Scala analysis: 145_C3
Chromatic tetrachord 24/23 * 391/378 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 24/23 73.6807 vicesimotertial minor semitone 2: 391/378 58.5388 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 391/378 58.539 cents 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 23/18 424.364 cents vicesimotertial major third 2: 1 504/391 439.506 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 : 73.7 132.2 498.0 73.7 : 58.5 424.4 498.0 132.2: 365.8 439.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.5388 .. 365.8255 cents 7938/6647, 307.2867 cents 391/378, 58.5388 cents 2: 132.2195 .. 439.5062 cents 7938/6647, 307.2867 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 391/378, 58.5388 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 2.835980 Largest / Average step : 2.203569 Largest / Smallest step : 6.249277 Median interval of one step : 24/23, 73.6807 cents, amount: 1 Least squares average step : 130.87533 cents, oct.: 392.62600 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1744-tone equal temperament with octave 4/3 degrees: 258 463 1744 Least number of segments generator : 873 of 249.308 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1561 of 445.785 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 58.53885 cents Scale diversity : 0.664711 Lumma stability : 0.235075 Lumma impropriety factor : 0.469046 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 : 9072/8993, 15.1418 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% Limited inverse transpositions with margin 307.2867 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 391 (O: 391 U: 391) Highest odd numerator or denominator: 63 Scale harmonicity : 0.010696 Average absolute harmonicity : 0.085391 Specific harmonicity : 0.056509 Fundamental : 1/1449, -10.5008 octaves, 0.1806 Hz. Guide tone : 408, 8.6724 octaves, 106743.231 Hz. Exponens Consonantiae : 5.911920E+05, 19.17327 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 92.5, average 30.83333 Mersenne's string divisions : 43099 Sum of van Prooijen's expressibility: 3.63819, average 1.21273 Sum of Tenney's harmonic distance : 7.45297, average 2.48432 Vogel's harmonic complexity : 32.00000 Wille's k value : 241 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.50206, average 2.75034 Lattice compactness (without 2's) : 12.29592, average 2.04932 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 .. 1 -0.66667 4 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 29 30| Scale is weakly epimorphic with val: <6 10 18 29 33| Scale is weakly epimorphic with val: <6 10 18 29 36| Scale is weakly epimorphic with val: <6 10 19 30 30| Scale is weakly epimorphic with val: <6 10 19 30 33| Scale is weakly epimorphic with val: <6 10 19 30 36| Scale is weakly epimorphic with val: <6 10 20 31 33| Scale is weakly epimorphic with val: <6 10 20 31 36| Scale is weakly epimorphic with val: <6 10 21 32 33| Scale is weakly epimorphic with val: <6 10 21 32 36| Scale is weakly epimorphic with val: <6 10 22 33 33| Scale is weakly epimorphic with val: <6 10 22 33 36| Scale is weakly epimorphic with val: <6 11 18 31 33| Scale is weakly epimorphic with val: <6 11 18 31 36| Scale is weakly epimorphic with val: <6 11 19 32 33| Scale is weakly epimorphic with val: <6 11 19 32 36| Scale is weakly epimorphic with val: <6 11 20 33 33| Scale is weakly epimorphic with val: <6 11 20 33 36| Scale is weakly epimorphic with val: <7 10 18 27 32| Scale is weakly epimorphic with val: <7 10 18 27 35| Scale is weakly epimorphic with val: <7 10 19 28 32| Scale is weakly epimorphic with val: <7 10 19 28 35| Scale is weakly epimorphic with val: <7 10 20 29 32| Scale is weakly epimorphic with val: <7 10 20 29 35| Scale is weakly epimorphic with val: <7 10 21 30 32| Scale is weakly epimorphic with val: <7 10 21 30 35| Scale is weakly epimorphic with val: <7 10 22 31 32| Scale is weakly epimorphic with val: <7 10 22 31 35| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is JI-epimorphic with val: <7 11 18 28 31| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is weakly epimorphic with val: <7 11 18 31 31| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 33 33| Scale is weakly epimorphic with val: <7 11 18 33 36| Scale is weakly epimorphic with val: <7 11 19 28 30| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is JI-epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 29 34| Scale is weakly epimorphic with val: <7 11 19 31 33| Scale is weakly epimorphic with val: <7 11 19 31 36| Scale is weakly epimorphic with val: <7 11 19 32 34| Scale is weakly epimorphic with val: <7 11 20 27 31| Scale is weakly epimorphic with val: <7 11 20 27 34| Scale is weakly epimorphic with val: <7 11 20 29 30| Scale is weakly epimorphic with val: <7 11 20 29 33| Scale is weakly epimorphic with val: <7 11 20 29 36| Scale is JI-epimorphic with val: <7 11 20 30 31| Scale is weakly epimorphic with val: <7 11 20 30 34| Scale is weakly epimorphic with val: <7 11 20 32 33| Scale is weakly epimorphic with val: <7 11 20 32 36| Scale is weakly epimorphic with val: <7 11 20 33 34| Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 27 36| Scale is weakly epimorphic with val: <7 11 21 28 31| Scale is weakly epimorphic with val: <7 11 21 28 34| Scale is weakly epimorphic with val: <7 11 21 30 30| Scale is weakly epimorphic with val: <7 11 21 30 33| Scale is weakly epimorphic with val: <7 11 21 30 36| Scale is JI-epimorphic with val: <7 11 21 31 31| Scale is weakly epimorphic with val: <7 11 21 31 34| Scale is weakly epimorphic with val: <7 11 21 33 33| Scale is weakly epimorphic with val: <7 11 21 33 36| Scale is weakly epimorphic with val: <7 11 22 28 30| Scale is weakly epimorphic with val: <7 11 22 28 33| Scale is weakly epimorphic with val: <7 11 22 28 36| Scale is weakly epimorphic with val: <7 11 22 29 31| Scale is weakly epimorphic with val: <7 11 22 29 34| Scale is weakly epimorphic with val: <7 11 22 31 33| Scale is weakly epimorphic with val: <7 11 22 31 36| Scale is weakly epimorphic with val: <7 11 22 32 34| Scale is weakly epimorphic with val: <7 12 18 29 30| Scale is weakly epimorphic with val: <7 12 18 31 32| Scale is weakly epimorphic with val: <7 12 18 31 35| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 30 30| Scale is weakly epimorphic with val: <7 12 19 32 32| Scale is weakly epimorphic with val: <7 12 19 32 35| Scale is weakly epimorphic with val: <7 12 20 28 30| Scale is weakly epimorphic with val: <7 12 20 33 35| Scale is weakly epimorphic with val: <7 12 21 29 30| Scale is weakly epimorphic with val: <7 12 22 27 30| Scale is weakly epimorphic with val: <7 12 22 30 30| Scale is weakly epimorphic with val: <8 11 18 27 31| Scale is weakly epimorphic with val: <8 11 18 27 34| Scale is weakly epimorphic with val: <8 11 18 28 32| Scale is weakly epimorphic with val: <8 11 18 31 32| Scale is weakly epimorphic with val: <8 11 19 28 31| Scale is weakly epimorphic with val: <8 11 19 28 34| Scale is weakly epimorphic with val: <8 11 19 29 32| Scale is weakly epimorphic with val: <8 11 19 32 32| Scale is weakly epimorphic with val: <8 11 20 27 32| Scale is weakly epimorphic with val: <8 11 20 29 31| Scale is weakly epimorphic with val: <8 11 20 29 34| Scale is weakly epimorphic with val: <8 11 20 30 32| Scale is weakly epimorphic with val: <8 11 21 28 32| Scale is weakly epimorphic with val: <8 11 21 30 31| Scale is weakly epimorphic with val: <8 11 21 30 34| Scale is weakly epimorphic with val: <8 11 21 31 32| Scale is weakly epimorphic with val: <8 11 22 29 32| Scale is weakly epimorphic with val: <8 11 22 31 31| Scale is weakly epimorphic with val: <8 11 22 31 34| Scale is weakly epimorphic with val: <8 11 22 32 32| Scale is weakly epimorphic with val: <8 12 18 28 33| Scale is weakly epimorphic with val: <8 12 18 29 31| Scale is weakly epimorphic with val: <8 12 18 29 34| Scale is weakly epimorphic with val: <8 12 18 31 33| Scale is weakly epimorphic with val: <8 12 19 29 33| Scale is weakly epimorphic with val: <8 12 19 30 31| Scale is weakly epimorphic with val: <8 12 19 30 34| Scale is weakly epimorphic with val: <8 12 19 32 33| Scale is weakly epimorphic with val: <8 12 20 27 33| Scale is weakly epimorphic with val: <8 12 20 30 33| Scale is weakly epimorphic with val: <8 12 20 31 31| Scale is weakly epimorphic with val: <8 12 20 31 34| Scale is weakly epimorphic with val: <8 12 20 33 33| Scale is weakly epimorphic with val: <8 12 21 28 33| Scale is weakly epimorphic with val: <8 12 21 31 33| Scale is weakly epimorphic with val: <8 12 21 32 34| Scale is weakly epimorphic with val: <8 12 22 29 33| Scale is weakly epimorphic with val: <8 12 22 32 33| Scale is weakly epimorphic with val: <8 12 22 33 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 46.8009 c. M: 73.6807 c. 4: 1 0 3 N G T3 SD: 29.6826 c. M:-50.8306 c. 5: 1 0 4 N G T3 SD: 24.0536 c. M: 32.6105 c. 6: 1 1 4 N M DE S SD: 20.2413 c. M:-33.7955 c. 7: 1 1 5 N M DE S SD: 5.9999 c. M:-10.0791 c. 12: 2 1 9 N T3 SD: 6.9859 c. M:-9.3268 c. 15: 2 2 11 N M DE S SD: 4.2139 c. M: 7.2747 c. 19: 3 2 14 N T3 SD: 2.9392 c. M:-4.9580 c. 26: 4 3 19 N T3 SD: 2.0123 c. M:-2.9417 c. 27: 4 3 20 N T3 SD: 1.7889 c. M: 3.0967 c. 34: 5 4 25 N T3 SD: 0.3366 c. M: 0.4387 c. 94: 14 11 69 N T3 SD: 0.3181 c. M:-0.4963 c. 128: 19 15 94 N T3 SD: 0.1493 c. M:-0.2479 c. 162: 24 19 119 N T3 SD: 0.0613 c. M:-0.1038 c. 196: 29 23 144 N T3 SD: 0.0495 c. M: 0.0851 c. 358: 53 42 263 N T3 SD: 0.0445 c. M: 0.0567 c. 554: 82 65 407 N T3 SD: 0.0441 c. M: 0.0668 c. 561: 83 66 412 N T3 SD: 0.0347 c. M:-0.0598 c. 595: 88 70 437 N T3 SD: 0.0231 c. M:-0.0345 c. 757: 112 89 556 N T3 SD: 0.0134 c. M:-0.0223 c. 791: 117 93 581 N T3 SD: 0.0079 c. M: 0.0128 c. 953: 141 112 700 N T3 SD: 0.0040 c. M:-0.0070 c. 1744: 258 205 1281 N T3 SD: 0.0018 c. M:-0.0023 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: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16 x 17:21 SD: 19.2786 cents 17:18 x 23 SD: 17.8714 cents 18:19 x 24 SD: 9.9612 cents 21:22:23:28 SD: 8.7291 cents 23:24:25:31 SD: 7.4351 cents 24:25:26:32 SD: 2.3431 cents 63:66:68:84 SD: 2.2855 cents 66:69:71:88 SD: 2.2192 cents 75:78:81:100 SD: 1.9565 cents 87:91:94:116 SD: 1.4991 cents 90:94:97:120 SD: 1.0032 cents 114:119:123:152 SD: 0.3072 cents 138:144:149:184 SD: 0.1845 cents 252:263:272:336 SD: 0.0954 cents 390:407:421:520 SD: 0.0898 cents