Scala analysis: 012_H3
Hyperenharmonic tetrachord 85/84 * 56/55 * 22/17, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85/84 20.488216 2: 34/33 51.682466 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/17 446.3625 1: 85/84 20.4882 2: 56/55 31.1943 undecimal diesis, konbini comma 3: 22/17 446.3625
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85/84 20.488 cents 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 22/17 446.363 cents 2: 1 34/33 51.682 cents 2: 1 55/42 466.851 cents 2: 1 112/85 477.557 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 : 20.5 51.7 498.0 20.5 : 31.2 477.6 498.0 51.7 : 446.4 466.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.4882 .. 446.3625 cents 1848/1445, 425.8743 cents 85/84, 20.4882 cents 2: 51.6825 .. 477.5568 cents 1848/1445, 425.8743 cents 289/363,-394.6801 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 85/84, 20.4882 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/17, 446.3625 cents Average / Smallest step : 8.102950 Largest / Average step : 2.688688 Largest / Smallest step : 21.786305 Median interval of one step : 56/55, 31.1943 cents, amount: 1 Least squares average step : 115.57058 cents, oct.: 346.71175 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2091-tone equal temperament with octave 4/3 degrees: 86 217 2091 Least number of segments generator : 1046 of 249.142 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1096 of 261.051 cents and inv. generated superset size: 45 = 42 more = 1500.000% 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 20.48822 cents Scale diversity : 0.066314 Lumma stability : 0.082275 Lumma impropriety factor : 0.792459 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 : 4704/4675, 10.7060 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 415.1683 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 85 (O: 85 U: 85) Highest odd numerator or denominator: 85 Scale harmonicity : 0.013956 Average absolute harmonicity : 0.084319 Specific harmonicity : 0.065021 Fundamental : 1/924, -9.8517 octaves, 0.2831 Hz. Guide tone : 340, 8.4094 octaves, 88952.692 Hz. Exponens Consonantiae : 3.141600E+05, 18.26114 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 121.5, average 40.50000 Mersenne's string divisions : 79261 Sum of van Prooijen's expressibility: 3.92505, average 1.30835 Sum of Tenney's harmonic distance : 7.98287, average 2.66096 Vogel's harmonic complexity : 27.33333 Wille's k value : 467 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.61955, average 2.76992 Lattice compactness (without 2's) : 9.61037, average 1.60173 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 17: 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 weakly epimorphic with val: <7 11 16 19 25 30| Scale is weakly epimorphic with val: <7 11 16 19 26 29| Scale is JI-epimorphic with val: <7 11 16 20 24 30| Scale is weakly epimorphic with val: <7 11 16 20 26 31| Scale is weakly epimorphic with val: <7 11 16 21 24 29| Scale is JI-epimorphic with val: <7 11 16 21 25 31| Scale is weakly epimorphic with val: <7 11 17 19 24 29| Scale is weakly epimorphic with val: <7 11 17 19 25 31| Scale is weakly epimorphic with val: <7 11 17 20 25 30| = patent Scale is weakly epimorphic with val: <7 11 17 20 26 29| Scale is JI-epimorphic with val: <7 11 17 21 24 30| Scale is weakly epimorphic with val: <7 11 17 21 26 31| Scale is weakly epimorphic with val: <7 11 18 19 24 30| Scale is weakly epimorphic with val: <7 11 18 19 26 31| Scale is weakly epimorphic with val: <7 11 18 20 24 29| Scale is weakly epimorphic with val: <7 11 18 20 25 31| Scale is weakly epimorphic with val: <7 11 18 21 25 30| Scale is weakly epimorphic with val: <7 11 18 21 26 29| Scale is weakly epimorphic with val: <7 12 17 19 25 31| Scale is weakly epimorphic with val: <7 12 18 19 24 30| Scale is weakly epimorphic with val: <7 12 18 20 25 31|
FIT/MODE
3: 0 0 3 N M DE S SD: 32.0980 c. M: 51.6825 c. 7: 0 1 6 N G T3 SD: 16.3169 c. M: 20.4882 c. 8: 0 1 7 N G T3 SD: 13.3111 c. M: 20.4882 c. 9: 0 1 8 N G T3 SD: 12.0157 c. M: 20.4882 c. 10: 0 1 9 N G T3 SD: 11.8785 c. M: 20.4882 c. 11: 0 1 10 N G T3 SD: 12.3935 c. M: 20.4882 c. 12: 0 1 11 N G T3 SD: 13.2082 c. M: 20.4882 c. 16: 1 1 14 N M DE S SD: 8.6601 c. M:-10.6396 c. 17: 1 1 15 N M DE S SD: 6.4641 c. M:-8.8085 c. 18: 1 1 16 N M DE S SD: 4.6523 c. M:-7.1810 c. 19: 1 1 17 N M DE S SD: 3.3329 c. M:-5.7247 c. 20: 1 1 18 N M DE S SD: 2.7695 c. M:-4.4140 c. 21: 1 1 19 N M DE S SD: 3.0812 c. M: 4.2496 c. 27: 1 2 24 N T3 SD: 2.4177 c. M:-3.6559 c. 28: 1 2 25 N T3 SD: 1.8363 c. M: 2.7009 c. 29: 1 2 26 N T3 SD: 1.9157 c. M: 3.3143 c. 46: 2 3 41 N T3 SD: 1.5680 c. M:-2.4529 c. 47: 2 3 42 N T3 SD: 0.8544 c. M:-1.3010 c. 48: 2 3 43 N T3 SD: 0.1901 c. M:-0.2637 c. 145: 6 9 130 N T3 SD: 0.1159 c. M: 0.1606 c. 193: 8 12 173 N T3 SD: 0.0992 c. M:-0.1561 c. 241: 10 15 216 N T3 SD: 0.1030 c. M:-0.1776 c. 270: 11 17 242 N T3 SD: 0.1156 c. M: 0.1975 c. 289: 12 18 259 N T3 SD: 0.1112 c. M:-0.1919 c. 317: 13 20 284 N T3 SD: 0.1018 c. M:-0.1645 c. 318: 13 20 285 N T3 SD: 0.0738 c. M: 0.1279 c. 366: 15 23 328 N T3 SD: 0.0469 c. M: 0.0765 c. 414: 17 26 371 N T3 SD: 0.0345 c. M:-0.0468 c. 462: 19 29 414 N T3 SD: 0.0362 c. M:-0.0625 c. 463: 19 29 415 N T3 SD: 0.0406 c. M: 0.0501 c. 511: 21 32 458 N T3 SD: 0.0192 c. M: 0.0261 c. 559: 23 35 501 N T3 SD: 0.0046 c. M: 0.0070 c. 2091: 86 131 1874 N T3 SD: 0.0033 c. M: 0.0043 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: 107.5942 cents 7 x 8:9 S SD: 95.1069 cents 8 x 9:11 SD: 80.6400 cents 9 x 10:12 S SD: 65.3606 cents 10 x 11:13 SD: 60.7515 cents 11 x 12:15 S SD: 53.1641 cents 12 x 13:16 SD: 43.4451 cents 13 x 14:17 SD: 41.8333 cents 14 x 15:19 SD: 37.1833 cents 15 x 16:20 S SD: 30.0244 cents 16 x 17:21 SD: 29.9221 cents 17 x 18:23 SD: 26.8022 cents 18 x 19:24 SD: 20.9603 cents 19 x 20:25 S SD: 21.8150 cents 20 x 21:27 SD: 19.6046 cents 21 x 22:28 SD: 14.4273 cents 22 x 23:29 SD: 16.0487 cents 23 x 24:31 SD: 14.4414 cents 24 x 25:32 SD: 9.4950 cents 25 x 26:33 SD: 11.8928 cents 26 x 27:35 SD: 10.7345 cents 27 x 28:36 SD: 5.6392 cents 28 x 29:37 SD: 8.9906 cents 29 x 30:39 SD: 8.2152 cents 30 x 31:40 SD: 2.5422 cents 31 x 32:41 SD: 7.1986 cents 32 x 33:43 SD: 6.7831 cents 33 x 34:44 SD: 0.0000 cents 34 x 35:45 SD: 6.4321 cents 35 x 36:47 SD: 6.3307 cents 36 x 37:48 SD: 2.1242 cents 37 x 38:49 SD: 6.4838 cents 38 x 39:51 SD: 6.5943 cents 39 x 40:52 SD: 3.9257 cents 40 x 41:53 SD: 7.0290 cents 41 x 42:55 SD: 7.2464 cents 42 x 43:56 SD: 5.4728 cents 43 x 44:57 SD: 7.7957 cents 44 x 45:59 SD: 8.0538 cents 45 x 46:60 SD: 6.8159 cents 46 x 47:61 SD: 8.6287 cents 47 x 48:63 SD: 8.8942 cents 48:49 x 64 SD: 7.6043 cents 49:50 x 65 SD: 8.4898 cents 50:51:52:67 SD: 7.6585 cents 51:52:53:68 SD: 6.6226 cents 53:54:55:71 SD: 6.3438 cents 54:55:56:72 SD: 5.3167 cents 56:57:58:75 SD: 5.2155 cents 57:58:59:76 SD: 4.1754 cents 60:61:62:80 SD: 3.1957 cents 63:64:65:84 SD: 2.3987 cents 66:67:68:88 SD: 1.8486 cents 69:70:71:92 SD: 1.6486 cents 93:94:96:124 SD: 1.2763 cents 96:97:99:128 SD: 1.0012 cents 159:161:164:212 SD: 0.7466 cents 162:164:167:216 SD: 0.4024 cents 165:167:170:220 SD: 0.1234 cents 591:598:609:788 SD: 0.0928 cents 594:601:612:792 SD: 0.0686 cents