ozan's 18 out of 79 tone improved system :RE: [tuning] Re: reality of using tuning systems in fretted instruments

Dear ozan

Thanks for your comments , your 18 out of 79 tone improved system is
nearly parts of 119-EDL and 150-EDL . so for fretting instrument ,
considering compensation, we must fret according to these 2 to have a
sounding around your system :

119-EDL :

0: -- 1/1 -- 0.000 unison, perfect prime

7: -- 17/16 -- 104.955 17th harmonic

9: -- 119/110 -- 136.150

13: -- 119/106 -- 200.277

19: -- 119/100 -- 301.154

21: -- 17/14 -- 336.130 supraminor third

24: -- 119/95 -- 389.955

30: -- 119/89 -- 502.901

32: -- 119/87 -- 542.249

35: -- 17/12 -- 603.000 2nd septendecimal tritone

__________________________________________________________________

150-EDL:

46: 75/52 -- 634.055

50: 3/2 -- 701.955 perfect fifth

56: 75/47 -- 809.076

58: 75/46 -- 846.308

61: 150/89 -- 903.702

65: 30/17 -- 983.313

68: 75/41 -- 1045.520

71: 150/79 -- 1110.046

75: 2/1 -- 1200.000 octave

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: Sunday, April 09, 2006 10:08 PM
To: tuning@yahoogroups.com
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 <mailto:shahinm@kayson-ir.com>

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

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