0: 1/1 0.000000 unison, perfect prime
1: 256/243 90.224996 limma, Pythagorean minor second
2: 9/8 203.910002 major whole tone
3: 32/27 294.134997 Pythagorean minor third
4: 81/64 407.820003 Pythagorean major third
5: 4/3 498.044999 perfect fourth
6: 1024/729 588.269995 Pythagorean diminished fifth
7: 3/2 701.955001 perfect fifth
8: 128/81 792.179997 Pythagorean minor sixth
9: 27/16 905.865003 Pythagorean major sixth
10: 16/9 996.089998 Pythagorean minor seventh
11: 243/128 1109.775004 Pythagorean major seventh
12: 2/1 1200.000000 octave
|
Number of notes : 12
-- Interval properties --
Smallest interval : 256/243, 90.2250 cents, class 1
Average step (divided formal octave): 100.0000 cents
Largest one step interval : 2187/2048, 113.6850 cents
Average / Smallest step : 1.108340
Largest / Average step : 1.136850
Largest / Smallest step : 1.260017
Median interval of one step : 256/243, 90.2250 cents, amount: 7
Most common interval of one step : 256/243, 90.2250 cents, amount: 7
Least squares average step : 100.00602 cents, oct.: 1200.07218 cents
Scale is strictly proper
Scale has Myhill's property
chromas: 531441/524288, 23.4600 cents and 134217728/129140163, 66.7650 cents
generators: 5 of 498.04500 cents and 7 of 701.95500 cents
ET pair of linear temperament : 12&41
Scale is maximally even for L / S <= 2
Scale is distributional even
Scale is a mode of a 665-tone equal temperament with octave 2/1
degrees: 50 113 163 226 276 326 389 439 502 552 615 665
generators: 276 and 389
Number of contiguous 1-step segments: 0
Interval pattern alph. order: ABABAABABABA
Interval pattern size order : SLSLSSLSLSLS
Scale is a Constant Structure, by a margin of 66.76499 cents
Ratio Whole / Half tone: 2.260017
Rothenberg stability : 1.000000 = 1
Lumma stability : 0.784950
Rothenberg efficiency : 0.722222 redundancy: 0.277778
Efficiency x scale size : 8.666667
Number of different interval sizes : 22 = 2.00000 / class
Number of one step interval sizes : 2
Highest interval variety : 2
Mean interval variety : 2.00000 = 2
Median interval variety : 2
Lowest interval variety : 2
Smallest interval difference : 531441/524288, 23.4600 cents
Most common intervals : 4/3, 498.0450 cents & inv., amount: 11
Scale is a chain of 6 triads 0.0 90.225 701.955 cents
Most common triad is 0.0 498.045 701.955 cents, amount: 10
Number of recognisable fifths : 11, average 701.9550 cents
Scale contains two identical disjunct hexachords
Best fifths form a closed circle
Scale is a complete genus musicum : 2^m 3^11
Scale contains a complete diamond : 1 3 9 27 81 243
Formal octave complements present : 11 = 91.6667%
Scale is n-1 differentially coherent in interval classes 4 and 5 combined
Scale is n-1 differentially coherent in interval class 5
Scale is n-1 differentially coherent in interval classes 6 and 7 combined
Scale is n-1 differentially coherent in interval class 7
Limited inverse transpositions :
5
Inversional symmetry on intervals :
2-3 8-9
-- Rational properties --
Prime limit : 3
Odd number limit : 177147 (O: 177147 U: 177147)
Highest odd numerator or denominator: 729
Scale harmonicity : 0.021583
Average absolute harmonicity : 0.177127
Specific harmonicity : 0.124021
Fundamental : 1/93312, -16.5098 octaves, 0.0028 Hz.
Guide tone : 248832, 17.9248 octaves, 65100812.665 Hz.
Exponens Consonantiae : 2.321901E+10, 34.43459 octaves
Euler's gradus suavitatis : 40
Sum of Mann's harmonic distance : 1568.0, average 130.66667
Mersenne's string divisions : too high to compute
Sum of van Prooijen's expressibility: 17.17637, average 1.43136
Sum of Tenney's harmonic distance : 34.63610, average 2.88634
Vogel's harmonic complexity : 24.83333
Wille's k value : 88573
Wilson's harmonic complexity : 33
Rectangular lattice diameter : 11
Triangular lattice diameter : 11
Lattice compactness : 598.75278, average 7.67632
Lattice compactness (without 2's) : 322.00000, average 4.12821
Number of different primes : 2
Prime exponents' range, average, count, tones@limit:
2: -7 .. 10 1.33333 58 1
3: -6 .. 5 -0.50000 36 11
Average exponent except 2's :-6 / 12 =-0.50000
Average absolute exponent except 2's: 36 / 12 = 3.00000
Scale is JI-epimorphic in non-monotonic order: <12 17|
Scale is JI-epimorphic: <12 19| = standard
credits
from Polysemy,
released October 12, 2018
Art: Dionysos by Wayne McMillan
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