Scala analysis: 023_H7
Hyperenharmonic tetrachord 90/89 * 89/87 * 58/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90/89 19.343598 2: 30/29 58.691521 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 58/45 439.3535 1: 90/89 19.3436 2: 89/87 39.3479 3: 58/45 439.3535
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 90/89 19.344 cents 1: 1 89/87 39.348 cents 1: 1 58/45 439.353 cents 2: 1 30/29 58.692 cents 2: 1 116/89 458.697 cents 2: 1 178/135 478.701 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 : 19.3 58.7 498.0 19.3 : 39.3 478.7 498.0 58.7 : 439.4 458.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.3436 .. 439.3535 cents 2581/2025, 420.0099 cents 90/89, 19.3436 cents 2: 58.6915 .. 478.7014 cents 2581/2025, 420.0099 cents 675/841,-380.6620 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 90/89, 19.3436 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 58/45, 439.3535 cents Average / Smallest step : 8.582426 Largest / Average step : 2.646469 Largest / Smallest step : 22.713120 Median interval of one step : 89/87, 39.3479 cents, amount: 1 Least squares average step : 116.49012 cents, oct.: 349.47035 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1468-tone equal temperament with octave 4/3 degrees: 57 173 1468 Least number of segments generator : 735 of 249.362 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1065 of 361.320 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 19.34360 cents Scale diversity : 0.105893 Lumma stability : 0.077678 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 : 90/89, 19.3436 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% Limited inverse transpositions with margin 400.0056 cents: 2 -- Rational properties -- Prime limit : 89 Odd number limit : 135 (O: 89 U: 135) Highest odd numerator or denominator: 89 Scale harmonicity : 0.014191 Fundamental : 1/7743, -12.9187 octaves, 0.0338 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.393740E+06, 20.41053 octaves Euler's gradus suavitatis : 129 Sum of Mann's harmonic distance : 122.5, average 40.83333 Mersenne's string divisions : 73927 Sum of van Prooijen's expressibility: 3.88891, average 1.29630 Sum of Tenney's harmonic distance : 7.92233, average 2.64078 Vogel's harmonic complexity : 88.33333 Wille's k value : 2002 Wilson's harmonic complexity : 132 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.06215, average 2.34369 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 29: -1 .. 0 -0.33333 1 1 89: -1 .. 0 -0.33333 1 1 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: <6 10 19 32 47| Scale is weakly epimorphic with val: <6 11 18 32 47| Scale is weakly epimorphic with val: <6 11 19 33 48| Scale is weakly epimorphic with val: <7 10 18 32 46| Scale is weakly epimorphic with val: <7 10 19 33 47| Scale is weakly epimorphic with val: <7 11 15 32 48| Scale is weakly epimorphic with val: <7 11 15 34 46| Scale is weakly epimorphic with val: <7 11 15 35 48| Scale is weakly epimorphic with val: <7 11 15 37 46| Scale is weakly epimorphic with val: <7 11 15 38 48| Scale is weakly epimorphic with val: <7 11 16 32 47| Scale is weakly epimorphic with val: <7 11 16 33 46| Scale is weakly epimorphic with val: <7 11 16 35 47| Scale is weakly epimorphic with val: <7 11 16 36 46| Scale is weakly epimorphic with val: <7 11 16 38 47| Scale is weakly epimorphic with val: <7 11 17 33 48| Scale is weakly epimorphic with val: <7 11 17 34 47| Scale is weakly epimorphic with val: <7 11 17 36 48| Scale is weakly epimorphic with val: <7 11 17 37 47| Scale is weakly epimorphic with val: <7 11 18 32 48| Scale is JI-epimorphic with val: <7 11 18 34 46| Scale is weakly epimorphic with val: <7 11 18 35 48| Scale is weakly epimorphic with val: <7 11 18 37 46| Scale is weakly epimorphic with val: <7 11 18 38 48| Scale is weakly epimorphic with val: <7 11 19 32 47| Scale is weakly epimorphic with val: <7 11 19 33 46| Scale is JI-epimorphic with val: <7 11 19 35 47| Scale is weakly epimorphic with val: <7 11 19 36 46| Scale is weakly epimorphic with val: <7 11 19 38 47| Scale is weakly epimorphic with val: <7 12 16 32 46| Scale is weakly epimorphic with val: <7 12 17 33 47| Scale is weakly epimorphic with val: <7 12 18 33 46| Scale is weakly epimorphic with val: <7 12 18 34 48| Scale is weakly epimorphic with val: <7 12 18 36 46| Scale is weakly epimorphic with val: <7 12 19 34 47| Scale is weakly epimorphic with val: <7 12 19 35 46| Scale is weakly epimorphic with val: <7 12 19 37 47| Scale is weakly epimorphic with val: <8 11 16 32 48| Scale is weakly epimorphic with val: <8 11 17 33 46| Scale is weakly epimorphic with val: <8 11 18 34 47| Scale is weakly epimorphic with val: <8 11 19 34 46| Scale is weakly epimorphic with val: <8 11 19 35 48| Scale is weakly epimorphic with val: <8 11 19 37 46| Scale is weakly epimorphic with val: <8 12 15 32 48| Scale is weakly epimorphic with val: <8 12 16 33 46| Scale is weakly epimorphic with val: <8 12 17 32 46| Scale is weakly epimorphic with val: <8 12 17 34 47| Scale is weakly epimorphic with val: <8 12 17 35 46| Scale is weakly epimorphic with val: <8 12 17 38 46| Scale is weakly epimorphic with val: <8 12 18 33 47| Scale is weakly epimorphic with val: <8 12 18 35 48| Scale is weakly epimorphic with val: <8 12 18 36 47| Scale is weakly epimorphic with val: <8 12 19 34 48| Scale is weakly epimorphic with val: <8 12 19 36 46| Scale is weakly epimorphic with val: <8 12 19 37 48|
FIT/MODE
3: 0 0 3 N M DE S SD: 35.6785 c. M: 58.6915 c. 6: 0 1 5 N G T3 SD: 17.9392 c. M:-24.3160 c. 7: 0 1 6 N G T3 SD: 13.2837 c. M: 19.3436 c. 8: 0 1 7 N G T3 SD: 11.3560 c. M: 19.3436 c. 9: 0 1 8 N G T3 SD: 11.3346 c. M: 19.3436 c. 10: 0 1 9 N G T3 SD: 12.2903 c. M: 19.3436 c. 15: 1 1 13 N M DE S SD: 9.1578 c. M:-13.8594 c. 16: 1 1 14 N M DE S SD: 7.1080 c. M:-11.7842 c. 17: 1 1 15 N M DE S SD: 5.7467 c. M:-9.9532 c. 18: 1 1 16 N M DE S SD: 5.1820 c. M:-8.3256 c. 19: 1 1 17 N M DE S SD: 5.3680 c. M:-6.8693 c. 22: 1 2 19 N T3 SD: 5.6549 c. M:-9.2237 c. 23: 1 2 20 N T3 SD: 3.8584 c. M:-6.2709 c. 24: 1 2 21 N T3 SD: 2.2125 c. M:-3.5641 c. 25: 1 2 22 N T3 SD: 0.7042 c. M:-1.0739 c. 51: 2 4 45 N T3 SD: 0.1222 c. M:-0.1876 c. 178: 7 14 157 N T3 SD: 0.1452 c. M:-0.2424 c. 229: 9 18 202 N T3 SD: 0.1340 c. M:-0.2302 c. 280: 11 22 247 N T3 SD: 0.1285 c. M:-0.2225 c. 331: 13 26 292 N T3 SD: 0.1255 c. M:-0.2171 c. 332: 13 26 293 N T3 SD: 0.1411 c. M: 0.1862 c. 364: 14 29 321 N T3 SD: 0.1365 c. M: 0.1880 c. 382: 15 30 337 N T3 SD: 0.1237 c. M:-0.2131 c. 383: 15 30 338 N T3 SD: 0.1375 c. M: 0.1745 c. 390: 15 31 344 N T3 SD: 0.1127 c. M: 0.1880 c. 415: 16 33 366 N T3 SD: 0.1050 c. M: 0.1419 c. 416: 16 33 367 N T3 SD: 0.1097 c. M: 0.1880 c. 441: 17 35 389 N T3 SD: 0.0859 c. M: 0.1446 c. 466: 18 37 411 N T3 SD: 0.0804 c. M: 0.1058 c. 467: 18 37 412 N T3 SD: 0.0873 c. M: 0.1470 c. 492: 19 39 434 N T3 SD: 0.0648 c. M: 0.1102 c. 517: 20 41 456 N T3 SD: 0.0608 c. M: 0.0769 c. 518: 20 41 457 N T3 SD: 0.0701 c. M: 0.1141 c. 543: 21 43 479 N T3 SD: 0.0478 c. M: 0.0822 c. 568: 22 45 501 N T3 SD: 0.0449 c. M:-0.0567 c. 594: 23 47 524 N T3 SD: 0.0341 c. M: 0.0590 c. 619: 24 49 546 N T3 SD: 0.0319 c. M:-0.0440 c. 645: 25 51 569 N T3 SD: 0.0232 c. M: 0.0395 c. 670: 26 53 591 N T3 SD: 0.0214 c. M:-0.0332 c. 696: 27 55 614 N T3 SD: 0.0154 c. M: 0.0229 c. 721: 28 57 636 N T3 SD: 0.0139 c. M:-0.0239 c. 747: 29 59 659 N T3 SD: 0.0123 c. M: 0.0196 c. 772: 30 61 681 N T3 SD: 0.0110 c. M:-0.0159 c. 1417: 55 112 1250 N T3 SD: 0.0077 c. M: 0.0123 c. 1468: 57 116 1295 N T3 SD: 0.0033 c. M: 0.0053 c. 1519: 59 120 1340 N T3 SD: 0.0011 c. M: 0.0016 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 44:45:46:59 SD: 9.5014 cents 45:46:47:60 SD: 8.3348 cents 47:48:49:63 SD: 7.8735 cents 48:49:50:64 SD: 6.7575 cents 50:51:52:67 SD: 6.5196 cents 51:52:53:68 SD: 5.4384 cents 53:54:55:71 SD: 5.4299 cents 54:55:56:72 SD: 4.3787 cents 57:58:59:76 SD: 3.6044 cents 60:61:62:80 SD: 3.1567 cents 63:64:65:84 SD: 3.0508 cents 78:79:81:104 SD: 2.3925 cents 81:82:84:108 SD: 1.5575 cents 84:85:87:112 SD: 0.7855 cents 87:88:90:116 SD: 0.1474 cents