Scala analysis: 303_C23
Chromatic tetrachord 512/481 * 481/450 * 75/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 512/481 108.128299 2: 256/225 223.462571 Neapolitan diminished third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 75/64 274.5824 classic augmented second 1: 512/481 108.1283 2: 481/450 115.3343 3: 75/64 274.5824 classic augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 512/481 108.128 cents 1: 1 481/450 115.334 cents 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 600/481 382.711 cents 2: 1 481/384 389.917 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 : 108.1 223.5 498.0 108.1: 115.3 389.9 498.0 223.5: 274.6 382.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 108.1283 .. 274.5824 cents 36075/32768, 166.4541 cents 512/481, 108.1283 cents 2: 223.4626 .. 389.9167 cents 36075/32768, 166.4541 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 512/481, 108.1283 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.535352 Largest / Average step : 1.653962 Largest / Smallest step : 2.539413 Median interval of one step : 481/450, 115.3343 cents, amount: 1 Least squares average step : 146.37060 cents, oct.: 439.11181 cents Scale is not proper Scale has trivalence property Scale is a mode of a 760-tone equal temperament with octave 4/3 degrees: 165 341 760 Least number of segments generator : 381 of 249.678 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 419 of 274.580 cents and inv. generated superset size: 26 = 23 more = 866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 51.11986 cents Scale diversity : 1.134082 Lumma stability : 0.434211 Lumma impropriety factor : 0.102641 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 : 231361/230400, 7.2060 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 159.2482 cents: 2 -- Rational properties -- Prime limit : 37 Odd number limit : 481 (O: 481 U: 481) Highest odd numerator or denominator: 481 Scale harmonicity : 0.020289 Fundamental : 1/108225, -16.7237 octaves, 0.0024 Hz. Guide tone : 512, 9.0000 octaves, 133952.289 Hz. Exponens Consonantiae : 5.541120E+07, 25.72367 octaves Euler's gradus suavitatis : 70 Sum of Mann's harmonic distance : 740.5, average 246.83333 Mersenne's string divisions : 3343431 Sum of van Prooijen's expressibility: 5.51145, average 1.83715 Sum of Tenney's harmonic distance : 11.23102, average 3.74367 Vogel's harmonic complexity : 49.33333 Wille's k value : 18037 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 36.48356, average 6.08059 Lattice compactness (without 2's) : 11.47871, average 1.91312 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 9 6.33333 19 3: -2 .. 0 -1.00000 3 1 5: -2 .. 0 -0.66667 2 1 13: -1 .. 0 -0.33333 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 17 25 35| Scale is weakly epimorphic with val: <7 11 15 25 36| Scale is weakly epimorphic with val: <7 11 15 25 39| Scale is weakly epimorphic with val: <7 11 15 26 35| Scale is weakly epimorphic with val: <7 11 15 26 38| Scale is weakly epimorphic with val: <7 11 15 26 41| Scale is weakly epimorphic with val: <7 11 15 27 37| Scale is weakly epimorphic with val: <7 11 15 27 40| Scale is weakly epimorphic with val: <7 11 15 28 36| Scale is weakly epimorphic with val: <7 11 15 28 39| Scale is weakly epimorphic with val: <7 11 15 29 35| Scale is weakly epimorphic with val: <7 11 15 29 38| Scale is weakly epimorphic with val: <7 11 15 29 41| Scale is weakly epimorphic with val: <7 11 15 30 37| Scale is weakly epimorphic with val: <7 11 15 30 40| Scale is JI-epimorphic with val: <7 11 16 25 37| Scale is weakly epimorphic with val: <7 11 16 25 40| Scale is JI-epimorphic with val: <7 11 16 26 36| Scale is weakly epimorphic with val: <7 11 16 26 39| Scale is JI-epimorphic with val: <7 11 16 27 35| Scale is weakly epimorphic with val: <7 11 16 27 38| Scale is weakly epimorphic with val: <7 11 16 27 41| Scale is weakly epimorphic with val: <7 11 16 28 37| Scale is weakly epimorphic with val: <7 11 16 28 40| Scale is weakly epimorphic with val: <7 11 16 29 36| Scale is weakly epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 30 35| Scale is weakly epimorphic with val: <7 11 16 30 38| Scale is weakly epimorphic with val: <7 11 16 30 41| Scale is weakly epimorphic with val: <7 11 18 25 36| Scale is weakly epimorphic with val: <7 11 18 25 39| Scale is weakly epimorphic with val: <7 11 18 26 35| Scale is weakly epimorphic with val: <7 11 18 26 38| Scale is weakly epimorphic with val: <7 11 18 26 41| Scale is weakly epimorphic with val: <7 11 18 27 37| Scale is weakly epimorphic with val: <7 11 18 27 40| Scale is weakly epimorphic with val: <7 11 18 28 36| Scale is weakly epimorphic with val: <7 11 18 28 39| Scale is weakly epimorphic with val: <7 11 18 29 35| Scale is weakly epimorphic with val: <7 11 18 29 38| Scale is weakly epimorphic with val: <7 11 18 29 41| Scale is weakly epimorphic with val: <7 11 18 30 37| Scale is weakly epimorphic with val: <7 11 18 30 40| Scale is weakly epimorphic with val: <7 11 19 25 37| Scale is weakly epimorphic with val: <7 11 19 25 40| Scale is weakly epimorphic with val: <7 11 19 26 36| Scale is weakly epimorphic with val: <7 11 19 26 39| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 11 19 27 38| Scale is weakly epimorphic with val: <7 11 19 27 41| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is weakly epimorphic with val: <7 11 19 28 40| Scale is weakly epimorphic with val: <7 11 19 29 36| Scale is weakly epimorphic with val: <7 11 19 29 39| Scale is weakly epimorphic with val: <7 11 19 30 35| Scale is weakly epimorphic with val: <7 11 19 30 38| Scale is weakly epimorphic with val: <7 11 19 30 41| Scale is weakly epimorphic with val: <7 12 17 25 35| Scale is weakly epimorphic with val: <8 11 16 28 41| Scale is weakly epimorphic with val: <8 11 16 29 40| Scale is weakly epimorphic with val: <8 11 16 30 39| Scale is weakly epimorphic with val: <8 11 19 28 41| Scale is weakly epimorphic with val: <8 11 19 29 40| Scale is weakly epimorphic with val: <8 11 19 30 39| Scale is weakly epimorphic with val: <8 12 16 28 41| Scale is weakly epimorphic with val: <8 12 16 29 40| Scale is weakly epimorphic with val: <8 12 16 30 39| Scale is weakly epimorphic with val: <8 12 19 28 41| Scale is weakly epimorphic with val: <8 12 19 29 40| Scale is weakly epimorphic with val: <8 12 19 30 39|
FIT/MODE
3: 0 1 2 N G T3 SD: 70.6917 c. M: 108.1283 c. 4: 1 1 2 P M ME S SD: 17.5282 c. M:-25.5599 c. 5: 1 1 3 N M DE S SD: 14.8366 c. M: 24.2446 c. 9: 2 2 5 N M DE S SD: 1.9099 c. M:-2.5484 c. 38: 8 9 21 N T3 SD: 1.9290 c. M: 3.2767 c. 42: 9 10 23 N T3 SD: 1.3380 c. M:-1.8435 c. 47: 10 11 26 N T3 SD: 1.3589 c. M: 2.1613 c. 51: 11 12 28 N T3 SD: 0.7774 c. M:-1.1460 c. 60: 13 14 33 N T3 SD: 0.4001 c. M:-0.6577 c. 69: 15 16 38 N T3 SD: 0.1900 c. M:-0.2968 c. 147: 32 34 81 N T3 SD: 0.1882 c. M:-0.2897 c. 194: 42 45 107 N T3 SD: 0.1872 c. M: 0.3041 c. 203: 44 47 112 N T3 SD: 0.1549 c. M: 0.2010 c. 263: 57 61 145 N T3 SD: 0.1080 c. M: 0.1870 c. 272: 59 63 150 N T3 SD: 0.0705 c. M: 0.0965 c. 341: 74 79 188 N T3 SD: 0.0278 c. M: 0.0482 c. 419: 91 97 231 N T3 SD: 0.0226 c. M:-0.0390 c. 691: 150 160 381 N T3 SD: 0.0177 c. M: 0.0270 c. 760: 165 176 419 N T3 SD: 0.0014 c. M:-0.0024 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 6:7 S SD: 62.5132 cents 6 x 7:8 S SD: 21.7042 cents 7 x 8:9 S SD: 31.7157 cents 8 x 9:11 SD: 28.3739 cents 9 x 10:12 S SD: 20.5294 cents 10:11 x 13 SD: 35.9028 cents 11:12:13:15 SD: 29.1421 cents 12:13:14:16 S SD: 17.6734 cents 13:14:15:17 SD: 15.3709 cents 14:15:16:19 SD: 11.1874 cents 15:16:17:20 SD: 2.5581 cents 66:70:75:88 SD: 2.2072 cents 78:83:89:104 SD: 1.6557 cents 93:99:106:124 SD: 1.0178 cents 108:115:123:144 SD: 0.5971 cents 123:131:140:164 SD: 0.3888 cents 261:278:297:348 SD: 0.3793 cents 297:316:338:396 SD: 0.2920 cents 312:332:355:416 SD: 0.1891 cents 327:348:372:436 SD: 0.1491 cents 435:463:495:580 SD: 0.0893 cents 450:479:512:600 SD: 0.0025 cents