Scala analysis: 025_H7
Hyperenharmonic tetrachord 120/119 * 119/116 * 58/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/119 14.487399 2: 30/29 58.691521 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 58/45 439.3535 1: 120/119 14.4874 2: 119/116 44.2041 3: 58/45 439.3535
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/119 14.487 cents 1: 1 119/116 44.204 cents 1: 1 58/45 439.353 cents 2: 1 30/29 58.692 cents 2: 1 464/357 453.841 cents 2: 1 119/90 483.558 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 : 14.5 58.7 498.0 14.5 : 44.2 483.6 498.0 58.7 : 439.4 453.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.4874 .. 439.3535 cents 3451/2700, 424.8661 cents 120/119, 14.4874 cents 2: 58.6915 .. 483.5576 cents 3451/2700, 424.8661 cents 675/841,-380.6620 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/119, 14.4874 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 58/45, 439.3535 cents Average / Smallest step : 11.459269 Largest / Average step : 2.646469 Largest / Smallest step : 30.326595 Median interval of one step : 119/116, 44.2041 cents, amount: 1 Least squares average step : 116.14325 cents, oct.: 348.42974 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1994-tone equal temperament with octave 4/3 degrees: 58 235 1994 Least number of segments generator : 999 of 249.522 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1817 of 453.835 cents and inv. generated superset size: 57 = 54 more = 1900.000% 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 14.48740 cents Scale diversity : 0.093048 Lumma stability : 0.058177 Lumma impropriety factor : 0.764312 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 : 120/119, 14.4874 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.5576 cents Number of appreciable 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 : 29 Odd number limit : 357 (O: 119 U: 357) Highest odd numerator or denominator: 119 Scale harmonicity : 0.009157 Average absolute harmonicity : 0.082978 Specific harmonicity : 0.047381 Fundamental : 1/10353, -13.3378 octaves, 0.0253 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.242360E+06, 20.24465 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 152.5, average 50.83333 Mersenne's string divisions : 98707 Sum of van Prooijen's expressibility: 4.01507, average 1.33836 Sum of Tenney's harmonic distance : 8.17343, average 2.72448 Vogel's harmonic complexity : 44.66667 Wille's k value : 2677 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.96155, average 2.66026 Lattice compactness (without 2's) : 11.55934, average 1.92656 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 16 19 30 33| Scale is weakly epimorphic with val: <7 11 16 19 30 36| Scale is weakly epimorphic with val: <7 11 16 19 31 35| Scale is weakly epimorphic with val: <7 11 16 20 29 33| Scale is weakly epimorphic with val: <7 11 16 20 29 36| Scale is weakly epimorphic with val: <7 11 16 20 30 35| Scale is weakly epimorphic with val: <7 11 16 21 29 35| Scale is weakly epimorphic with val: <7 11 16 21 31 33| Scale is weakly epimorphic with val: <7 11 16 21 31 36| Scale is JI-epimorphic with val: <7 11 17 19 29 33| Scale is weakly epimorphic with val: <7 11 17 19 29 36| Scale is weakly epimorphic with val: <7 11 17 19 31 34| Scale is weakly epimorphic with val: <7 11 17 19 31 37| Scale is weakly epimorphic with val: <7 11 17 20 30 34| Scale is weakly epimorphic with val: <7 11 17 20 30 37| Scale is weakly epimorphic with val: <7 11 17 20 31 33| Scale is weakly epimorphic with val: <7 11 17 20 31 36| Scale is weakly epimorphic with val: <7 11 17 21 29 34| Scale is weakly epimorphic with val: <7 11 17 21 29 37| Scale is weakly epimorphic with val: <7 11 17 21 30 33| Scale is weakly epimorphic with val: <7 11 17 21 30 36| Scale is weakly epimorphic with val: <7 11 18 19 29 35| Scale is JI-epimorphic with val: <7 11 18 19 30 34| Scale is weakly epimorphic with val: <7 11 18 19 30 37| Scale is JI-epimorphic with val: <7 11 18 20 29 34| Scale is weakly epimorphic with val: <7 11 18 20 29 37| Scale is weakly epimorphic with val: <7 11 18 20 31 35| Scale is weakly epimorphic with val: <7 11 18 21 30 35| Scale is weakly epimorphic with val: <7 11 18 21 31 34| Scale is weakly epimorphic with val: <7 11 18 21 31 37| Scale is weakly epimorphic with val: <7 12 17 19 30 33| Scale is weakly epimorphic with val: <7 12 17 20 29 33| Scale is weakly epimorphic with val: <7 12 17 21 31 33| Scale is weakly epimorphic with val: <7 12 18 19 29 33| Scale is weakly epimorphic with val: <7 12 18 19 29 36| Scale is weakly epimorphic with val: <7 12 18 19 31 34| Scale is weakly epimorphic with val: <7 12 18 20 30 34| Scale is weakly epimorphic with val: <7 12 18 21 29 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 34.9026 c. M: 58.6915 c. 5: 0 1 4 N G T3 SD: 25.0608 c. M:-40.9175 c. 6: 0 1 5 N G T3 SD: 16.3417 c. M:-24.3160 c. 7: 0 1 6 N G T3 SD: 11.0315 c. M: 14.4874 c. 8: 0 1 7 N G T3 SD: 8.6137 c. M: 14.4874 c. 9: 0 1 8 N G T3 SD: 8.5854 c. M: 14.4874 c. 10: 0 1 9 N G T3 SD: 9.8126 c. M: 14.4874 c. 15: 0 2 13 N G T3 SD: 9.4762 c. M: 14.4874 c. 16: 0 2 14 N G T3 SD: 8.6137 c. M: 14.4874 c. 17: 0 2 15 N G T3 SD: 8.3645 c. M: 14.4874 c. 19: 0 2 17 N G T3 SD: 9.1131 c. M: 14.4874 c. 23: 1 2 20 N T3 SD: 5.4981 c. M:-7.1667 c. 24: 1 2 21 N T3 SD: 4.1612 c. M:-6.2645 c. 25: 1 2 22 N T3 SD: 3.1982 c. M:-5.4344 c. 26: 1 2 23 N T3 SD: 2.7864 c. M:-4.6682 c. 27: 1 2 24 N T3 SD: 2.9953 c. M:-3.9587 c. 31: 1 3 27 N T3 SD: 3.3438 c. M:-5.5724 c. 32: 1 3 28 N T3 SD: 2.1496 c. M:-3.5641 c. 33: 1 3 29 N T3 SD: 1.0296 c. M:-1.6776 c. 34: 1 3 30 N T3 SD: 0.1088 c. M:-0.1610 c. 339: 10 30 299 N T3 SD: 0.1256 c. M:-0.2042 c. 347: 10 31 306 N T3 SD: 0.1186 c. M:-0.1553 c. 348: 10 31 307 N T3 SD: 0.1018 c. M: 0.1758 c. 381: 11 34 336 N T3 SD: 0.0988 c. M:-0.1327 c. 382: 11 34 337 N T3 SD: 0.0851 c. M: 0.1458 c. 415: 12 37 366 N T3 SD: 0.0824 c. M:-0.1138 c. 416: 12 37 367 N T3 SD: 0.0715 c. M: 0.1207 c. 449: 13 40 396 N T3 SD: 0.0685 c. M:-0.0978 c. 450: 13 40 397 N T3 SD: 0.0605 c. M: 0.0994 c. 483: 14 43 426 N T3 SD: 0.0568 c. M:-0.0840 c. 484: 14 43 427 N T3 SD: 0.0516 c. M: 0.0811 c. 517: 15 46 456 N T3 SD: 0.0468 c. M:-0.0720 c. 518: 15 46 457 N T3 SD: 0.0446 c. M: 0.0652 c. 551: 16 49 486 N T3 SD: 0.0384 c. M:-0.0615 c. 552: 16 49 487 N T3 SD: 0.0394 c. M: 0.0513 c. 585: 17 52 516 N T3 SD: 0.0313 c. M:-0.0522 c. 586: 17 52 517 N T3 SD: 0.0357 c. M: 0.0480 c. 619: 18 55 546 N T3 SD: 0.0255 c. M:-0.0440 c. 653: 19 58 576 N T3 SD: 0.0213 c. M:-0.0366 c. 687: 20 61 606 N T3 SD: 0.0186 c. M:-0.0299 c. 721: 21 64 636 N T3 SD: 0.0175 c. M:-0.0239 c. 1171: 34 104 1033 N T3 SD: 0.0154 c. M: 0.0267 c. 1205: 35 107 1063 N T3 SD: 0.0123 c. M: 0.0214 c. 1239: 36 110 1093 N T3 SD: 0.0096 c. M: 0.0164 c. 1273: 37 113 1123 N T3 SD: 0.0075 c. M: 0.0116 c. 1307: 38 116 1153 N T3 SD: 0.0063 c. M: 0.0083 c. 1926: 56 171 1699 N T3 SD: 0.0061 c. M:-0.0085 c. 1960: 57 174 1729 N T3 SD: 0.0043 c. M:-0.0066 c. 1994: 58 177 1759 N T3 SD: 0.0028 c. M:-0.0049 c. 2028: 59 180 1789 N T3 SD: 0.0022 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 104.0897 cents 7 x 8:9 S SD: 91.8073 cents 8 x 9:11 SD: 77.3408 cents 9 x 10:12 S SD: 61.8561 cents 10 x 11:13 SD: 57.4969 cents 11 x 12:15 S SD: 49.9190 cents 12 x 13:16 SD: 39.9406 cents 13 x 14:17 SD: 38.6498 cents 14 x 15:19 SD: 34.0208 cents 15 x 16:20 S SD: 26.5199 cents 16 x 17:21 SD: 26.8499 cents 17 x 18:23 SD: 23.7691 cents 18 x 19:24 SD: 17.4557 cents 19 x 20:25 S SD: 18.9234 cents 20 x 21:27 SD: 16.7847 cents 21 x 22:28 SD: 10.9228 cents 22 x 23:29 SD: 13.4637 cents 23 x 24:31 SD: 11.9893 cents 24 x 25:32 SD: 5.9905 cents 25 x 26:33 SD: 9.8430 cents 26 x 27:35 SD: 8.9251 cents 27 x 28:36 SD: 2.1347 cents 28 x 29:37 SD: 7.8314 cents 29 x 30:39 SD: 7.4302 cents 30 x 31:40 SD: 0.9623 cents 31 x 32:41 SD: 7.2526 cents 32 x 33:43 SD: 7.2608 cents 33 x 34:44 SD: 3.5045 cents 34 x 35:45 SD: 7.6749 cents 35 x 36:47 SD: 7.9098 cents 36 x 37:48 SD: 5.6287 cents 37 x 38:49 SD: 8.5816 cents 38 x 39:51 SD: 8.9046 cents 39 x 40:52 SD: 7.4302 cents 40 x 41:53 SD: 9.6435 cents 41 x 42:55 SD: 9.9855 cents 42 x 43:56 SD: 8.9774 cents 43 x 44:57 SD: 10.7096 cents 44 x 46:59 SD: 10.3660 cents 45 x 47:60 SD: 8.2957 cents 46 x 48:61 SD: 8.8556 cents 48:49:50:64 SD: 8.1198 cents 50:51:52:67 SD: 7.8260 cents 51:52:53:68 SD: 6.8993 cents 53:54:55:71 SD: 6.7935 cents 54:55:56:72 SD: 5.9330 cents 57:58:59:76 SD: 5.2182 cents 60:61:62:80 SD: 4.7531 cents 63:64:65:84 SD: 4.5249 cents 66:67:68:88 SD: 4.5025 cents 75:76:78:100 SD: 4.1645 cents 77:78:80:103 SD: 4.0697 cents 78:79:81:104 SD: 3.3570 cents 81:82:84:108 SD: 2.6637 cents 84:85:87:112 SD: 2.1148 cents 87:88:90:116 SD: 1.7661 cents 90:91:93:120 SD: 1.6752 cents 108:109:112:144 SD: 1.5050 cents 111:112:115:148 SD: 0.9326 cents 114:115:118:152 SD: 0.3979 cents 117:118:121:156 SD: 0.1838 cents 231:233:239:308 SD: 0.1678 cents 348:351:360:464 SD: 0.1244 cents 465:469:481:620 SD: 0.1210 cents