Scala analysis: 028_H8
Hyperenharmonic tetrachord 84/83 * 83/81 * 9/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 84/83 20.733590 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: 84/83 20.7336 2: 83/81 42.2273 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 84/83 20.734 cents 1: 1 83/81 42.227 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: 1 108/83 455.818 cents 2: 1 83/63 477.311 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 : 20.7 63.0 498.0 20.7 : 42.2 477.3 498.0 63.0 : 435.1 455.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.7336 .. 435.0841 cents 249/196, 414.3505 cents 84/83, 20.7336 cents 2: 62.9609 .. 477.3114 cents 249/196, 414.3505 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 84/83, 20.7336 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 8.007055 Largest / Average step : 2.620752 Largest / Smallest step : 20.984504 Median interval of one step : 83/81, 42.2273 cents, amount: 1 Least squares average step : 117.19931 cents, oct.: 351.59794 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1321-tone equal temperament with octave 4/3 degrees: 55 167 1321 Least number of segments generator : 661 of 249.211 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1228 of 462.982 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 20.73359 cents Scale diversity : 0.134755 Lumma stability : 0.083260 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 : 84/83, 20.7336 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 392.8568 cents: 2 -- Rational properties -- Prime limit : 83 Odd number limit : 83 (O: 83 U: 83) Highest odd numerator or denominator: 83 Scale harmonicity : 0.043568 Fundamental : 1/2241, -11.1299 octaves, 0.1167 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 1.882440E+05, 17.52224 octaves Euler's gradus suavitatis : 99 Sum of Mann's harmonic distance : 114.5, average 38.16667 Mersenne's string divisions : 64295 Sum of van Prooijen's expressibility: 3.82756, average 1.27585 Sum of Tenney's harmonic distance : 7.80106, average 2.60035 Vogel's harmonic complexity : 68.00000 Wille's k value : 373 Wilson's harmonic complexity : 102 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.89935, average 2.81656 Lattice compactness (without 2's) : 14.04863, average 2.34144 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 .. 1 -1.00000 5 1 7: 0 .. 1 0.66667 2 1 83: -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 21 45| Scale is weakly epimorphic with val: <7 10 19 47| Scale is weakly epimorphic with val: <7 11 18 45| Scale is weakly epimorphic with val: <7 11 20 46| = patent Scale is JI-epimorphic with val: <7 11 21 45| Scale is weakly epimorphic with val: <8 11 20 46| Scale is weakly epimorphic with val: <8 11 21 45| Scale is weakly epimorphic with val: <8 12 22 47|
FIT/MODE
3: 0 0 3 N M DE S SD: 38.2708 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 24.3102 c. M:-36.6481 c. 6: 0 1 5 N G T3 SD: 16.6508 c. M: 20.7336 c. 7: 0 1 6 N G T3 SD: 12.8703 c. M: 20.7336 c. 8: 0 1 7 N G T3 SD: 11.9775 c. M: 20.7336 c. 9: 0 1 8 N G T3 SD: 12.7539 c. M: 20.7336 c. 14: 1 1 12 N M DE S SD: 9.7862 c. M:-14.8411 c. 15: 1 1 13 N M DE S SD: 7.4689 c. M:-12.4694 c. 16: 1 1 14 N M DE S SD: 6.0149 c. M:-10.3942 c. 17: 1 1 15 N M DE S SD: 5.5498 c. M:-8.5632 c. 18: 1 1 16 N M DE S SD: 5.9500 c. M: 7.6226 c. 21: 1 2 18 N T3 SD: 5.0315 c. M:-8.1884 c. 22: 1 2 19 N T3 SD: 3.0645 c. M:-4.9543 c. 23: 1 2 20 N T3 SD: 1.2719 c. M:-2.0015 c. 24: 1 2 21 N T3 SD: 0.4073 c. M: 0.7053 c. 47: 2 4 41 N T3 SD: 0.4453 c. M:-0.6193 c. 71: 3 6 62 N T3 SD: 0.2048 c. M:-0.3106 c. 95: 4 8 83 N T3 SD: 0.1397 c. M:-0.2367 c. 119: 5 10 104 N T3 SD: 0.1531 c. M:-0.1927 c. 166: 7 14 145 N T3 SD: 0.1571 c. M:-0.2683 c. 214: 9 18 187 N T3 SD: 0.1418 c. M:-0.2122 c. 309: 13 26 270 N T3 SD: 0.1396 c. M:-0.2198 c. 340: 14 29 297 N T3 SD: 0.1313 c. M: 0.2259 c. 363: 15 31 317 N T3 SD: 0.1247 c. M: 0.1532 c. 364: 15 31 318 N T3 SD: 0.1217 c. M: 0.2098 c. 387: 16 33 338 N T3 SD: 0.1002 c. M: 0.1426 c. 388: 16 33 339 N T3 SD: 0.1188 c. M: 0.1957 c. 411: 17 35 359 N T3 SD: 0.0826 c. M: 0.1332 c. 435: 18 37 380 N T3 SD: 0.0723 c. M: 0.1248 c. 458: 19 39 400 N T3 SD: 0.0762 c. M:-0.1103 c. 459: 19 39 401 N T3 SD: 0.0695 c. M: 0.1173 c. 482: 20 41 421 N T3 SD: 0.0561 c. M:-0.0697 c. 506: 21 43 442 N T3 SD: 0.0414 c. M: 0.0637 c. 530: 22 45 463 N T3 SD: 0.0347 c. M: 0.0600 c. 554: 23 47 484 N T3 SD: 0.0373 c. M: 0.0566 c. 577: 24 49 504 N T3 SD: 0.0306 c. M:-0.0500 c. 601: 25 51 525 N T3 SD: 0.0148 c. M:-0.0198 c. 625: 26 53 546 N T3 SD: 0.0098 c. M: 0.0149 c. 1226: 51 104 1071 N T3 SD: 0.0096 c. M: 0.0156 c. 1297: 54 110 1133 N T3 SD: 0.0086 c. M:-0.0147 c. 1321: 55 112 1154 N T3 SD: 0.0018 c. M:-0.0026 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 41:42:43:55 SD: 10.1716 cents 42:43:44:56 SD: 8.8760 cents 44:45:46:59 SD: 8.3154 cents 45:46:47:60 SD: 7.0845 cents 47:48:49:63 SD: 6.7959 cents 48:49:50:64 SD: 5.6112 cents 50:51:52:67 SD: 5.6030 cents 51:52:53:68 SD: 4.4621 cents 54:55:56:72 SD: 3.6777 cents 57:58:59:76 SD: 3.3084 cents 72:73:75:96 SD: 2.7762 cents 75:76:78:100 SD: 1.8020 cents 78:79:81:104 SD: 0.9062 cents 81:82:84:108 SD: 0.1696 cents 591:598:613:788 SD: 0.1564 cents 594:601:616:792 SD: 0.1504 cents