Scala analysis: 036_H9
Hyperenharmonic tetrachord 81/79 * 79/78 * 104/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/79 43.283106 2: 27/26 65.337341 tridecimal comma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 104/81 432.7077 1: 81/79 43.2831 2: 79/78 22.0542 3: 104/81 432.7077
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 79/78 22.054 cents 1: 1 81/79 43.283 cents 1: 1 104/81 432.708 cents 2: 1 27/26 65.337 cents tridecimal comma 2: 1 316/243 454.762 cents 2: 1 104/79 475.991 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 : 43.3 65.3 498.0 43.3 : 22.1 454.8 498.0 65.3 : 432.7 476.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.0542 .. 432.7077 cents 2704/2133, 410.6534 cents 79/78, 22.0542 cents 2: 65.3373 .. 475.9908 cents 2704/2133, 410.6534 cents 2187/2704,-367.3703 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 79/78, 22.0542 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 104/81, 432.7077 cents Average / Smallest step : 7.527579 Largest / Average step : 2.606437 Largest / Smallest step : 19.620162 Median interval of one step : 81/79, 43.2831 cents, amount: 1 Least squares average step : 119.14948 cents, oct.: 357.44845 cents Scale is not proper Scale has trivalence property 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 22.05424 cents Scale diversity : 0.152287 Lumma stability : 0.088563 Lumma impropriety factor : 0.737625 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 : 6318/6241, 21.2289 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 410.6534 cents: 2 -- Rational properties -- Prime limit : 79 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.025983 Fundamental : 1/6162, -12.5892 octaves, 0.0425 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.996488E+06, 20.92903 octaves Euler's gradus suavitatis : 104 Sum of Mann's harmonic distance : 110.0, average 36.66667 Mersenne's string divisions : 59360 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.73163, average 2.57721 Vogel's harmonic complexity : 71.66667 Wille's k value : 3199 Wilson's harmonic complexity : 107 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 21.76893, average 3.62815 Lattice compactness (without 2's) : 18.69960, average 3.11660 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 4 2.00000 8 1 13: -1 .. 0 -0.33333 1 1 79: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 11 25 45| Scale is weakly epimorphic with val: <7 11 27 46| = patent Scale is weakly epimorphic with val: <7 11 28 45| Scale is weakly epimorphic with val: <7 11 30 46| Scale is weakly epimorphic with val: <7 12 25 45| Scale is weakly epimorphic with val: <7 12 26 47| Scale is weakly epimorphic with val: <7 12 28 45| Scale is weakly epimorphic with val: <8 12 25 46| Scale is weakly epimorphic with val: <8 12 26 45| Scale is weakly epimorphic with val: <8 12 29 45|
FIT/MODE
3: 0 0 3 N M DE S SD: 45.2489 c. M: 65.3373 c. 5: 0 1 4 N G T3 SD: 31.8746 c. M: 43.2831 c. 6: 1 0 5 N G T3 SD: 25.1015 c. M:-39.7244 c. 7: 1 0 6 N G T3 SD: 16.4347 c. M:-27.8662 c. 8: 1 0 7 N G T3 SD: 11.0973 c. M:-18.9725 c. 9: 1 0 8 N G T3 SD: 9.0427 c. M:-12.0552 c. 12: 1 1 10 N M DE S SD: 10.2535 c. M:-17.6702 c. 13: 1 1 11 N M DE S SD: 7.1197 c. M:-11.2850 c. 14: 1 1 12 N M DE S SD: 5.5737 c. M: 7.7085 c. 15: 1 1 13 N M DE S SD: 5.8524 c. M: 10.0801 c. 20: 2 1 17 N T3 SD: 6.5908 c. M:-9.3694 c. 21: 2 1 18 N T3 SD: 4.1231 c. M:-5.8119 c. 22: 2 1 19 N T3 SD: 1.8815 c. M:-2.5779 c. 23: 2 1 20 N T3 SD: 0.2170 c. M: 0.3749 c. 114: 10 5 99 N T3 SD: 0.2595 c. M:-0.4051 c. 137: 12 6 119 N T3 SD: 0.2052 c. M:-0.3413 c. 160: 14 7 139 N T3 SD: 0.1717 c. M:-0.2958 c. 183: 16 8 159 N T3 SD: 0.1516 c. M:-0.2618 c. 206: 18 9 179 N T3 SD: 0.1402 c. M:-0.2354 c. 229: 20 10 199 N T3 SD: 0.1345 c. M:-0.2143 c. 252: 22 11 219 N T3 SD: 0.1323 c. M:-0.1970 c. 275: 24 12 239 N T3 SD: 0.1324 c. M:-0.1826 c. 298: 26 13 259 N T3 SD: 0.1338 c. M:-0.1705 c. 312: 27 14 271 N T3 SD: 0.1236 c. M: 0.1831 c. 335: 29 15 291 N T3 SD: 0.1072 c. M: 0.1688 c. 358: 31 16 311 N T3 SD: 0.0945 c. M: 0.1563 c. 381: 33 17 331 N T3 SD: 0.0850 c. M: 0.1453 c. 404: 35 18 351 N T3 SD: 0.0783 c. M: 0.1356 c. 426: 37 19 370 N T3 SD: 0.0784 c. M:-0.1334 c. 427: 37 19 371 N T3 SD: 0.0742 c. M: 0.1270 c. 449: 39 20 390 N T3 SD: 0.0634 c. M:-0.1073 c. 450: 39 20 391 N T3 SD: 0.0723 c. M: 0.1192 c. 472: 41 21 410 N T3 SD: 0.0499 c. M:-0.0838 c. 495: 43 22 430 N T3 SD: 0.0377 c. M:-0.0625 c. 518: 45 23 450 N T3 SD: 0.0267 c. M:-0.0431 c. 541: 47 24 470 N T3 SD: 0.0169 c. M:-0.0253 c. 564: 49 25 490 N T3 SD: 0.0092 c. M: 0.0132 c. 587: 51 26 510 N T3 SD: 0.0076 c. M: 0.0117 c. 1151: 100 51 1000 N T3 SD: 0.0072 c. M: 0.0125 c. 1738: 151 77 1510 N T3 SD: 0.0071 c. M: 0.0122 c. 1784: 155 79 1550 N T3 SD: 0.0090 c. M: 0.0113 c. 1875: 163 83 1629 N T3 SD: 0.0086 c. M:-0.0136 c. 1898: 165 84 1649 N T3 SD: 0.0080 c. M:-0.0137 c. 2279: 198 101 1980 N T3 SD: 0.0080 c. M: 0.0129 c. 2325: 202 103 2020 N T3 SD: 0.0071 c. M: 0.0121 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: 100.7668 cents 7 x 8:9 S SD: 88.6932 cents 8 x 9:11 SD: 74.2300 cents 9 x 10:12 S SD: 58.5332 cents 10 x 11:13 SD: 54.4395 cents 11 x 12:15 S SD: 46.8767 cents 12 x 13:16 SD: 36.6177 cents 13 x 14:17 SD: 35.6868 cents 14 x 15:19 SD: 31.0900 cents 15 x 16:20 S SD: 23.1970 cents 16 x 17:21 SD: 24.0464 cents 17 x 18:23 SD: 21.0291 cents 18 x 19:24 SD: 14.1328 cents 19 x 20:25 S SD: 16.4038 cents 20 x 21:27 SD: 14.3916 cents 21 x 22:28 SD: 7.5998 cents 22 x 23:29 SD: 11.4726 cents 23 x 24:31 SD: 10.2458 cents 24 x 25:32 SD: 2.6675 cents 25 x 26:33 SD: 8.7936 cents 26 x 27:35 SD: 8.2835 cents 27 x 28:36 SD: 1.1882 cents 28 x 29:37 SD: 8.0950 cents 29 x 30:39 SD: 8.1394 cents 30 x 31:40 SD: 4.2852 cents 31 x 32:41 SD: 8.7193 cents 32:33 x 43 SD: 8.3862 cents 33:34 x 44 SD: 4.1997 cents 34:35 x 45 SD: 7.2607 cents 35:36 x 47 SD: 6.7443 cents 36:37 x 48 SD: 2.0755 cents 37:38 x 49 SD: 6.0434 cents 38:39 x 51 SD: 5.7385 cents 42:43:44:56 SD: 5.1372 cents 45:46:47:60 SD: 3.7460 cents 48:49:50:64 SD: 3.0915 cents 60 x 62:80 SD: 4.2852 cents 61 x 63:81 SD: 5.9274 cents 62 x 64:83 SD: 6.2477 cents 63:65 x 84 SD: 5.4112 cents 64:66 x 85 SD: 6.0355 cents 65:67:68:87 SD: 5.6934 cents 66:68:69:88 SD: 4.7790 cents 68:70:71:91 SD: 4.4274 cents 69:71:72:92 SD: 3.4618 cents 71:73:74:95 SD: 3.3330 cents 72:74:75:96 SD: 2.2532 cents 75:77:78:100 SD: 1.1431 cents 78:80:81:104 SD: 0.1826 cents 393:403:408:524 SD: 0.1786 cents 471:483:489:628 SD: 0.1636 cents 519:532:539:692 SD: 0.1565 cents 549:563:570:732 SD: 0.1563 cents 594:609:617:792 SD: 0.1483 cents 597:612:620:796 SD: 0.1132 cents