Scala analysis: 021_H6
Hyperenharmonic tetrachord 93/91 * 91/90 * 40/31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93/91 37.637005 2: 31/30 56.766858 31st-partial chroma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/31 441.2781 1: 93/91 37.6370 2: 91/90 19.1299 medium tridecimal comma, superleap 3: 40/31 441.2781
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 91/90 19.130 cents medium tridecimal comma, superleap 1: 1 93/91 37.637 cents 1: 1 40/31 441.278 cents 2: 1 31/30 56.767 cents 31st-partial chroma 2: 1 364/279 460.408 cents 2: 1 120/91 478.915 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 : 37.6 56.8 498.0 37.6 : 19.1 460.4 498.0 56.8 : 441.3 478.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.1299 .. 441.2781 cents 3600/2821, 422.1483 cents 91/90, 19.1299 cents 2: 56.7669 .. 478.9151 cents 3600/2821, 422.1483 cents 961/1200,-384.5113 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 91/90, 19.1299 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/31, 441.2781 cents Average / Smallest step : 8.678321 Largest / Average step : 2.658062 Largest / Smallest step : 23.067514 Median interval of one step : 93/91, 37.6370 cents, amount: 1 Least squares average step : 117.52184 cents, oct.: 352.56551 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1588-tone equal temperament with octave 4/3 degrees: 120 181 1588 Least number of segments generator : 795 of 249.336 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1527 of 478.914 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.12985 cents Scale diversity : 0.093928 Lumma stability : 0.076820 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 : 8370/8281, 18.5072 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 422.1483 cents: 2 -- Rational properties -- Prime limit : 31 Odd number limit : 279 (O: 93 U: 279) Highest odd numerator or denominator: 93 Scale harmonicity : 0.021199 Fundamental : 1/2730, -11.4147 octaves, 0.0958 Hz. Guide tone : 372, 8.5392 octaves, 97324.710 Hz. Exponens Consonantiae : 1.015560E+06, 19.95384 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 126.0, average 42.00000 Mersenne's string divisions : 78568 Sum of van Prooijen's expressibility: 3.93697, average 1.31232 Sum of Tenney's harmonic distance : 7.97519, average 2.65840 Vogel's harmonic complexity : 40.66667 Wille's k value : 1410 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.85315, average 2.47553 Lattice compactness (without 2's) : 10.24151, average 1.70692 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 31: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 16 19 27 36| Scale is weakly epimorphic with val: <7 11 16 19 28 35| Scale is weakly epimorphic with val: <7 11 16 19 28 38| Scale is JI-epimorphic with val: <7 11 16 20 26 36| Scale is weakly epimorphic with val: <7 11 16 20 27 35| Scale is weakly epimorphic with val: <7 11 16 20 27 38| Scale is weakly epimorphic with val: <7 11 16 21 26 35| Scale is weakly epimorphic with val: <7 11 16 21 26 38| Scale is weakly epimorphic with val: <7 11 16 21 28 36| Scale is weakly epimorphic with val: <7 11 17 19 26 36| Scale is weakly epimorphic with val: <7 11 17 19 28 34| Scale is JI-epimorphic with val: <7 11 17 19 28 37| Scale is weakly epimorphic with val: <7 11 17 20 27 34| Scale is JI-epimorphic with val: <7 11 17 20 27 37| Scale is weakly epimorphic with val: <7 11 17 20 28 36| Scale is weakly epimorphic with val: <7 11 17 21 26 34| Scale is JI-epimorphic with val: <7 11 17 21 26 37| Scale is weakly epimorphic with val: <7 11 17 21 27 36| Scale is weakly epimorphic with val: <7 11 18 19 26 35| Scale is weakly epimorphic with val: <7 11 18 19 26 38| Scale is weakly epimorphic with val: <7 11 18 19 27 34| Scale is weakly epimorphic with val: <7 11 18 19 27 37| Scale is weakly epimorphic with val: <7 11 18 20 26 34| Scale is weakly epimorphic with val: <7 11 18 20 26 37| Scale is weakly epimorphic with val: <7 11 18 20 28 35| Scale is JI-epimorphic with val: <7 11 18 20 28 38| Scale is weakly epimorphic with val: <7 11 18 21 27 35| Scale is JI-epimorphic with val: <7 11 18 21 27 38| Scale is weakly epimorphic with val: <7 11 18 21 28 34| Scale is weakly epimorphic with val: <7 11 18 21 28 37| Scale is weakly epimorphic with val: <7 12 16 19 26 36| Scale is weakly epimorphic with val: <7 12 16 19 27 38| Scale is weakly epimorphic with val: <7 12 16 20 26 38| Scale is weakly epimorphic with val: <7 12 16 21 28 38| Scale is weakly epimorphic with val: <7 12 17 19 27 37| Scale is weakly epimorphic with val: <7 12 17 20 26 37| Scale is weakly epimorphic with val: <7 12 18 19 28 38| Scale is weakly epimorphic with val: <7 12 18 20 27 38| Scale is weakly epimorphic with val: <7 12 18 21 26 38|
FIT/MODE
3: 0 0 3 N M DE S SD: 39.3235 c. M: 56.7669 c. 6: 0 1 5 N G T3 SD: 26.4897 c. M: 37.6370 c. 7: 1 0 6 N G T3 SD: 21.0549 c. M:-33.5123 c. 8: 1 0 7 N G T3 SD: 14.5625 c. M:-24.6186 c. 9: 1 0 8 N G T3 SD: 10.2531 c. M:-17.7013 c. 10: 1 0 9 N G T3 SD: 8.0937 c. M:-12.1675 c. 11: 1 0 10 N G T3 SD: 7.9663 c. M: 11.4900 c. 14: 1 1 12 N M DE S SD: 8.3886 c. M:-14.3824 c. 15: 1 1 13 N M DE S SD: 6.1257 c. M:-9.6391 c. 16: 1 1 14 N M DE S SD: 4.9158 c. M: 6.5092 c. 17: 1 1 15 N M DE S SD: 4.9294 c. M: 8.3402 c. 18: 1 1 16 N M DE S SD: 5.8137 c. M: 9.9678 c. 23: 2 1 20 N T3 SD: 5.7541 c. M:-8.1955 c. 24: 2 1 21 N T3 SD: 3.8764 c. M:-5.4888 c. 25: 2 1 22 N T3 SD: 2.1494 c. M:-2.9985 c. 26: 2 1 23 N T3 SD: 0.5610 c. M:-0.6999 c. 53: 4 2 47 N T3 SD: 0.2237 c. M: 0.3844 c. 79: 6 3 70 N T3 SD: 0.1104 c. M:-0.1892 c. 132: 10 5 117 N T3 SD: 0.1125 c. M: 0.1708 c. 211: 16 8 187 N T3 SD: 0.1008 c. M:-0.1294 c. 290: 22 11 257 N T3 SD: 0.0997 c. M:-0.1457 c. 412: 31 16 365 N T3 SD: 0.0981 c. M: 0.1627 c. 438: 33 17 388 N T3 SD: 0.0826 c. M: 0.1131 c. 464: 35 18 411 N T3 SD: 0.0809 c. M:-0.1219 c. 465: 35 18 412 N T3 SD: 0.0865 c. M: 0.1497 c. 491: 37 19 435 N T3 SD: 0.0648 c. M: 0.1061 c. 517: 39 20 458 N T3 SD: 0.0559 c. M:-0.0700 c. 544: 41 21 482 N T3 SD: 0.0581 c. M: 0.1005 c. 570: 43 22 505 N T3 SD: 0.0409 c. M: 0.0652 c. 596: 45 23 528 N T3 SD: 0.0380 c. M:-0.0571 c. 623: 47 24 552 N T3 SD: 0.0371 c. M: 0.0638 c. 649: 49 25 575 N T3 SD: 0.0232 c. M: 0.0342 c. 702: 53 27 622 N T3 SD: 0.0211 c. M: 0.0353 c. 728: 55 28 645 N T3 SD: 0.0108 c. M:-0.0157 c. 781: 59 30 692 N T3 SD: 0.0098 c. M: 0.0126 c. 807: 61 31 715 N T3 SD: 0.0086 c. M:-0.0115 c. 860: 65 33 762 N T3 SD: 0.0082 c. M: 0.0129 c. 1509: 114 58 1337 N T3 SD: 0.0066 c. M: 0.0113 c. 1588: 120 61 1407 N T3 SD: 0.0008 c. M: 0.0014 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 37:38 x 49 SD: 7.2553 cents 38:39 x 51 SD: 6.7573 cents 39:40 x 52 SD: 3.0970 cents 40:41 x 53 SD: 5.9988 cents 41:42 x 55 SD: 5.6440 cents 42:43 x 56 SD: 1.5499 cents 43:44 x 57 SD: 5.1619 cents 44:45 x 59 SD: 4.9452 cents 48:49:50:64 SD: 4.6801 cents 51:52:53:68 SD: 3.5392 cents 54:55:56:72 SD: 2.8446 cents 57:58:59:76 SD: 2.6935 cents 69 x 71:92 SD: 3.6498 cents 70 x 72:93 SD: 5.0574 cents 71 x 73:95 SD: 5.2978 cents 72 x 74:96 SD: 4.6664 cents 73:75 x 97 SD: 5.4567 cents 74:76 x 99 SD: 5.1693 cents 75:77:78:100 SD: 4.5552 cents 77:79:80:103 SD: 4.2889 cents 78:80:81:104 SD: 3.5248 cents 80:82:83:107 SD: 3.3968 cents 81:83:84:108 SD: 2.5698 cents 84:86:87:112 SD: 1.6827 cents 87:89:90:116 SD: 0.8584 cents 90:92:93:120 SD: 0.1379 cents 453:463:468:604 SD: 0.1349 cents 543:555:561:724 SD: 0.1236 cents