Full 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
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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 [email protected], "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: [email protected] [mailto:[email protected]] On Behalf
Of Aaron Wolf
Sent: Wednesday, March 15, 2006 6:46 PM
To: [email protected]
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
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From: Dave Keenan (2006-03-19)
Subject: Re: reality of using tuning systems in fretted instruments
--- In [email protected], "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: [email protected]
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: [email protected] [mailto:[email protected]] 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:[email protected]>
To: [email protected]
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):
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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: [email protected] [mailto:[email protected]] On Behalf
Of Ozan Yarman
Sent: Saturday, April 08, 2006 9:21 PM
To: [email protected]
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
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From: Gene Ward Smith (2006-04-09)
Subject: Re: reality of using tuning systems in fretted instruments
--- In [email protected], "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: [email protected]
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 [email protected], "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In [email protected], "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.