Scala analysis: 015_H4
Hyperenharmonic tetrachord 99/97 * 97/96 * 128/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99/97 35.332533 2: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 128/99 444.7721 1: 99/97 35.3325 2: 97/96 17.9404 3: 128/99 444.7721
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 97/96 17.940 cents 1: 1 99/97 35.333 cents 1: 1 128/99 444.772 cents 2: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 2: 1 388/297 462.712 cents 2: 1 128/97 480.105 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 : 35.3 53.3 498.0 35.3 : 17.9 462.7 498.0 53.3 : 444.8 480.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.9404 .. 444.7721 cents 4096/3201, 426.8316 cents 97/96, 17.9404 cents 2: 53.2729 .. 480.1046 cents 4096/3201, 426.8316 cents 3267/4096,-391.4991 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 97/96, 17.9404 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 128/99, 444.7721 cents Average / Smallest step : 9.253691 Largest / Average step : 2.679108 Largest / Smallest step : 24.791633 Median interval of one step : 99/97, 35.3325 cents, amount: 1 Least squares average step : 116.85810 cents, oct.: 350.57430 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 17.94041 cents Scale diversity : 0.070397 Lumma stability : 0.072043 Lumma impropriety factor : 0.786072 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 : 9504/9409, 17.3921 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.1046 cents Number of appreciable 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 426.8316 cents: 2 -- Rational properties -- Prime limit : 97 Odd number limit : 297 (O: 99 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.030137 Fundamental : 1/9312, -13.1849 octaves, 0.0281 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 3.687552E+06, 21.81423 octaves Euler's gradus suavitatis : 120 Sum of Mann's harmonic distance : 134.0, average 44.66667 Mersenne's string divisions : 12740 Sum of van Prooijen's expressibility: 3.99127, average 1.33042 Sum of Tenney's harmonic distance : 8.08525, average 2.69508 Vogel's harmonic complexity : 81.00000 Wille's k value : 4801 Wilson's harmonic complexity : 117 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 25.85743, average 4.30957 Lattice compactness (without 2's) : 11.04863, average 1.84144 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.00000 7 3: -1 .. 2 0.66667 4 1 11: 0 .. 1 0.66667 2 1 97: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 23 48| Scale is weakly epimorphic with val: <7 11 23 47| Scale is weakly epimorphic with val: <7 11 25 48| = patent Scale is JI-epimorphic with val: <7 11 26 47| Scale is weakly epimorphic with val: <7 12 26 49| Scale is weakly epimorphic with val: <7 12 27 48| Scale is weakly epimorphic with val: <8 12 27 48|
FIT/MODE
3: 0 0 3 N M DE S SD: 36.9071 c. M: 53.2729 c. 6: 0 1 5 N G T3 SD: 26.6617 c. M: 35.3325 c. 7: 1 0 6 N G T3 SD: 23.1113 c. M:-35.8168 c. 8: 1 0 7 N G T3 SD: 16.3864 c. M:-26.9231 c. 9: 1 0 8 N G T3 SD: 11.6117 c. M:-20.0058 c. 10: 1 0 9 N G T3 SD: 8.5920 c. M:-14.4720 c. 11: 1 0 10 N G T3 SD: 7.3672 c. M:-9.9443 c. 15: 1 1 13 N M DE S SD: 7.6814 c. M:-13.1331 c. 16: 1 1 14 N M DE S SD: 5.7262 c. M:-8.9827 c. 17: 1 1 15 N M DE S SD: 4.6454 c. M: 6.0358 c. 18: 1 1 16 N M DE S SD: 4.5823 c. M: 7.6634 c. 19: 1 1 17 N M DE S SD: 5.2879 c. M: 9.1196 c. 24: 2 1 21 N T3 SD: 6.2921 c. M:-8.9827 c. 25: 2 1 22 N T3 SD: 4.5644 c. M:-6.4925 c. 26: 2 1 23 N T3 SD: 2.9699 c. M:-4.1938 c. 27: 2 1 24 N T3 SD: 1.4943 c. M:-2.0654 c. 28: 2 1 25 N T3 SD: 0.1489 c. M:-0.2421 c. 169: 12 6 151 N T3 SD: 0.1322 c. M: 0.2267 c. 197: 14 7 176 N T3 SD: 0.1108 c. M: 0.1819 c. 225: 16 8 201 N T3 SD: 0.0983 c. M: 0.1481 c. 253: 18 9 226 N T3 SD: 0.0916 c. M: 0.1219 c. 281: 20 10 251 N T3 SD: 0.0885 c. M:-0.1155 c. 309: 22 11 276 N T3 SD: 0.0878 c. M:-0.1270 c. 337: 24 12 301 N T3 SD: 0.0884 c. M:-0.1365 c. 365: 26 13 326 N T3 SD: 0.0898 c. M:-0.1446 c. 393: 28 14 351 N T3 SD: 0.0916 c. M:-0.1516 c. 421: 30 15 376 N T3 SD: 0.0936 c. M:-0.1576 c. 467: 33 17 417 N T3 SD: 0.0853 c. M: 0.1388 c. 495: 35 18 442 N T3 SD: 0.0743 c. M: 0.1172 c. 523: 37 19 467 N T3 SD: 0.0649 c. M: 0.0980 c. 551: 39 20 492 N T3 SD: 0.0570 c. M: 0.0807 c. 579: 41 21 517 N T3 SD: 0.0505 c. M: 0.0651 c. 607: 43 22 542 N T3 SD: 0.0453 c. M:-0.0597 c. 635: 45 23 567 N T3 SD: 0.0415 c. M:-0.0610 c. 663: 47 24 592 N T3 SD: 0.0390 c. M:-0.0622 c. 691: 49 25 617 N T3 SD: 0.0376 c. M:-0.0633 c. 692: 49 25 618 N T3 SD: 0.0391 c. M: 0.0663 c. 719: 51 26 642 N T3 SD: 0.0372 c. M:-0.0643 c. 720: 51 26 643 N T3 SD: 0.0319 c. M: 0.0543 c. 748: 53 27 668 N T3 SD: 0.0252 c. M: 0.0432 c. 776: 55 28 693 N T3 SD: 0.0191 c. M: 0.0330 c. 804: 57 29 718 N T3 SD: 0.0135 c. M: 0.0234 c. 832: 59 30 743 N T3 SD: 0.0086 c. M: 0.0144 c. 860: 61 31 768 N T3 SD: 0.0051 c. M:-0.0063 c. 888: 63 32 793 N T3 SD: 0.0052 c. M:-0.0089 c. 1748: 124 63 1561 N T3 SD: 0.0046 c. M:-0.0076 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: 106.7990 cents 7 x 8:9 S SD: 94.3569 cents 8 x 9:11 SD: 79.8898 cents 9 x 10:12 S SD: 64.5654 cents 10 x 11:13 SD: 60.0105 cents 11 x 12:15 S SD: 52.4248 cents 12 x 13:16 SD: 42.6499 cents 13 x 14:17 SD: 41.1063 cents 14 x 15:19 SD: 36.4602 cents 15 x 16:20 S SD: 29.2292 cents 16 x 17:21 SD: 29.2165 cents 17 x 18:23 SD: 26.1036 cents 18 x 19:24 SD: 20.1650 cents 19 x 20:25 S SD: 21.1426 cents 20 x 21:27 SD: 18.9447 cents 21 x 22:28 SD: 13.6320 cents 22 x 23:29 SD: 15.4303 cents 23 x 24:31 SD: 13.8453 cents 24 x 25:32 SD: 8.6997 cents 25 x 26:33 SD: 11.3655 cents 26 x 27:35 SD: 10.2471 cents 27 x 28:36 SD: 4.8440 cents 28 x 29:37 SD: 8.6170 cents 29 x 30:39 SD: 7.9088 cents 30 x 31:40 SD: 1.7470 cents 31 x 32:41 SD: 7.0599 cents 32 x 33:43 SD: 6.7364 cents 33 x 34:44 SD: 0.7952 cents 34 x 35:45 SD: 6.5724 cents 35 x 36:47 SD: 6.5594 cents 36 x 37:48 SD: 2.9195 cents 37 x 38:49 SD: 6.8598 cents 38 x 39:51 SD: 7.0325 cents 39:40 x 52 SD: 4.2493 cents 40:41 x 53 SD: 6.5729 cents 41:42 x 55 SD: 6.1551 cents 42:43 x 56 SD: 2.7021 cents 43:44 x 57 SD: 5.5196 cents 44:45 x 59 SD: 5.2197 cents 45:46 x 60 SD: 1.3590 cents 46:47 x 61 SD: 4.8120 cents 47:48 x 63 SD: 4.6259 cents 51:52:53:68 SD: 4.4771 cents 54:55:56:72 SD: 3.4411 cents 57:58:59:76 SD: 2.7616 cents 60:61:62:80 SD: 2.5236 cents 73 x 75:97 SD: 4.3950 cents 74 x 76:99 SD: 4.5978 cents 75 x 77:100 SD: 3.8558 cents 76 x 78:101 SD: 5.0369 cents 77 x 79:103 SD: 5.2523 cents 78:80 x 104 SD: 4.2493 cents 79:81 x 105 SD: 4.8302 cents 80:82:83:107 SD: 4.6380 cents 81:83:84:108 SD: 3.9636 cents 83:85:86:111 SD: 3.7858 cents 84:86:87:112 SD: 3.0756 cents 86:88:89:115 SD: 3.0239 cents 87:89:90:116 SD: 2.2481 cents 90:92:93:120 SD: 1.4756 cents 93:95:96:124 SD: 0.7544 cents 96:98:99:128 SD: 0.1214 cents 483:493:498:644 SD: 0.1189 cents 579:591:597:772 SD: 0.1089 cents