Scala analysis: 032_H8
Hyperenharmonic tetrachord 112/111 * 37/36 * 9/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 112/111 15.526867 2: 28/27 62.960904 Archytas' 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/7 435.0841 septimal major third, BP third 1: 112/111 15.5269 2: 37/36 47.4340 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 112/111 15.527 cents 1: 1 37/36 47.434 cents 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 48/37 450.611 cents 2: 1 37/28 482.518 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 : 15.5 63.0 498.0 15.5 : 47.4 482.5 498.0 63.0 : 435.1 450.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 15.5269 .. 435.0841 cents 999/784, 419.5572 cents 112/111, 15.5269 cents 2: 62.9609 .. 482.5181 cents 999/784, 419.5572 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 112/111, 15.5269 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 10.692112 Largest / Average step : 2.620752 Largest / Smallest step : 28.021371 Median interval of one step : 37/36, 47.4340 cents, amount: 1 Least squares average step : 116.82741 cents, oct.: 350.48222 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1155-tone equal temperament with octave 4/3 degrees: 36 146 1155 Least number of segments generator : 578 of 249.238 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 758 of 326.856 cents and inv. generated superset size: 56 = 53 more = 1866.667% 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 15.52687 cents Scale diversity : 0.120439 Lumma stability : 0.062351 Lumma impropriety factor : 0.747168 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 : 112/111, 15.5269 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 482.5181 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 37 Odd number limit : 111 (O: 37 U: 111) Highest odd numerator or denominator: 111 Scale harmonicity : 0.044872 Fundamental : 1/999, -9.9643 octaves, 0.2619 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 1.118880E+05, 16.77170 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 142.5, average 47.50000 Mersenne's string divisions : 85855 Sum of van Prooijen's expressibility: 3.95381, average 1.31794 Sum of Tenney's harmonic distance : 8.05224, average 2.68408 Vogel's harmonic complexity : 36.00000 Wille's k value : 166 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 17.52093, average 2.92015 Lattice compactness (without 2's) : 10.81256, average 1.80209 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -3 ..-1 -1.66667 5 1 7: 0 .. 1 0.66667 2 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 21 37| Scale is weakly epimorphic with val: <6 10 21 40| Scale is weakly epimorphic with val: <7 10 19 35| Scale is weakly epimorphic with val: <7 10 19 38| Scale is weakly epimorphic with val: <7 10 19 41| Scale is weakly epimorphic with val: <7 10 21 36| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 11 18 40| Scale is weakly epimorphic with val: <7 11 20 35| Scale is weakly epimorphic with val: <7 11 20 38| = patent Scale is weakly epimorphic with val: <7 11 20 41| Scale is JI-epimorphic with val: <7 11 21 37| Scale is weakly epimorphic with val: <7 11 21 40| Scale is weakly epimorphic with val: <8 11 18 36| Scale is weakly epimorphic with val: <8 11 20 37| Scale is weakly epimorphic with val: <8 11 20 40| Scale is weakly epimorphic with val: <8 11 21 39| Scale is weakly epimorphic with val: <8 12 19 36| Scale is weakly epimorphic with val: <8 12 22 39|
FIT/MODE
3: 0 0 3 N M DE S SD: 37.4395 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 22.9795 c. M:-36.6481 c. 6: 0 1 5 N G T3 SD: 14.6396 c. M:-20.0466 c. 7: 0 1 6 N G T3 SD: 10.1346 c. M: 15.5269 c. 8: 0 1 7 N G T3 SD: 8.9737 c. M: 15.5269 c. 9: 0 1 8 N G T3 SD: 9.9864 c. M: 15.5269 c. 15: 0 2 13 N G T3 SD: 9.1825 c. M: 15.5269 c. 16: 0 2 14 N G T3 SD: 8.9737 c. M: 15.5269 c. 21: 1 2 18 N T3 SD: 6.6863 c. M:-8.1896 c. 22: 1 2 19 N T3 SD: 5.0040 c. M:-7.1115 c. 23: 1 2 20 N T3 SD: 3.7215 c. M:-6.1273 c. 24: 1 2 21 N T3 SD: 3.0440 c. M:-5.2250 c. 25: 1 2 22 N T3 SD: 3.1372 c. M:-4.3949 c. 29: 1 3 25 N T3 SD: 3.4449 c. M:-5.7350 c. 30: 1 3 26 N T3 SD: 2.0835 c. M:-3.4451 c. 31: 1 3 27 N T3 SD: 0.8141 c. M:-1.3030 c. 32: 1 3 28 N T3 SD: 0.4078 c. M: 0.7053 c. 63: 2 6 55 N T3 SD: 0.2315 c. M:-0.2841 c. 95: 3 9 83 N T3 SD: 0.1195 c. M:-0.2009 c. 158: 5 15 138 N T3 SD: 0.1433 c. M:-0.2341 c. 222: 7 21 194 N T3 SD: 0.1320 c. M:-0.1773 c. 253: 8 24 221 N T3 SD: 0.1293 c. M:-0.2216 c. 292: 9 28 255 N T3 SD: 0.1327 c. M: 0.1762 c. 293: 9 28 256 N T3 SD: 0.1376 c. M: 0.2286 c. 317: 10 30 277 N T3 SD: 0.1258 c. M:-0.1843 c. 324: 10 31 283 N T3 SD: 0.0967 c. M: 0.1551 c. 356: 11 34 311 N T3 SD: 0.0796 c. M: 0.1378 c. 387: 12 37 338 N T3 SD: 0.0748 c. M:-0.0991 c. 388: 12 37 339 N T3 SD: 0.0801 c. M: 0.1234 c. 419: 13 40 366 N T3 SD: 0.0481 c. M: 0.0744 c. 451: 14 43 394 N T3 SD: 0.0394 c. M: 0.0665 c. 483: 15 46 422 N T3 SD: 0.0492 c. M: 0.0608 c. 514: 16 49 449 N T3 SD: 0.0184 c. M: 0.0235 c. 546: 17 52 477 N T3 SD: 0.0168 c. M: 0.0212 c. 609: 19 58 532 N T3 SD: 0.0089 c. M:-0.0115 c. 1155: 36 110 1009 N T3 SD: 0.0033 c. M: 0.0046 c. 1764: 55 168 1541 N T3 SD: 0.0011 c. M:-0.0017 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: 101.9550 cents 7 x 8:9 S SD: 89.8050 cents 8 x 9:11 SD: 75.3403 cents 9 x 10:12 S SD: 59.7214 cents 10 x 11:13 SD: 55.5293 cents 11 x 12:15 S SD: 47.9603 cents 12 x 13:16 SD: 37.8059 cents 13 x 14:17 SD: 36.7392 cents 14 x 15:19 SD: 32.1292 cents 15 x 16:20 S SD: 24.3852 cents 16 x 17:21 SD: 25.0343 cents 17 x 18:23 SD: 21.9904 cents 18 x 19:24 SD: 15.3211 cents 19 x 20:25 S SD: 17.2736 cents 20 x 21:27 SD: 15.2072 cents 21 x 22:28 SD: 8.7881 cents 22 x 23:29 SD: 12.1177 cents 23 x 24:31 SD: 10.7844 cents 24 x 25:32 SD: 3.8558 cents 25 x 26:33 SD: 9.0435 cents 26 x 27:35 SD: 8.3683 cents 27 x 28:36 SD: 0.0000 cents 28 x 29:37 SD: 7.8417 cents 29 x 30:39 SD: 7.7308 cents 30 x 31:40 SD: 3.0970 cents 31 x 32:41 SD: 8.0693 cents 32 x 33:43 SD: 8.2971 cents 33 x 34:44 SD: 5.6392 cents 34 x 35:45 SD: 9.0345 cents 35 x 36:47 SD: 9.3968 cents 36 x 37:48 SD: 7.7634 cents 37 x 38:49 SD: 10.2437 cents 38 x 39:51 SD: 10.6368 cents 39 x 40:52 SD: 9.5649 cents 40 x 41:53 SD: 11.4711 cents 41 x 43:55 SD: 11.0769 cents 42 x 44:56 SD: 8.7881 cents 43 x 45:57 SD: 9.3516 cents 45:46:47:60 SD: 8.5580 cents 47:48:49:63 SD: 8.2085 cents 48:49:50:64 SD: 7.1979 cents 50:51:52:67 SD: 7.0769 cents 51:52:53:68 SD: 6.1505 cents 54:55:56:72 SD: 5.4133 cents 57:58:59:76 SD: 4.9806 cents 60:61:62:80 SD: 4.8269 cents 69:70:72:92 SD: 4.7488 cents 71:72:74:95 SD: 4.5697 cents 72:73:75:96 SD: 3.7894 cents 74:75:77:99 SD: 3.7661 cents 75:76:78:100 SD: 2.9667 cents 78:79:81:104 SD: 2.3155 cents 81:82:84:108 SD: 1.9052 cents 84:85:87:112 SD: 1.8104 cents 102:103:106:136 SD: 1.2935 cents 105:106:109:140 SD: 0.6581 cents 108:109:112:144 SD: 0.1431 cents 564:569:585:752 SD: 0.1370 cents 567:572:588:756 SD: 0.1091 cents