Scala analysis: 158_C5
Chromatic tetrachord 40/39 * 39/37 * 37/30
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 40/37 134.969675 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 37/30 363.0753 1: 40/39 43.8311 tridecimal minor diesis 2: 39/37 91.1386 3: 37/30 363.0753
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 39/37 91.139 cents 1: 1 37/30 363.075 cents 2: 1 40/37 134.970 cents 2: 1 148/117 406.906 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 135.0 498.0 43.8 : 91.1 454.2 498.0 135.0: 363.1 406.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 363.0753 cents 481/400, 319.2443 cents 40/39, 43.8311 cents 2: 134.9697 .. 454.2139 cents 481/400, 319.2443 cents 1200/1369,-228.1056 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 37/30, 363.0753 cents Average / Smallest step : 3.787612 Largest / Average step : 2.187003 Largest / Smallest step : 8.283519 Median interval of one step : 39/37, 91.1386 cents, amount: 1 Least squares average step : 129.13610 cents, oct.: 387.40830 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1000-tone equal temperament with octave 4/3 degrees: 88 271 1000 Least number of segments generator : 501 of 249.521 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 909 of 452.723 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 43.83105 cents Scale diversity : 0.634557 Lumma stability : 0.176012 Lumma impropriety factor : 0.458002 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 : 40/39, 43.8311 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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% -- Rational properties -- Prime limit : 37 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.029222 Fundamental : 1/1443, -10.4949 octaves, 0.1813 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 5.772000E+04, 15.81678 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 81.5, average 27.16667 Mersenne's string divisions : 6083 Sum of van Prooijen's expressibility: 3.63639, average 1.21213 Sum of Tenney's harmonic distance : 7.44257, average 2.48086 Vogel's harmonic complexity : 40.33333 Wille's k value : 240 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.74076, average 2.29013 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 17 25 36| Scale is weakly epimorphic with val: <7 10 17 25 39| Scale is weakly epimorphic with val: <7 10 17 26 35| Scale is weakly epimorphic with val: <7 10 17 29 35| Scale is weakly epimorphic with val: <7 10 18 26 37| Scale is weakly epimorphic with val: <7 10 18 26 40| Scale is weakly epimorphic with val: <7 10 18 27 36| Scale is weakly epimorphic with val: <7 10 18 30 36| Scale is weakly epimorphic with val: <7 10 19 25 37| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 19 27 38| Scale is weakly epimorphic with val: <7 10 19 27 41| Scale is weakly epimorphic with val: <7 10 19 28 37| 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 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 35| Scale is weakly epimorphic with val: <7 11 16 25 38| Scale is weakly epimorphic with val: <7 11 16 25 41| Scale is weakly epimorphic with val: <7 11 16 27 36| Scale is weakly epimorphic with val: <7 11 16 27 39| Scale is weakly epimorphic with val: <7 11 16 28 35| Scale is weakly epimorphic with val: <7 11 16 28 38| Scale is weakly epimorphic with val: <7 11 16 28 41| Scale is weakly epimorphic with val: <7 11 16 30 36| Scale is weakly epimorphic with val: <7 11 16 30 39| Scale is weakly epimorphic with val: <7 11 17 25 37| Scale is weakly epimorphic with val: <7 11 17 25 40| Scale is JI-epimorphic with val: <7 11 17 26 36| Scale is weakly epimorphic with val: <7 11 17 26 39| Scale is weakly epimorphic with val: <7 11 17 28 37| Scale is weakly epimorphic with val: <7 11 17 28 40| Scale is weakly epimorphic with val: <7 11 17 29 36| Scale is weakly epimorphic with val: <7 11 17 29 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 JI-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 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 35| Scale is weakly epimorphic with val: <7 11 19 25 38| Scale is weakly epimorphic with val: <7 11 19 25 41| Scale is weakly epimorphic with val: <7 11 19 27 36| Scale is weakly epimorphic with val: <7 11 19 27 39| Scale is weakly epimorphic with val: <7 11 19 28 35| Scale is JI-epimorphic with val: <7 11 19 28 38| Scale is weakly epimorphic with val: <7 11 19 28 41| Scale is weakly epimorphic with val: <7 11 19 30 36| Scale is weakly epimorphic with val: <7 11 19 30 39| Scale is weakly epimorphic with val: <7 12 17 25 35| Scale is weakly epimorphic with val: <7 12 17 28 35| Scale is weakly epimorphic with val: <7 12 18 26 36| Scale is weakly epimorphic with val: <7 12 18 29 36| Scale is weakly epimorphic with val: <7 12 19 25 36| Scale is weakly epimorphic with val: <7 12 19 25 39| Scale is weakly epimorphic with val: <7 12 19 27 37| Scale is weakly epimorphic with val: <7 12 19 30 37| Scale is weakly epimorphic with val: <8 11 15 25 35| Scale is weakly epimorphic with val: <8 11 15 25 38| Scale is weakly epimorphic with val: <8 11 15 25 41| Scale is weakly epimorphic with val: <8 11 15 27 36| Scale is weakly epimorphic with val: <8 11 15 30 36| Scale is weakly epimorphic with val: <8 11 16 25 37| Scale is weakly epimorphic with val: <8 11 16 26 36| Scale is weakly epimorphic with val: <8 11 16 26 39| Scale is weakly epimorphic with val: <8 11 16 28 37| Scale is weakly epimorphic with val: <8 11 17 26 38| Scale is weakly epimorphic with val: <8 11 17 27 37| Scale is weakly epimorphic with val: <8 11 17 27 40| Scale is weakly epimorphic with val: <8 11 17 29 38| Scale is weakly epimorphic with val: <8 11 18 27 39| Scale is weakly epimorphic with val: <8 11 18 28 35| Scale is weakly epimorphic with val: <8 11 18 28 38| Scale is weakly epimorphic with val: <8 11 18 28 41| Scale is weakly epimorphic with val: <8 11 18 30 39| Scale is weakly epimorphic with val: <8 11 19 25 40| Scale is weakly epimorphic with val: <8 11 19 28 40| Scale is weakly epimorphic with val: <8 11 19 29 36| Scale is weakly epimorphic with val: <8 11 19 29 39| Scale is weakly epimorphic with val: <8 12 15 25 36| Scale is weakly epimorphic with val: <8 12 15 28 36| Scale is weakly epimorphic with val: <8 12 16 25 35| Scale is weakly epimorphic with val: <8 12 16 25 38| Scale is weakly epimorphic with val: <8 12 16 25 41| Scale is weakly epimorphic with val: <8 12 16 26 37| Scale is weakly epimorphic with val: <8 12 16 29 37| Scale is weakly epimorphic with val: <8 12 17 26 36| Scale is weakly epimorphic with val: <8 12 17 26 39| Scale is weakly epimorphic with val: <8 12 17 27 38| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 18 25 39| Scale is weakly epimorphic with val: <8 12 18 27 37| Scale is weakly epimorphic with val: <8 12 18 27 40| Scale is weakly epimorphic with val: <8 12 18 28 39| Scale is weakly epimorphic with val: <8 12 19 26 40| Scale is weakly epimorphic with val: <8 12 19 28 35| Scale is weakly epimorphic with val: <8 12 19 28 38| Scale is weakly epimorphic with val: <8 12 19 28 41| Scale is weakly epimorphic with val: <8 12 19 29 40|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.0106 c. M: 43.8311 c. 4: 0 1 3 N G T3 SD: 26.0163 c. M: 43.8311 c. 7: 1 1 5 N M DE S SD: 16.3299 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 12.2317 c. M:-18.4246 c. 10: 1 2 7 N T3 SD: 9.0242 c. M:-14.4438 c. 11: 1 2 8 N T3 SD: 0.9715 c. M:-1.4458 c. 59: 5 11 43 N T3 SD: 0.9391 c. M: 1.6238 c. 67: 6 12 49 N T3 SD: 0.8070 c. M: 1.1665 c. 70: 6 13 51 N T3 SD: 0.6705 c. M: 1.1415 c. 78: 7 14 57 N T3 SD: 0.7128 c. M: 0.8806 c. 81: 7 15 59 N T3 SD: 0.4883 c. M: 0.7901 c. 92: 8 17 67 N T3 SD: 0.3693 c. M: 0.5228 c. 103: 9 19 75 N T3 SD: 0.3028 c. M:-0.4212 c. 114: 10 21 83 N T3 SD: 0.2801 c. M:-0.4636 c. 125: 11 23 91 N T3 SD: 0.2879 c. M:-0.4986 c. 136: 12 25 99 N T3 SD: 0.3118 c. M:-0.5279 c. 137: 12 25 100 N T3 SD: 0.2918 c. M: 0.4612 c. 148: 13 27 108 N T3 SD: 0.2151 c. M: 0.3629 c. 159: 14 29 116 N T3 SD: 0.1612 c. M: 0.2783 c. 170: 15 31 124 N T3 SD: 0.1352 c. M: 0.2046 c. 181: 16 33 132 N T3 SD: 0.1385 c. M:-0.1950 c. 240: 21 44 175 N T3 SD: 0.1532 c. M: 0.2521 c. 251: 22 46 183 N T3 SD: 0.1053 c. M: 0.1777 c. 262: 23 48 191 N T3 SD: 0.0633 c. M: 0.1095 c. 273: 24 50 199 N T3 SD: 0.0326 c. M: 0.0469 c. 284: 25 52 207 N T3 SD: 0.0373 c. M:-0.0637 c. 443: 39 81 323 N T3 SD: 0.0352 c. M: 0.0591 c. 557: 49 102 406 N T3 SD: 0.0294 c. M:-0.0479 c. 705: 62 129 514 N T3 SD: 0.0286 c. M: 0.0383 c. 716: 63 131 522 N T3 SD: 0.0150 c. M: 0.0245 c. 727: 64 133 530 N T3 SD: 0.0100 c. M:-0.0134 c. 1000: 88 183 729 N T3 SD: 0.0018 c. M: 0.0031 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: 99.7208 cents 6 x 7:8 S SD: 65.9506 cents 7 x 8:9 S SD: 57.4877 cents 8 x 9:11 SD: 43.5625 cents 9 x 10:12 S SD: 23.7170 cents 10 x 11:13 SD: 26.5671 cents 11 x 12:15 S SD: 20.9710 cents 12 x 13:16 SD: 1.8015 cents 13 x 14:17 SD: 17.1364 cents 14 x 15:19 SD: 17.1757 cents 15 x 16:20 S SD: 11.6192 cents 16 x 17:21 SD: 20.2743 cents 17 x 18:23 SD: 21.9992 cents 18 x 19:24 SD: 20.6833 cents 20:21:22:27 SD: 18.3057 cents 21:22:23:28 SD: 14.3552 cents 22:23:24:29 SD: 13.8814 cents 23:24:25:31 SD: 12.1534 cents 24:25:26:32 SD: 9.0274 cents 27:28:29:36 SD: 7.3988 cents 33:34:36:44 SD: 5.8415 cents 35:36:38:47 SD: 5.0667 cents 36:37:39:48 SD: 1.6985 cents 75:77:81:100 SD: 0.8161 cents 111:114:120:148 SD: 0.7793 cents 123:126:133:164 SD: 0.7139 cents 159:163:172:212 SD: 0.4536 cents 198:203:214:264 SD: 0.2628 cents 234:240:253:312 SD: 0.0617 cents