Re: ozan's 18 out of 79 tone improved system

Brother, what you propose is this:

0: 1/1 0.000 unison, perfect prime
1: 17/16 104.955 17th harmonic
2: 119/110 136.150
3: 119/106 200.277
4: 119/100 301.154
5: 17/14 336.130 supraminor third
6: 119/95 389.955
7: 119/89 502.901
8: 119/87 542.249
9: 17/12 603.000 2nd septendecimal tritone
10: 75/52 634.055
11: 3/2 701.955 perfect fifth
12: 75/47 809.076
13: 75/46 846.308
14: 150/89 903.702
15: 30/17 983.313
16: 75/41 1045.520
17: 150/79 1110.046
18: 2/1 1200.000 octave

Compared with 18 out of my 79-tone system, the maximum difference is 7 cents:

1: 1: 0.929 cents 0.928770 0.1492 Hertz, 8.9501 cycles/min.
2: 2: -0.013 cents -0.012849 0.0021 Hertz, 0.1260 cycles/min.
3: 3: -3.635 cents -3.634720 0.6160 Hertz, 36.9600 cycles/min.
4: 4: 1.372 cents 1.372351 0.2469 Hertz, 14.8136 cycles/min.
5: 5: -3.351 cents -3.350643 0.6143 Hertz, 36.8557 cycles/min.
6: 6: 3.330 cents 3.329524 0.6309 Hertz, 37.8529 cycles/min.
7: 7: -3.733 cents -3.732908 0.7535 Hertz, 45.2076 cycles/min.
8: 8: 2.298 cents 2.298109 0.4753 Hertz, 28.5208 cycles/min.
9: 9: 2.052 cents 2.052071 0.4396 Hertz, 26.3750 cycles/min.
10: 10: 1.250 cents 1.250333 0.2726 Hertz, 16.3575 cycles/min.
11: 11: -0.000 cents -0.000000 0.0000 Hertz, 0.0000 cycles/min.
12: 12: -1.237 cents -1.236626 0.2981 Hertz, 17.8864 cycles/min.
13: 13: 6.910 cents 6.910038 1.7060 Hertz, 102.3591 cycles/min.
14: 14: -5.105 cents -5.105251 1.2984 Hertz, 77.9029 cycles/min.
15: 15: 6.042 cents 6.041624 1.6140 Hertz, 96.8411 cycles/min.
16: 16: 4.340 cents 4.340146 1.2013 Hertz, 72.0779 cycles/min.
17: 17: 0.320 cents 0.319889 0.0918 Hertz, 5.5078 cycles/min.
18: 18: 1.123 cents 1.123290 0.3396 Hertz, 20.3769 cycles/min.
Mode: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Total absolute difference : 47.0392 cents
Average absolute difference: 2.6133 cents
Root mean square difference: 3.2940 cents
Highest absolute difference: 6.9100 cents
Number of notes different: 17

I'm sure there is a better EDL cardinality that we can agree upon.

Manuel, can you implement New Scale|EDL into SCALA?

Cordially,
Ozan

----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 10 Nisan 2006 Pazartesi 6:32
Subject: 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

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