=pCxzd_uR0dRaYO3MB1Fpvw> Music education online <http://groups.yahoo.com/gads?t=ms&k=Music+education+online&w1=Music+edu cation&w2=Music+production+education&w3=Music+education+degree&w4=Degree +education+music+online&w5=Music+business+education&w6=Music+education+o nline&c=6&s=174&.sig=DaqBb8P8ErSmB8MxxA-ePw> ________________________________ YAHOO! GROUPS LINKS * Visit your group "tuning <http://groups.yahoo.com/group/tuning> " on the web. * To unsubscribe from this group, send an email to: tuning-unsubscribe@yahoogroups.com <mailto:tuning-unsubscribe@yahoogroups.com?subject=Unsubscribe> * Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service <http://docs.yahoo.com/info/terms/> . ________________________________
From: Dave Keenan (2006-03-19) Subject: Re: reality of using tuning systems in fretted instruments --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote: > > > Hi Shaahin, > > > > You may find this article useful: > > "Optimising JI guitar designs using linear microtemperaments > > or > > If it aint Baroque don't waste your lute fixing it" > > http://users.bigpond.net.au/d.keenan/Music/MicroGuitar.pdf > > > > It shows how linear temperaments (non-equal) can be implemented > > on fretted instruments using only continuous frets, and it gives > > a number of linear temperaments that approach just intonation > > with errors less than typical fretting+playing errors. > > I always thought this was one of your coolest projects. > I'm not a guitarist, but it seemed to be really good thinking, > and the state transition diagrams were the bomb. Thanks Carl. > I wish > some more guitarists would take note of this paper (maybe > they have and I haven't heard of it). I haven't heard of any either. :-( Maybe it's a bit too mathematical or something. -- Dave Keenan
From: Ozan Yarman (2006-03-21) Subject: Re: [tuning] Re: reality of using tuning systems in fretted instruments Brother, remind me again what the difference between EDL and EDS was with some examples? Cordially, Oz. ----- Original Message ----- From: Mohajeri Shahin To: tuning@yahoogroups.com Sent: 16 Mart 2006 Perşembe 6:04 Subject: RE: [tuning] Re: reality of using tuning systems in fretted instruments Dear Aaron I know all the things you wrote , Please notice to EDL , it is not the same as EDO : EDL is equal divisions of length as discussed before in group in some mail , It is proposed by ozan instead of my EDS(equal divisions of string). Best for you Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html www.harmonytalk.com/archives/000288.html My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm
From: Mohajeri Shahin (2006-03-26) Subject: RE: [tuning] Re: reality of using tuning systems in fretted instruments Dear ozan Excuse me for late reply because of new persian year and nowrouz. Equal divisions of string length is a concept I found in farabi's musighi-al-kabir used in fretting of tanbour of baghdad . he also used this method in his theoretical concepts. I proposed a name for this system as EDS ( equal divisions of string length) and in a mail you mentioned it as EDL , although equal divisions of pipe length may show different sounding as strings. Consider a 640-mm length string from nut to bridge , so with accuracy of 1 mm you have 640 equal part in string length from 640/640 to 640/320 (from 1/1 to 2/1) so middle of string is octave. In strings with even size of length you can have octave but in odd sizes you cant have this. In 640-EdL you cant have pure fifth of 3/2 but in 642-EDL you can have it(642/428=3/2). Fretting of string instrument like divan,tar,baghlama , guitar and so on regardless of compensation (which change N-EDL to N'-EDL , N'<N) is related to this system. For example , consider a 640 mm length of string . you want to fret your instrument like tanbour of baghdad in 40-EDL . you have 40-EDL intervals as : 0:-- 1/1 -- 0.000 unison, perfect prime 1: -- 40/39 -- 43.831 tridecimal minor diesis 2: -- 20/19 -- 88.801 small undevicesimal semitone 3: -- 40/37 -- 134.970 4: -- 10/9 -- 182.404 minor whole tone 5: -- 8/7 -- 231.174 septimal whole tone 6: -- 20/17 -- 281.358 septendecimal augmented second 7: -- 40/33 -- 333.041 8: -- 5/4 -- 386.314 major third 9: -- 40/31 -- 441.278 10: -- 4/3 -- 498.045 perfect fourth 11: -- 40/29 -- 556.737 12: -- 10/7 -- 617.488 Euler's tritone 13: -- 40/27 -- 680.449 grave fifth 14: -- 20/13 -- 745.786 tridecimal semi-augmented fifth 15: -- 8/5 -- 813.686 minor sixth 16: -- 5/3 -- 884.359 major sixth, BP sixth 17: -- 40/23 -- 958.039 18: -- 20/11 -- 1034.996 large minor seventh 19: -- 40/21 -- 1115.533 acute major seventh 20: -- 2/1 -- 1200.000 octave You must find psitions of intervals with these distances on string length in mm from nut : 0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 But you must consider compensation so the octave fret on neck of string is less than 320mm from nut. you must first find the exact position of octave fret on neck then double it to have new EDL system to have your new positions of fret. You see that here you havn't any fifth.so two string of tanbour of baghdad were tuned in fourth. As I told before string lengths and compensation and .... impose tuning systems to your instrument. Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html www.harmonytalk.com/archives/000288.html My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm ________________________________ From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman Sent: Tuesday, March 21, 2006 11:24 PM To: Tuning List Subject: Re: [tuning] Re: reality of using tuning systems in fretted instruments Brother, remind me again what the difference between EDL and EDS was with some examples? Cordially, Oz. ----- Original Message ----- From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com> To: tuning@yahoogroups.com Sent: 16 Mart 2006 Perşembe 6:04 Subject: RE: [tuning] Re: reality of using tuning systems in fretted instruments Dear Aaron I know all the things you wrote , Please notice to EDL , it is not the same as EDO : EDL is equal divisions of length as discussed before in group in some mail , It is proposed by ozan instead of my EDS(equal divisions of string). Best for you Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html <http://www.harmonytalk.com/archives/000296.html> www.harmonytalk.com/archives/000288.html <http://www.harmonytalk.com/archives/000288.html> My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm <http://www.drumdojo.com/world/persia/tonbak_acoustics.htm> 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. 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From: Ozan Yarman (2006-04-08)
Subject: Re: [tuning] Re: reality of using tuning systems in fretted instruments
Dear Mohajeri, forgive my absent mindedness... indeed here is my response:
I am thankful that you outlined these concepts. It is perhaps necessary to distinguish EDS from EDP, which would be `Equal divisions of the Pipe`, such as that of the Church Organ or Ney.
In the case of the Ney, the regular procedure is to take 7 out of 26 EDP and make calibrations thereby. Sadly, I cannot begin to calculate the devilish mathematics of air-blown instruments.
EDL (equal divisions of lenght) is nevertheless interesting in that the same distances might yield different pitches from varying mediums of sound production.
There was also some logarithmic equal division we mentioned? Perhaps you will remember...
40-EDL for the Tanbur does not seem to produce satisfactory results with the lack of a consonant fifth... how about 60 EDL?
Cordially,
Ozan
Dear brother in music , ozan
I'm waiting to know your points about EDL interrvallic system.please
tell me your points.
Dear ozan
Excuse me for late reply because of new persian year and nowrouz.
Equal divisions of string length is a concept I found in farabi's musighi-al-kabir used in fretting of tanbour of baghdad . he also used this method in his theoretical concepts.
I proposed a name for this system as EDS ( equal divisions of string length) and in a mail you mentioned it as EDL , although equal divisions of pipe length may show different sounding as strings.
Consider a 640-mm length string from nut to bridge , so with accuracy of 1 mm you have 640 equal part in string length from 640/640 to 640/320 (from 1/1 to 2/1) so middle of string is octave.
In strings with even size of length you can have octave but in odd sizes you cant have this. In 640-EdL you cant have pure fifth of 3/2 but in 642-EDL you can have it(642/428=3/2).
Fretting of string instrument like divan,tar,baghlama , guitar and so on regardless of compensation (which change N-EDL to N'-EDL , N'<N) is related to this system.
For example , consider a 640 mm length of string . you want to fret your instrument like tanbour of baghdad in 40-EDL . you have 40-EDL intervals as :
0:-- 1/1 -- 0.000 unison, perfect prime
1: -- 40/39 -- 43.831 tridecimal minor diesis
2: -- 20/19 -- 88.801 small undevicesimal semitone
3: -- 40/37 -- 134.970
4: -- 10/9 -- 182.404 minor whole tone
5: -- 8/7 -- 231.174 septimal whole tone
6: -- 20/17 -- 281.358 septendecimal augmented second
7: -- 40/33 -- 333.041
8: -- 5/4 -- 386.314 major third
9: -- 40/31 -- 441.278
10: -- 4/3 -- 498.045 perfect fourth
11: -- 40/29 -- 556.737
12: -- 10/7 -- 617.488 Euler's tritone
13: -- 40/27 -- 680.449 grave fifth
14: -- 20/13 -- 745.786 tridecimal semi-augmented fifth
15: -- 8/5 -- 813.686 minor sixth
16: -- 5/3 -- 884.359 major sixth, BP sixth
17: -- 40/23 -- 958.039
18: -- 20/11 -- 1034.996 large minor seventh
19: -- 40/21 -- 1115.533 acute major seventh
20: -- 2/1 -- 1200.000 octave
You must find psitions of intervals with these distances on string length in mm from nut :
0
16
32
48
64
80
96
112
128
144
160
176
192
208
224
240
256
272
288
304
320
But you must consider compensation so the octave fret on neck of string is less than 320mm from nut. you must first find the exact position of octave fret on neck then double it to have new EDL system to have your new positions of fret.
You see that here you havn't any fifth.so two string of tanbour of baghdad were tuned in fourth.
As I told before string lengths and compensation and …. impose tuning systems to your instrument.
Shaahin Mohaajeri
Tombak Player & Researcher , Composer
www.geocities.com/acousticsoftombak
My tombak musics : www.rhythmweb.com/gdg
My articles in ''Harmonytalk'':
www.harmonytalk.com/archives/000296.html
www.harmonytalk.com/archives/000288.html
My article in DrumDojo:
www.drumdojo.com/world/persia/tonbak_acoustics.htm
From: Mohajeri Shahin (2006-04-09) Subject: RE: [tuning] Re: reality of using tuning systems in fretted instruments Hi dear OZAN Here is an example of 18-tone actual system of iranian music based on 108-EDL system as an potential system.i say actual because we use them and I say potential because actual is subset of it . 0: -- 1/1 --- 0.000 unison, perfect prime 1: -- 18/17 -- 98.955 Arabic lute index finger 2: -- 27/25 -- 133.238 large limma, BP small semitone 3: -- 9/8 -- 203.910 major whole tone 4: --- 108/91 -- 296.511 5: -- 108/89 -- 334.985 6: -- 54/43 -- 394.347 7: -- 4/3 -- 498.045 perfect fourth 8: -- 108/79 -- 541.328 9: -- 27/19 -- 608.352 10: --- 36/25 -- 631.283 classic diminished fifth 11: --- 3/2 -- 701.955 perfect fifth 12: --- 27/17 -- 800.910 septendecimal minor sixth 13: --- 18/11 -- 852.592 undecimal neutral sixth 14: -- 27/16 905.865 Pythagorean major sixth 15: --- 108/61 -- 988.980 16: --- 108/59 -- 1046.693 17: --- 36/19 -- 1106.397 smaller undevicesimal major seventh 18: --- 2/1 -- 1200.000 octave And in its 12-semitonal scale as scala ( tone circle ) told , we have : - 6 different tone - 12 different semitone - and 7 different fifth and so on. All these changes can be simulated by an edo system. I have a graphical temperament analyzer in excell spreadsheet to show changes of all semitones , fifths , fourths and so on. This is nature of iranain music so I think it as an irregular temperament which shows Different tastes of an intervall in different tetrachords. 60-EDL is not sounding good to me because of its 12/11( 150.637---- 3/4-tone, undecimal neutral second ) EDL system as I told before is actually used for fretting considering change of octave position on neck of instrument . Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html www.harmonytalk.com/archives/000288.html My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm ________________________________ From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman Sent: Saturday, April 08, 2006 9:21 PM To: tuning@yahoogroups.com Subject: Re: [tuning] Re: reality of using tuning systems in fretted instruments Dear Mohajeri, forgive my absent mindedness... indeed here is my response: I am thankful that you outlined these concepts. It is perhaps necessary to distinguish EDS from EDP, which would be `Equal divisions of the Pipe`, such as that of the Church Organ or Ney. In the case of the Ney, the regular procedure is to take 7 out of 26 EDP and make calibrations thereby. Sadly, I cannot begin to calculate the devilish mathematics of air-blown instruments. EDL (equal divisions of lenght) is nevertheless interesting in that the same distances might yield different pitches from varying mediums of sound production. There was also some logarithmic equal division we mentioned? Perhaps you will remember... 40-EDL for the Tanbur does not seem to produce satisfactory results with the lack of a consonant fifth... how about 60 EDL? Cordially, Ozan Dear brother in music , ozan I'm waiting to know your points about EDL interrvallic system.please tell me your points. Dear ozan Excuse me for late reply because of new persian year and nowrouz. Equal divisions of string length is a concept I found in farabi's musighi-al-kabir used in fretting of tanbour of baghdad . he also used this method in his theoretical concepts. I proposed a name for this system as EDS ( equal divisions of string length) and in a mail you mentioned it as EDL , although equal divisions of pipe length may show different sounding as strings. Consider a 640-mm length string from nut to bridge , so with accuracy of 1 mm you have 640 equal part in string length from 640/640 to 640/320 (from 1/1 to 2/1) so middle of string is octave. In strings with even size of length you can have octave but in odd sizes you cant have this. In 640-EdL you cant have pure fifth of 3/2 but in 642-EDL you can have it(642/428=3/2). Fretting of string instrument like divan,tar,baghlama , guitar and so on regardless of compensation (which change N-EDL to N'-EDL , N'<N) is related to this system. For example , consider a 640 mm length of string . you want to fret your instrument like tanbour of baghdad in 40-EDL . you have 40-EDL intervals as : 0:-- 1/1 -- 0.000 unison, perfect prime 1: -- 40/39 -- 43.831 tridecimal minor diesis 2: -- 20/19 -- 88.801 small undevicesimal semitone 3: -- 40/37 -- 134.970 4: -- 10/9 -- 182.404 minor whole tone 5: -- 8/7 -- 231.174 septimal whole tone 6: -- 20/17 -- 281.358 septendecimal augmented second 7: -- 40/33 -- 333.041 8: -- 5/4 -- 386.314 major third 9: -- 40/31 -- 441.278 10: -- 4/3 -- 498.045 perfect fourth 11: -- 40/29 -- 556.737 12: -- 10/7 -- 617.488 Euler's tritone 13: -- 40/27 -- 680.449 grave fifth 14: -- 20/13 -- 745.786 tridecimal semi-augmented fifth 15: -- 8/5 -- 813.686 minor sixth 16: -- 5/3 -- 884.359 major sixth, BP sixth 17: -- 40/23 -- 958.039 18: -- 20/11 -- 1034.996 large minor seventh 19: -- 40/21 -- 1115.533 acute major seventh 20: -- 2/1 -- 1200.000 octave You must find psitions of intervals with these distances on string length in mm from nut : 0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 But you must consider compensation so the octave fret on neck of string is less than 320mm from nut. you must first find the exact position of octave fret on neck then double it to have new EDL system to have your new positions of fret. You see that here you havn't any fifth.so two string of tanbour of baghdad were tuned in fourth. As I told before string lengths and compensation and .... impose tuning systems to your instrument. Shaahin Mohaajeri Tombak Player & Researcher , Composer www.geocities.com/acousticsoftombak My tombak musics : www.rhythmweb.com/gdg My articles in ''Harmonytalk'': www.harmonytalk.com/archives/000296.html www.harmonytalk.com/archives/000288.html My article in DrumDojo: www.drumdojo.com/world/persia/tonbak_acoustics.htm 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. 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From: Gene Ward Smith (2006-04-09) Subject: Re: reality of using tuning systems in fretted instruments --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote: > Here is an example of 18-tone actual system of iranian music based on > 108-EDL system as an potential system.i say actual because we use them > and I say potential because actual is subset of it . Here it is as a Scala scl file: ! shahin.scl Mohajeri Shahin Iranian style scale tuning@yahoo April 9 2006 18 ! 18/17 27/25 9/8 108/91 108/89 54/43 4/3 108/79 27/19 36/25 3/2 27/17 18/11 27/16 108/61 108/59 36/19 2 > All these changes can be simulated by an edo system. Here is a 118edo version: ! shahin118.scl Shahin scale in 118-et 18 ! 101.694915 132.203390 203.389831 294.915254 335.593220 396.610169 498.305085 538.983051 610.169492 630.508475 701.694915 803.389831 854.237288 905.084746 986.440678 1047.457627 1108.474576 1200.000000
From: Ozan Yarman (2006-04-09)
Subject: Re: [tuning] Re: reality of using tuning systems in fretted instruments
Brother, while it seems you reject 11-limit consonances, you certainly do want to preserve 13-limit intervals. Would you perhaps consider 18 out of my proposed 79 tone improved system? The maximum error is about 7 cents compared with your JI scale:
1: 7: -6.930 cents -6.929587 1.1110 Hertz, 66.6617 cycles/min.
2: 9: -2.899 cents -2.899235 0.4736 Hertz, 28.4149 cycles/min.
3: 13: 7.268 cents 7.267951 1.2330 Hertz, 73.9825 cycles/min.
4: 20: -6.015 cents -6.014805 1.0806 Hertz, 64.8387 cycles/min.
5: 22: 2.206 cents 2.206025 0.4043 Hertz, 24.2573 cycles/min.
6: 26: 1.063 cents 1.063187 0.2017 Hertz, 12.1026 cycles/min.
7: 33: -1.123 cents -1.123290 0.2264 Hertz, 13.5846 cycles/min.
8: 36: -3.219 cents -3.219125 0.6657 Hertz, 39.9405 cycles/min.
9: 40: 3.300 cents 3.299506 0.7079 Hertz, 42.4738 cycles/min.
10: 42: -4.023 cents -4.022526 0.8764 Hertz, 52.5825 cycles/min.
11: 46: 0.000 cents 0.000000 0.0000 Hertz, 0.0000 cycles/min.
12: 53: -6.930 cents -6.929586 1.6665 Hertz, 99.9925 cycles/min.
13: 56: -0.626 cents -0.626060 0.1548 Hertz, 9.2907 cycles/min.
14: 59: 7.268 cents 7.267942 1.8496 Hertz, 110.9736 cycles/min.
15: 65: -0.375 cents -0.374732 0.1003 Hertz, 6.0164 cycles/min.
16: 69: -3.167 cents -3.166826 0.8768 Hertz, 52.6101 cycles/min.
17: 73: -3.968 cents -3.968434 1.1376 Hertz, 68.2561 cycles/min.
18: 79: -1.123 cents -1.123290 0.3396 Hertz, 20.3769 cycles/min.
Mode: 7 2 4 7 2 4 7 3 4 2 4 7 3 3 6 4 4 6
Total absolute difference : 61.5021 cents
Average absolute difference: 3.4168 cents
Root mean square difference: 4.2067 cents
Highest absolute difference: 7.2680 cents
Number of notes different: 17
|
0: 1/1 C
1: 105.884 cents C#/| Db
2: 136.137 cents C#/|\ Db|)
3: 196.642 cents D
4: 302.526 cents D#/| Eb
5: 332.779 cents D#/|\ Eb|)
6: 393.284 cents E
7: 499.168 cents F
8: 544.547 cents F/|\ Gbb|)
9: 605.052 cents F#/| Gb
10: 635.305 cents F#/|\ Gb|)
11: 701.955 cents G
12: 807.839 cents G#/| Ab
13: 853.218 cents Gx!) A\!/
14: 898.597 cents A
15: 989.355 cents A# Bb\!
16: 1049.860 cents Ax!) B\!/
17: 1110.365 cents B/| Cb
18: 1201.123 cents C
I would also like to see that Excel spreadsheet you mention.
Cordially,
Ozan
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 09 Nisan 2006 Pazar 16:56
Subject: RE: [tuning] Re: reality of using tuning systems in fretted instruments
Hi dear OZAN
Here is an example of 18-tone actual system of iranian music based on 108-EDL system as an potential system.i say actual because we use them and I say potential because actual is subset of it .
0: -- 1/1 --- 0.000 unison, perfect prime
1: -- 18/17 -- 98.955 Arabic lute index finger
2: -- 27/25 -- 133.238 large limma, BP small semitone
3: -- 9/8 -- 203.910 major whole tone
4: --- 108/91 -- 296.511
5: -- 108/89 -- 334.985
6: -- 54/43 -- 394.347
7: -- 4/3 -- 498.045 perfect fourth
8: -- 108/79 -- 541.328
9: -- 27/19 -- 608.352
10: --- 36/25 -- 631.283 classic diminished fifth
11: --- 3/2 -- 701.955 perfect fifth
12: --- 27/17 -- 800.910 septendecimal minor sixth
13: --- 18/11 -- 852.592 undecimal neutral sixth
14: -- 27/16 905.865 Pythagorean major sixth
15: --- 108/61 -- 988.980
16: --- 108/59 -- 1046.693
17: --- 36/19 -- 1106.397 smaller undevicesimal major seventh
18: --- 2/1 -- 1200.000 octave
And in its 12-semitonal scale as scala ( tone circle ) told , we have :
- 6 different tone
- 12 different semitone
- and 7 different fifth and so on.
All these changes can be simulated by an edo system.
I have a graphical temperament analyzer in excell spreadsheet to show changes of all semitones , fifths , fourths and so on.
This is nature of iranain music so I think it as an irregular temperament which shows Different tastes of an intervall in different tetrachords.
60-EDL is not sounding good to me because of its 12/11( 150.637---- 3/4-tone, undecimal neutral second )
EDL system as I told before is actually used for fretting considering change of octave position on neck of instrument .
Shaahin Mohaajeri
Tombak Player & Researcher , Composer
www.geocities.com/acousticsoftombak
My tombak musics : www.rhythmweb.com/gdg
My articles in ''Harmonytalk'':
www.harmonytalk.com/archives/000296.html
www.harmonytalk.com/archives/000288.html
My article in DrumDojo:
www.drumdojo.com/world/persia/tonbak_acoustics.htm
From: Carl Lumma (2006-04-09) Subject: Re: reality of using tuning systems in fretted instruments --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@> wrote: > > > Here is an example of 18-tone actual system of iranian music > > based on 108-EDL system as an potential system.i say actual > > because we use them and I say potential because actual is > > subset of it. > > Here it is as a Scala scl file: > > ! shahin.scl > Mohajeri Shahin Iranian style scale tuning@yahoo April 9 2006 > 18 > ! > 18/17 > 27/25 > 9/8 > 108/91 > 108/89 > 54/43 > 4/3 > 108/79 > 27/19 > 36/25 > 3/2 > 27/17 > 18/11 > 27/16 > 108/61 > 108/59 > 36/19 > 2 Thanks, Mohajeri and Gene! -C.