Scala analysis: 002_H1
Hyperenharmonic tetrachord 60/59 * 118/117 * 13/10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 40/39 43.831051 tridecimal minor diesis 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/10 454.2139 tridecimal semi-diminished fourth 1: 60/59 29.0971 2: 118/117 14.7340 3: 13/10 454.2139 tridecimal semi-diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 118/117 14.734 cents 1: 1 60/59 29.097 cents 1: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 40/39 43.831 cents tridecimal minor diesis 2: 1 59/45 468.948 cents 2: 1 78/59 483.311 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 : 29.1 43.8 498.0 29.1 : 14.7 468.9 498.0 43.8 : 454.2 483.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.7340 .. 454.2139 cents 1521/1180, 439.4800 cents 118/117, 14.7340 cents 2: 43.8311 .. 483.3110 cents 1521/1180, 439.4800 cents 400/507,-410.3829 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 118/117, 14.7340 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/10, 454.2139 cents Average / Smallest step : 11.267480 Largest / Average step : 2.735981 Largest / Smallest step : 30.827615 Median interval of one step : 60/59, 29.0971 cents, amount: 1 Least squares average step : 115.06387 cents, oct.: 345.19160 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1284-tone equal temperament with octave 4/3 degrees: 75 113 1284 Least number of segments generator : 643 of 249.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 881 of 341.727 cents and inv. generated superset size: 74 = 71 more = 2466.667% 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 14.73400 cents Scale diversity : 0.007596 Lumma stability : 0.059167 Lumma impropriety factor : 0.823988 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 : 3510/3481, 14.3631 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.3110 cents Number of appreciable 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 439.4800 cents: 2 -- Rational properties -- Prime limit : 59 Odd number limit : 117 (O: 59 U: 117) Highest odd numerator or denominator: 59 Scale harmonicity : 0.027110 Fundamental : 1/2301, -11.1680 octaves, 0.1137 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.761200E+05, 18.07494 octaves Euler's gradus suavitatis : 82 Sum of Mann's harmonic distance : 102.5, average 34.16667 Mersenne's string divisions : 9401 Sum of van Prooijen's expressibility: 3.83904, average 1.27968 Sum of Tenney's harmonic distance : 7.82131, average 2.60710 Vogel's harmonic complexity : 55.66667 Wille's k value : 383 Wilson's harmonic complexity : 83 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.56727, average 2.42788 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 59: -1 .. 0 -0.33333 1 1 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: <7 10 17 25 42| Scale is weakly epimorphic with val: <7 10 18 26 43| Scale is weakly epimorphic with val: <7 10 19 27 44| Scale is weakly epimorphic with val: <7 11 15 26 42| Scale is weakly epimorphic with val: <7 11 15 27 44| Scale is weakly epimorphic with val: <7 11 15 29 42| Scale is weakly epimorphic with val: <7 11 15 30 44| Scale is weakly epimorphic with val: <7 11 16 25 42| Scale is weakly epimorphic with val: <7 11 16 27 43| Scale is weakly epimorphic with val: <7 11 16 28 42| Scale is weakly epimorphic with val: <7 11 16 30 43| Scale is weakly epimorphic with val: <7 11 17 25 44| Scale is weakly epimorphic with val: <7 11 17 26 43| Scale is weakly epimorphic with val: <7 11 17 28 44| Scale is weakly epimorphic with val: <7 11 17 29 43| Scale is JI-epimorphic with val: <7 11 18 26 42| Scale is weakly epimorphic with val: <7 11 18 27 44| Scale is weakly epimorphic with val: <7 11 18 29 42| Scale is weakly epimorphic with val: <7 11 18 30 44| Scale is weakly epimorphic with val: <7 11 19 25 42| Scale is JI-epimorphic with val: <7 11 19 27 43| Scale is weakly epimorphic with val: <7 11 19 28 42| Scale is weakly epimorphic with val: <7 11 19 30 43| Scale is weakly epimorphic with val: <7 12 19 25 44| Scale is weakly epimorphic with val: <7 12 19 27 42| Scale is weakly epimorphic with val: <7 12 19 30 42| Scale is weakly epimorphic with val: <8 11 15 25 44| Scale is weakly epimorphic with val: <8 11 16 26 42| Scale is weakly epimorphic with val: <8 11 17 27 43| Scale is weakly epimorphic with val: <8 11 18 27 42| Scale is weakly epimorphic with val: <8 11 18 28 44| Scale is weakly epimorphic with val: <8 11 18 30 42| Scale is weakly epimorphic with val: <8 11 19 25 43| Scale is weakly epimorphic with val: <8 11 19 28 43| Scale is weakly epimorphic with val: <8 11 19 29 42| Scale is weakly epimorphic with val: <8 12 16 25 42| Scale is weakly epimorphic with val: <8 12 17 26 43| Scale is weakly epimorphic with val: <8 12 17 27 42| Scale is weakly epimorphic with val: <8 12 17 30 42| Scale is weakly epimorphic with val: <8 12 18 25 43| Scale is weakly epimorphic with val: <8 12 18 27 44| Scale is weakly epimorphic with val: <8 12 18 28 43| Scale is weakly epimorphic with val: <8 12 19 26 44| Scale is weakly epimorphic with val: <8 12 19 28 42| Scale is weakly epimorphic with val: <8 12 19 29 44|
FIT/MODE
3: 0 0 3 N M DE S SD: 30.3743 c. M: 43.8311 c. 7: 0 1 6 N G T3 SD: 23.0429 c. M: 29.0971 c. 8: 1 0 7 N G T3 SD: 21.9010 c. M:-33.1586 c. 9: 1 0 8 N G T3 SD: 16.5431 c. M:-26.2413 c. 10: 1 0 9 N G T3 SD: 12.4429 c. M:-20.7074 c. 11: 1 0 10 N G T3 SD: 9.3786 c. M:-16.1798 c. 12: 1 0 11 N G T3 SD: 7.2879 c. M:-12.4067 c. 13: 1 0 12 N G T3 SD: 6.2013 c. M:-9.2141 c. 14: 1 0 13 N G T3 SD: 6.0588 c. M: 8.2564 c. 18: 1 1 16 N M DE S SD: 6.6947 c. M:-11.5073 c. 19: 1 1 17 N M DE S SD: 5.2341 c. M:-8.5947 c. 20: 1 1 18 N M DE S SD: 4.2142 c. M:-5.9734 c. 21: 1 1 19 N M DE S SD: 3.7383 c. M: 5.3806 c. 22: 1 1 20 N M DE S SD: 3.8212 c. M: 6.4586 c. 23: 1 1 21 N M DE S SD: 4.3078 c. M: 7.4429 c. 30: 2 1 27 N T3 SD: 4.1849 c. M:-5.9734 c. 31: 2 1 28 N T3 SD: 3.0703 c. M:-4.3669 c. 32: 2 1 29 N T3 SD: 2.0255 c. M:-2.8607 c. 33: 2 1 30 N T3 SD: 1.0445 c. M:-1.4458 c. 34: 2 1 31 N T3 SD: 0.1328 c. M:-0.1997 c. 137: 8 4 125 N T3 SD: 0.1196 c. M: 0.2067 c. 171: 10 5 156 N T3 SD: 0.0841 c. M: 0.1429 c. 205: 12 6 187 N T3 SD: 0.0665 c. M: 0.1003 c. 239: 14 7 218 N T3 SD: 0.0600 c. M:-0.0771 c. 273: 16 8 249 N T3 SD: 0.0598 c. M:-0.0924 c. 307: 18 9 280 N T3 SD: 0.0625 c. M:-0.1043 c. 444: 26 13 405 N T3 SD: 0.0622 c. M: 0.0839 c. 512: 30 15 467 N T3 SD: 0.0594 c. M:-0.0853 c. 704: 41 21 642 N T3 SD: 0.0558 c. M: 0.0916 c. 738: 43 22 673 N T3 SD: 0.0494 c. M: 0.0782 c. 772: 45 23 704 N T3 SD: 0.0440 c. M: 0.0659 c. 806: 47 24 735 N T3 SD: 0.0396 c. M: 0.0547 c. 840: 49 25 766 N T3 SD: 0.0362 c. M: 0.0444 c. 874: 51 26 797 N T3 SD: 0.0338 c. M:-0.0471 c. 875: 51 26 798 N T3 SD: 0.0394 c. M: 0.0681 c. 908: 53 27 828 N T3 SD: 0.0324 c. M:-0.0496 c. 909: 53 27 829 N T3 SD: 0.0336 c. M: 0.0581 c. 942: 55 28 859 N T3 SD: 0.0317 c. M:-0.0519 c. 943: 55 28 860 N T3 SD: 0.0284 c. M: 0.0488 c. 977: 57 29 891 N T3 SD: 0.0238 c. M: 0.0402 c. 1011: 59 30 922 N T3 SD: 0.0199 c. M: 0.0321 c. 1045: 61 31 953 N T3 SD: 0.0169 c. M: 0.0246 c. 1079: 63 32 984 N T3 SD: 0.0149 c. M:-0.0191 c. 1113: 65 33 1015 N T3 SD: 0.0142 c. M:-0.0220 c. 1147: 67 34 1046 N T3 SD: 0.0145 c. M:-0.0247 c. 1182: 69 35 1078 N T3 SD: 0.0146 c. M: 0.0234 c. 1216: 71 36 1109 N T3 SD: 0.0105 c. M: 0.0171 c. 1250: 73 37 1140 N T3 SD: 0.0067 c. M: 0.0112 c. 1284: 75 38 1171 N T3 SD: 0.0033 c. M: 0.0056 c. 1318: 77 39 1202 N T3 SD: 0.0017 c. M:-0.0030 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: 111.5199 cents 7 x 8:9 S SD: 98.8199 cents 8 x 9:11 SD: 84.3553 cents 9 x 10:12 S SD: 69.2863 cents 10 x 11:13 SD: 64.4284 cents 11 x 12:15 S SD: 56.8357 cents 12 x 13:16 SD: 47.3708 cents 13 x 14:17 SD: 45.4555 cents 14 x 15:19 SD: 40.7924 cents 15 x 16:20 S SD: 33.9501 cents 16 x 17:21 SD: 33.4646 cents 17 x 18:23 SD: 30.3207 cents 18 x 19:24 SD: 24.8860 cents 19 x 20:25 S SD: 25.2393 cents 20 x 21:27 SD: 22.9881 cents 21 x 22:28 SD: 18.3530 cents 22 x 23:29 SD: 19.2923 cents 23 x 24:31 SD: 17.6160 cents 24 x 25:32 SD: 13.4207 cents 25 x 26:33 SD: 14.8498 cents 26 x 27:35 SD: 13.5737 cents 27 x 28:36 SD: 9.5649 cents 28 x 29:37 SD: 11.4824 cents 29 x 30:39 SD: 10.5079 cents 30 x 31:40 SD: 6.4679 cents 31 x 32:41 SD: 8.9507 cents 32 x 33:43 SD: 8.2259 cents 33 x 34:44 SD: 3.9257 cents 34 x 35:45 SD: 7.1345 cents 35 x 36:47 SD: 6.6376 cents 36 x 37:48 SD: 1.8015 cents 37 x 38:49 SD: 5.9839 cents 38 x 39:51 SD: 5.7047 cents 39 x 40:52 SD: 0.0000 cents 40 x 41:53 SD: 5.4540 cents 41 x 42:55 SD: 5.3671 cents 42 x 43:56 SD: 1.5471 cents 43 x 44:57 SD: 5.4348 cents 44 x 45:59 SD: 5.4879 cents 45 x 46:60 SD: 2.8902 cents 46 x 47:61 SD: 5.7566 cents 47:48 x 63 SD: 5.8820 cents 48:49 x 64 SD: 3.2999 cents 49:50 x 65 SD: 5.3145 cents 50:51 x 67 SD: 5.0361 cents 51:52 x 68 SD: 2.2601 cents 52:53 x 69 SD: 4.6007 cents 53:54 x 71 SD: 4.3881 cents 54:55 x 72 SD: 1.3348 cents 55:56 x 73 SD: 4.0806 cents 56:57 x 75 SD: 3.9324 cents 57:58 x 76 SD: 0.5061 cents 58:59 x 77 SD: 3.7474 cents 63:64:65:84 SD: 3.4789 cents 66:67:68:88 SD: 2.8092 cents 69:70:71:92 SD: 2.3404 cents 72:73:74:96 SD: 2.1136 cents 89 x 91:119 SD: 3.6155 cents 90 x 92:120 SD: 2.8902 cents 91 x 93:121 SD: 3.9067 cents 92 x 94:123 SD: 4.0502 cents 93 x 95:124 SD: 3.4974 cents 94:96 x 125 SD: 4.3387 cents 95:97 x 127 SD: 4.1625 cents 96:98 x 128 SD: 3.2999 cents 97:99 x 129 SD: 3.8354 cents 98:100:101:131 SD: 3.7131 cents 99:101:102:132 SD: 3.2009 cents 101:103:104:135 SD: 3.1387 cents 102:104:105:136 SD: 2.5990 cents 105:107:108:140 SD: 2.0312 cents 108:110:111:144 SD: 1.4947 cents 111:113:114:148 SD: 0.9873 cents 114:116:117:152 SD: 0.5078 cents 117:119:120:156 SD: 0.0822 cents 588:598:603:784 SD: 0.0806 cents