Scala analysis: 020_H6
Hyperenharmonic tetrachord 93/92 * 46/45 * 40/31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93/92 18.716226 2: 31/30 56.766858 31st-partial chroma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/31 441.2781 1: 93/92 18.7162 2: 46/45 38.0506 23rd-partial chroma 3: 40/31 441.2781
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 93/92 18.716 cents 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 40/31 441.278 cents 2: 1 31/30 56.767 cents 31st-partial chroma 2: 1 30/23 459.994 cents 2: 1 368/279 479.329 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 : 18.7 56.8 498.0 18.7 : 38.1 479.3 498.0 56.8 : 441.3 460.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.7162 .. 441.2781 cents 3680/2883, 422.5619 cents 93/92, 18.7162 cents 2: 56.7669 .. 479.3288 cents 3680/2883, 422.5619 cents 961/1200,-384.5113 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 93/92, 18.7162 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/31, 441.2781 cents Average / Smallest step : 8.870111 Largest / Average step : 2.658062 Largest / Smallest step : 23.577303 Median interval of one step : 46/45, 38.0506 cents, amount: 1 Least squares average step : 116.17035 cents, oct.: 348.51106 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1623-tone equal temperament with octave 4/3 degrees: 61 185 1623 Least number of segments generator : 812 of 249.176 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1171 of 359.341 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 18.71623 cents Scale diversity : 0.092948 Lumma stability : 0.075159 Lumma impropriety factor : 0.772041 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 : 93/92, 18.7162 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 403.2275 cents: 2 -- Rational properties -- Prime limit : 31 Odd number limit : 279 (O: 93 U: 279) Highest odd numerator or denominator: 93 Scale harmonicity : 0.017295 Fundamental : 1/1380, -10.4305 octaves, 0.1896 Hz. Guide tone : 372, 8.5392 octaves, 97324.710 Hz. Exponens Consonantiae : 5.133600E+05, 18.96961 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 126.5, average 42.16667 Mersenne's string divisions : 78995 Sum of van Prooijen's expressibility: 3.93697, average 1.31232 Sum of Tenney's harmonic distance : 7.97993, average 2.65998 Vogel's harmonic complexity : 43.00000 Wille's k value : 697 Wilson's harmonic complexity : 65 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.80821, average 2.80137 Lattice compactness (without 2's) : 9.51398, average 1.58566 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 23: -1 .. 0 -0.33333 1 31: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 30 35| Scale is weakly epimorphic with val: <6 10 15 31 34| Scale is weakly epimorphic with val: <6 10 15 33 38| Scale is weakly epimorphic with val: <6 10 15 34 34| Scale is weakly epimorphic with val: <6 10 16 31 36| Scale is weakly epimorphic with val: <6 10 16 32 35| Scale is weakly epimorphic with val: <6 10 16 34 39| Scale is weakly epimorphic with val: <6 10 16 35 35| Scale is weakly epimorphic with val: <6 10 17 30 36| Scale is weakly epimorphic with val: <6 10 17 32 37| Scale is weakly epimorphic with val: <6 10 17 33 36| Scale is weakly epimorphic with val: <6 10 17 36 36| Scale is weakly epimorphic with val: <6 10 18 30 35| Scale is weakly epimorphic with val: <6 10 18 31 37| Scale is weakly epimorphic with val: <6 10 18 33 38| Scale is weakly epimorphic with val: <6 10 18 34 37| Scale is weakly epimorphic with val: <6 10 19 31 36| Scale is weakly epimorphic with val: <6 10 19 32 38| Scale is weakly epimorphic with val: <6 10 19 34 39| Scale is weakly epimorphic with val: <6 10 19 35 38| Scale is weakly epimorphic with val: <6 11 15 30 34| Scale is weakly epimorphic with val: <6 11 15 32 35| Scale is weakly epimorphic with val: <6 11 15 33 37| Scale is weakly epimorphic with val: <6 11 15 35 35| Scale is weakly epimorphic with val: <6 11 16 30 36| Scale is weakly epimorphic with val: <6 11 16 31 35| Scale is weakly epimorphic with val: <6 11 16 33 36| Scale is weakly epimorphic with val: <6 11 16 34 38| Scale is weakly epimorphic with val: <6 11 16 36 36| Scale is weakly epimorphic with val: <6 11 17 31 37| Scale is weakly epimorphic with val: <6 11 17 32 36| Scale is weakly epimorphic with val: <6 11 17 34 37| Scale is weakly epimorphic with val: <6 11 17 35 39| Scale is weakly epimorphic with val: <6 11 18 30 34| Scale is weakly epimorphic with val: <6 11 18 32 38| Scale is weakly epimorphic with val: <6 11 18 33 37| Scale is weakly epimorphic with val: <6 11 18 35 38| Scale is weakly epimorphic with val: <6 11 19 30 39| Scale is weakly epimorphic with val: <6 11 19 31 35| Scale is weakly epimorphic with val: <6 11 19 33 39| Scale is weakly epimorphic with val: <6 11 19 34 38| Scale is weakly epimorphic with val: <6 11 19 36 39| Scale is weakly epimorphic with val: <7 10 15 30 37| Scale is weakly epimorphic with val: <7 10 15 32 35| Scale is weakly epimorphic with val: <7 10 15 35 35| Scale is weakly epimorphic with val: <7 10 16 30 36| Scale is weakly epimorphic with val: <7 10 16 31 38| Scale is weakly epimorphic with val: <7 10 16 33 36| Scale is weakly epimorphic with val: <7 10 16 36 36| Scale is weakly epimorphic with val: <7 10 17 31 37| Scale is weakly epimorphic with val: <7 10 17 32 39| Scale is weakly epimorphic with val: <7 10 17 34 37| Scale is weakly epimorphic with val: <7 10 18 30 37| Scale is weakly epimorphic with val: <7 10 18 32 38| Scale is weakly epimorphic with val: <7 10 18 35 38| Scale is weakly epimorphic with val: <7 10 19 30 39| Scale is weakly epimorphic with val: <7 10 19 31 38| Scale is weakly epimorphic with val: <7 10 19 33 39| Scale is weakly epimorphic with val: <7 10 19 36 39| Scale is JI-epimorphic with val: <7 11 15 31 35| Scale is weakly epimorphic with val: <7 11 15 31 38| Scale is weakly epimorphic with val: <7 11 15 32 34| Scale is weakly epimorphic with val: <7 11 15 32 37| Scale is weakly epimorphic with val: <7 11 15 34 35| Scale is weakly epimorphic with val: <7 11 15 34 38| Scale is weakly epimorphic with val: <7 11 15 35 37| 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 32 33| Scale is JI-epimorphic with val: <7 11 16 32 36| Scale is weakly epimorphic with val: <7 11 16 32 39| Scale is weakly epimorphic with val: <7 11 16 33 35| Scale is weakly epimorphic with val: <7 11 16 33 38| Scale is weakly epimorphic with val: <7 11 16 35 36| Scale is weakly epimorphic with val: <7 11 16 35 39| Scale is weakly epimorphic with val: <7 11 16 36 38| Scale is weakly epimorphic with val: <7 11 17 30 34| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is weakly epimorphic with val: <7 11 17 31 33| Scale is weakly epimorphic with val: <7 11 17 31 36| Scale is weakly epimorphic with val: <7 11 17 31 39| Scale is weakly epimorphic with val: <7 11 17 33 34| Scale is JI-epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 34 36| Scale is weakly epimorphic with val: <7 11 17 34 39| Scale is weakly epimorphic with val: <7 11 17 36 37| Scale is weakly epimorphic with val: <7 11 18 31 35| Scale is weakly epimorphic with val: <7 11 18 31 38| Scale is weakly epimorphic with val: <7 11 18 32 34| Scale is weakly epimorphic with val: <7 11 18 32 37| Scale is weakly epimorphic with val: <7 11 18 34 35| Scale is JI-epimorphic with val: <7 11 18 34 38| Scale is weakly epimorphic with val: <7 11 18 35 37| 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 32 33| Scale is weakly epimorphic with val: <7 11 19 32 36| Scale is weakly epimorphic with val: <7 11 19 32 39| Scale is weakly epimorphic with val: <7 11 19 33 35| Scale is weakly epimorphic with val: <7 11 19 33 38| Scale is weakly epimorphic with val: <7 11 19 35 36| Scale is JI-epimorphic with val: <7 11 19 35 39| Scale is weakly epimorphic with val: <7 11 19 36 38| Scale is weakly epimorphic with val: <7 12 15 30 35| Scale is weakly epimorphic with val: <7 12 15 31 37| Scale is weakly epimorphic with val: <7 12 15 33 38| Scale is weakly epimorphic with val: <7 12 15 34 37| Scale is weakly epimorphic with val: <7 12 16 31 36| Scale is weakly epimorphic with val: <7 12 16 32 38| Scale is weakly epimorphic with val: <7 12 16 34 39| Scale is weakly epimorphic with val: <7 12 16 35 38| Scale is weakly epimorphic with val: <7 12 17 30 39| Scale is weakly epimorphic with val: <7 12 17 32 37| Scale is weakly epimorphic with val: <7 12 17 33 39| Scale is weakly epimorphic with val: <7 12 17 36 39| Scale is weakly epimorphic with val: <7 12 18 30 35| Scale is weakly epimorphic with val: <7 12 18 33 38| Scale is weakly epimorphic with val: <7 12 19 31 36| Scale is weakly epimorphic with val: <7 12 19 34 39| Scale is weakly epimorphic with val: <8 11 15 30 38| Scale is weakly epimorphic with val: <8 11 15 31 37| Scale is weakly epimorphic with val: <8 11 15 34 37| Scale is weakly epimorphic with val: <8 11 16 31 39| Scale is weakly epimorphic with val: <8 11 16 32 38| Scale is weakly epimorphic with val: <8 11 16 35 38| Scale is weakly epimorphic with val: <8 11 17 30 39| Scale is weakly epimorphic with val: <8 11 17 33 39| Scale is weakly epimorphic with val: <8 11 17 36 39| Scale is weakly epimorphic with val: <8 11 18 30 38| Scale is weakly epimorphic with val: <8 11 19 31 39| Scale is weakly epimorphic with val: <8 12 15 30 37| Scale is weakly epimorphic with val: <8 12 15 32 38| Scale is weakly epimorphic with val: <8 12 15 35 38| Scale is weakly epimorphic with val: <8 12 16 30 39| Scale is weakly epimorphic with val: <8 12 16 31 38| Scale is weakly epimorphic with val: <8 12 16 33 39| Scale is weakly epimorphic with val: <8 12 16 36 39| Scale is weakly epimorphic with val: <8 12 17 32 39| Scale is weakly epimorphic with val: <8 12 18 30 37| Scale is weakly epimorphic with val: <8 12 19 31 38|
FIT/MODE
3: 0 0 3 N M DE S SD: 34.5098 c. M: 56.7669 c. 6: 0 1 5 N G T3 SD: 18.6089 c. M:-26.2406 c. 7: 0 1 6 N G T3 SD: 13.6278 c. M: 18.7162 c. 8: 0 1 7 N G T3 SD: 11.2609 c. M: 18.7162 c. 9: 0 1 8 N G T3 SD: 10.8372 c. M: 18.7162 c. 10: 0 1 9 N G T3 SD: 11.5293 c. M: 18.7162 c. 11: 0 1 10 N G T3 SD: 12.6796 c. M: 18.7162 c. 15: 1 1 13 N M DE S SD: 10.0462 c. M:-14.4868 c. 16: 1 1 14 N M DE S SD: 7.8353 c. M:-12.4116 c. 17: 1 1 15 N M DE S SD: 6.1990 c. M:-10.5805 c. 18: 1 1 16 N M DE S SD: 5.2344 c. M:-8.9529 c. 19: 1 1 17 N M DE S SD: 5.0015 c. M:-7.4967 c. 20: 1 1 18 N M DE S SD: 5.3772 c. M: 6.9624 c. 23: 1 2 20 N T3 SD: 5.0265 c. M:-8.1955 c. 24: 1 2 21 N T3 SD: 3.3799 c. M:-5.4888 c. 25: 1 2 22 N T3 SD: 1.8659 c. M:-2.9985 c. 26: 1 2 23 N T3 SD: 0.4771 c. M:-0.6999 c. 53: 2 4 47 N T3 SD: 0.2265 c. M: 0.3844 c. 79: 3 6 70 N T3 SD: 0.1148 c. M:-0.1969 c. 132: 5 10 117 N T3 SD: 0.1309 c. M: 0.1708 c. 184: 7 14 163 N T3 SD: 0.1403 c. M:-0.2311 c. 211: 8 16 187 N T3 SD: 0.1178 c. M:-0.1670 c. 263: 10 20 233 N T3 SD: 0.1301 c. M:-0.2208 c. 290: 11 22 257 N T3 SD: 0.1144 c. M:-0.1751 c. 343: 13 26 304 N T3 SD: 0.1220 c. M:-0.1601 c. 369: 14 28 327 N T3 SD: 0.1133 c. M:-0.1798 c. 404: 15 31 358 N T3 SD: 0.1340 c. M: 0.2245 c. 421: 16 32 373 N T3 SD: 0.1227 c. M:-0.2118 c. 429: 16 33 380 N T3 SD: 0.1067 c. M: 0.1411 c. 430: 16 33 381 N T3 SD: 0.1067 c. M: 0.1843 c. 456: 17 35 404 N T3 SD: 0.0874 c. M: 0.1488 c. 482: 18 37 427 N T3 SD: 0.0770 c. M: 0.1170 c. 508: 19 39 450 N T3 SD: 0.0756 c. M:-0.0965 c. 509: 19 39 451 N T3 SD: 0.0728 c. M: 0.1252 c. 535: 20 41 474 N T3 SD: 0.0575 c. M: 0.0977 c. 561: 21 43 497 N T3 SD: 0.0514 c. M: 0.0728 c. 588: 22 45 521 N T3 SD: 0.0483 c. M: 0.0819 c. 614: 23 47 544 N T3 SD: 0.0354 c. M: 0.0598 c. 640: 24 49 567 N T3 SD: 0.0331 c. M:-0.0414 c. 667: 25 51 591 N T3 SD: 0.0301 c. M: 0.0489 c. 693: 26 53 614 N T3 SD: 0.0184 c. M: 0.0306 c. 746: 28 57 661 N T3 SD: 0.0172 c. M: 0.0228 c. 772: 29 59 684 N T3 SD: 0.0051 c. M: 0.0073 c. 1597: 60 122 1415 N T3 SD: 0.0052 c. M: 0.0078 c. 1623: 61 124 1438 N T3 SD: 0.0025 c. M:-0.0035 c. 2395: 90 183 2122 N T3 SD: 0.0024 c. M:-0.0040 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: 105.0520 cents 7 x 8:9 S SD: 92.7119 cents 8 x 9:11 SD: 78.2450 cents 9 x 10:12 S SD: 62.8184 cents 10 x 11:13 SD: 58.3877 cents 11 x 12:15 S SD: 50.8067 cents 12 x 13:16 SD: 40.9029 cents 13 x 14:17 SD: 39.5185 cents 14 x 15:19 SD: 34.8827 cents 15 x 16:20 S SD: 27.4822 cents 16 x 17:21 SD: 27.6833 cents 17 x 18:23 SD: 24.5895 cents 18 x 19:24 SD: 18.4181 cents 19 x 20:25 S SD: 19.6976 cents 20 x 21:27 SD: 17.5345 cents 21 x 22:28 SD: 11.8851 cents 22 x 23:29 SD: 14.1341 cents 23 x 24:31 SD: 12.6132 cents 24 x 25:32 SD: 6.9528 cents 25 x 26:33 SD: 10.3283 cents 26 x 27:35 SD: 9.3263 cents 27 x 28:36 SD: 3.0970 cents 28 x 29:37 SD: 8.0150 cents 29 x 30:39 SD: 7.4923 cents 30 x 31:40 SD: 0.0000 cents 31 x 32:41 SD: 7.0668 cents 32 x 33:43 SD: 6.9592 cents 33 x 34:44 SD: 2.5422 cents 34 x 35:45 SD: 7.1864 cents 35 x 36:47 SD: 7.3446 cents 36 x 37:48 SD: 4.6664 cents 37 x 38:49 SD: 7.9069 cents 38 x 39:51 SD: 8.1861 cents 39 x 40:52 SD: 6.4679 cents 40 x 41:53 SD: 8.8646 cents 41 x 42:55 SD: 9.1817 cents 42 x 43:56 SD: 8.0150 cents 43 x 44:57 SD: 9.8713 cents 44 x 45:59 SD: 10.1886 cents 45 x 47:60 SD: 9.2580 cents 46:47:48:61 SD: 8.9314 cents 47:48:49:63 SD: 8.4015 cents 48:49:50:64 SD: 7.3159 cents 50:51:52:67 SD: 6.9987 cents 51:52:53:68 SD: 5.9499 cents 53:54:55:71 SD: 5.8377 cents 54:55:56:72 SD: 4.8153 cents 57:58:59:76 SD: 3.9218 cents 60:61:62:80 SD: 3.3000 cents 63:64:65:84 SD: 2.9842 cents 66:67:68:88 SD: 2.9703 cents 81:82:84:108 SD: 2.2298 cents 84:85:87:112 SD: 1.4536 cents 87:88:90:116 SD: 0.7340 cents 90:91:93:120 SD: 0.1379 cents