Yahoo Tuning Groups Ultimate Backup tuning 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>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Carl Lumma <clumma@yahoo.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

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

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reality of using tuning systems in fretted instruments

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Carl Lumma <clumma@yahoo.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Carl Lumma <clumma@yahoo.com>