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Coul scale included in tuning experiment

🔗Joseph Pehrson <josephpehrson@compuserve.com>

5/27/2000 8:16:45 PM

I have included the "improved" scale that Manuel Op de Coul so kindly
suggested in my little "tuning experiment." The "fake" Wilson 19-31ji
scale has been unceremoniously removed...

If you recall, Mr. de Coul suggested the following:

Manuel de Coul's improvement on 19-31ji.scl
0: 1/1 0.000 unison, perfect prime
1: 135/128 92.179 major limma, large chroma
2: 15/14 119.443 major diatonic semitone
3: 9/8 203.910 major whole tone
4: 7/6 266.871 septimal minor third
5: 135/112 323.353
6: 5/4 386.314 major third
7: 21/16 470.781 narrow fourth
8: 4/3 498.045 perfect fourth
9: 45/32 590.224 tritone
10: 10/7 617.488 Euler's tritone
11: 3/2 701.955 perfect fifth
12: 14/9 764.916 septimal minor sixth
13: 45/28 821.398
14: 5/3 884.359 major sixth
15: 7/4 968.826 harmonic seventh
16: 16/9 996.090 Pythagorean minor seventh
17: 15/8 1088.269 classic major seventh
18: 63/32 1172.736 octave - septimal comma
19: 2/1 1200.000 octave

With the following characteristics:
Number of notes : 19
Smallest interval : 64/63, 27.2641 cents
Average interval (divided octave) : 63.158 cents
Average / Smallest interval : 2.316523
Largest interval of one step : 135/128, 92.1787 cents
Largest / Average interval : 1.459496
Largest / Smallest interval : 3.380957
Least squares average interval : 63.7858 cents
Median interval of one step : 28/27, 62.9609 cents
Interval standard deviation : 24.4176 cents
Interval skew : 0.0040 cents
Scale is not proper
Number of different intervals : 78 = 4.33333 / class
Lumma stability : 0.185202
Impropriety factor : 0.107511
Prime limit : 7
Odd number limit : 135 (O: 135 U: 9)
Average absolute harmonicity : 0.138724
Specific harmonicity : 0.112963
Fundamental : 1/8064,-12.977 octaves, 0.032 Hz.
Guide tone : 15120, 13.884 octaves, 3955778.55
Hz.
Exponens Consonantiae : 1.21928E+08, 26.8615 octaves
Euler's gradus suavitatis : 38
Wille's k value : 4252
Vogel's harmonic complexity : 2.28421E+01
Wilson's harmonic complexity : 34
Rectangular lattice dimensions : 8
Triangular lattice dimensions : 6
Prime exponents' range and average:
2: -7 .. 4 -1.63158
3: -2 .. 3 0.57895
5: 0 .. 1 0.47368
7: -1 .. 1 0.05263
Average exponent except of 2 : 1.10526
Average absolute exponent except of 2: 43 / 19 = 2.26316
Average distance from equal tempered : 14.0218 cents, 0.222011 steps
Standard deviation from equal tempered : 4.0184 cents, 0.063624 steps
Maximum distance from equal tempered : 35.8938 cents, 0.568318 steps
Geometric average of pitches 0..n : 608.358 cents
Arithmetic average of pitches 0..n : 3719/2560, 646.5251 cents
Harmonic average of pitches 0..n : 570.190 cents
Press RETURN to continue ...
Geometric average of pitches 1..n : 640.377 cents
Arithmetic average of pitches 1..n : 189/128, 674.6909 cents
Harmonic average of pitches 1..n : 606.062 cents
Geometric average of pitches 1..n-1: 609.286 cents
Arithmetic average of pitches 1..n-1: 3335/2304, 640.2553 cents
Harmonic average of pitches 1..n-1: 578.317 cents

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Joseph Pehrson