Scala analysis: 520_M28
Miscellaneous tetrachord 25/24 * 32/31 * 31/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 100/93 125.636854 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/25 372.4081 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 32/31 54.9644 Greek enharmonic 1/4-tone 3: 31/25 372.4081
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 31/25 372.408 cents 2: 1 100/93 125.637 cents 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 31/24 443.081 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 70.7 125.6 498.0 70.7 : 55.0 427.4 498.0 125.6: 372.4 443.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9644 .. 372.4081 cents 961/800, 317.4437 cents 32/31, 54.9644 cents 2: 125.6369 .. 443.0806 cents 961/800, 317.4437 cents 2500/2883,-246.7713 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 32/31, 54.9644 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/25, 372.4081 cents Average / Smallest step : 3.020408 Largest / Average step : 2.243220 Largest / Smallest step : 6.775439 Median interval of one step : 25/24, 70.6724 cents, amount: 1 Least squares average step : 129.72008 cents, oct.: 389.16024 cents Scale is not proper Scale has trivalence property Scale is a mode of a 444-tone equal temperament with octave 4/3 degrees: 63 112 444 Least number of segments generator : 223 of 250.144 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 437 of 490.193 cents and inv. generated superset size: 17 = 14 more = 566.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 54.96443 cents Scale diversity : 0.614199 Lumma stability : 0.220721 Lumma impropriety factor : 0.495480 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 775/768, 15.7080 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 317.4437 cents: 2 -- Rational properties -- Prime limit : 31 Odd number limit : 93 (O: 31 U: 93) Highest odd numerator or denominator: 93 Scale harmonicity : 0.048860 Fundamental : 1/744, -9.5392 octaves, 0.3516 Hz. Guide tone : 100, 6.6439 octaves, 26162.557 Hz. Exponens Consonantiae : 7.440000E+04, 16.18302 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 124.5, average 41.50000 Mersenne's string divisions : 9457 Sum of van Prooijen's expressibility: 3.84354, average 1.28118 Sum of Tenney's harmonic distance : 7.82582, average 2.60861 Vogel's harmonic complexity : 30.66667 Wille's k value : 387 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 21.36289, average 3.56048 Lattice compactness (without 2's) : 9.47214, average 1.57869 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.33333 7 3: -1 ..-1 -1.00000 3 1 5: 0 .. 2 1.33333 4 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 19 37| Scale is weakly epimorphic with val: <6 11 16 34| Scale is weakly epimorphic with val: <6 11 16 37| Scale is weakly epimorphic with val: <7 10 17 33| Scale is weakly epimorphic with val: <7 10 17 36| Scale is weakly epimorphic with val: <7 10 17 39| Scale is weakly epimorphic with val: <7 10 18 37| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 37| Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 17 36| = patent Scale is weakly epimorphic with val: <7 11 17 39| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 12 17 33| Scale is weakly epimorphic with val: <7 12 18 34| Scale is weakly epimorphic with val: <7 12 18 37| Scale is weakly epimorphic with val: <8 11 18 38| Scale is weakly epimorphic with val: <8 11 19 33| Scale is weakly epimorphic with val: <8 11 19 36| Scale is weakly epimorphic with val: <8 11 19 39| Scale is weakly epimorphic with val: <8 12 16 33| Scale is weakly epimorphic with val: <8 12 19 39|
FIT/MODE
3: 0 1 2 N G T3 SD: 46.9929 c. M: 70.6724 c. 4: 1 0 3 N G T3 SD: 31.0907 c. M:-53.8388 c. 5: 1 0 4 N G T3 SD: 22.4705 c. M:-28.9366 c. 6: 1 1 4 N M DE S SD: 24.3759 c. M:-40.3781 c. 7: 1 1 5 N M DE S SD: 9.6236 c. M:-16.6617 c. 8: 1 1 6 N M DE S SD: 4.9027 c. M: 8.4168 c. 15: 2 2 11 N M DE S SD: 4.8196 c. M:-7.1751 c. 19: 3 2 14 N T3 SD: 5.5654 c. M:-7.9663 c. 20: 3 2 15 N T3 SD: 2.4182 c. M:-4.0343 c. 27: 4 3 20 N T3 SD: 2.6979 c. M:-3.4859 c. 28: 4 3 21 N T3 SD: 0.7058 c. M: 1.1256 c. 63: 9 7 47 N T3 SD: 0.5631 c. M:-0.8508 c. 71: 10 8 53 N T3 SD: 0.4727 c. M:-0.6281 c. 91: 13 10 68 N T3 SD: 0.3089 c. M:-0.4769 c. 99: 14 11 74 N T3 SD: 0.1591 c. M: 0.2418 c. 127: 18 14 95 N T3 SD: 0.0967 c. M: 0.1452 c. 218: 31 24 163 N T3 SD: 0.0874 c. M:-0.1505 c. 317: 45 35 237 N T3 SD: 0.0345 c. M:-0.0527 c. 444: 63 49 332 N T3 SD: 0.0032 c. M: 0.0039 c. 2093: 297 231 1565 N T3 SD: 0.0028 c. M:-0.0047 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 70.6170 cents 7 x 8:9 S SD: 61.4455 cents 8 x 9:11 SD: 47.3410 cents 9 x 10:12 S SD: 28.3834 cents 10 x 11:13 SD: 29.4574 cents 11 x 12:15 S SD: 23.1229 cents 12 x 13:16 SD: 6.4679 cents 13 x 14:17 SD: 16.8612 cents 14 x 15:19 SD: 15.6309 cents 15 x 16:20 S SD: 6.9528 cents 16 x 17:21 SD: 17.1103 cents 17 x 18:23 SD: 18.3760 cents 18:19 x 24 SD: 11.4653 cents 19:20 x 25 S SD: 14.6155 cents 21:22:23:28 SD: 11.1163 cents 22:23:24:29 SD: 10.8319 cents 23:24:25:31 SD: 8.8797 cents 24:25:26:32 SD: 4.3119 cents 27:28:29:36 SD: 2.6494 cents 51:53:55:68 SD: 2.1726 cents 66:69:71:88 SD: 2.1110 cents 69:72:74:92 SD: 1.8104 cents 93:97:100:124 SD: 0.7441 cents 120:125:129:160 SD: 0.1443 cents 384:400:413:512 SD: 0.1352 cents 504:525:542:672 SD: 0.0687 cents