Scala analysis: 033_H8
Hyperenharmonic tetrachord 81/80 * 2240/2187 * 9/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/80 21.506290 syntonic comma, Didymus comma 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: 81/80 21.5063 syntonic comma, Didymus comma 2: 2240/2187 41.4546 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 2240/2187 41.455 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: 1 729/560 456.590 cents 2: 1 320/243 476.539 cents grave fourth 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 : 21.5 63.0 498.0 21.5 : 41.5 476.5 498.0 63.0 : 435.1 456.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 435.0841 cents 80/63, 413.5778 cents 81/80, 21.5063 cents 2: 62.9609 .. 476.5387 cents 80/63, 413.5778 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 7.719370 Largest / Average step : 2.620752 Largest / Smallest step : 20.230551 Median interval of one step : 2240/2187, 41.4546 cents, amount: 1 Least squares average step : 117.25451 cents, oct.: 351.76352 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1598-tone equal temperament with octave 4/3 degrees: 69 202 1598 Least number of segments generator : 801 of 249.646 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1373 of 427.920 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 21.50629 cents Scale diversity : 0.136662 Lumma stability : 0.086363 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 : 179200/177147, 19.9483 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 393.6295 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 729 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.024182 Average absolute harmonicity : 0.103683 Specific harmonicity : 0.124297 Fundamental : 1/2160, -11.0768 octaves, 0.1211 Hz. Guide tone : 2268, 11.1472 octaves, 593366.782 Hz. Exponens Consonantiae : 4.898880E+06, 22.22402 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 111.5, average 37.16667 Mersenne's string divisions : 8855 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.76928, average 2.58976 Vogel's harmonic complexity : 18.66667 Wille's k value : 1093 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 31.15974, average 5.19329 Lattice compactness (without 2's) : 22.76190, average 3.79365 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 0.00000 8 3: -3 .. 4 0.00000 8 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 21| Scale is weakly epimorphic with val: <6 10 18 21| Scale is weakly epimorphic with val: <6 11 17 20| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 11 15 18| Scale is JI-epimorphic with val: <7 11 15 21| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 12 17 20| Scale is weakly epimorphic with val: <8 11 17 20|
FIT/MODE
3: 0 0 3 N M DE S SD: 38.4127 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 24.5330 c. M:-36.6481 c. 6: 0 1 5 N G T3 SD: 16.9744 c. M: 21.5063 c. 7: 0 1 6 N G T3 SD: 13.2862 c. M: 21.5063 c. 8: 0 1 7 N G T3 SD: 12.4233 c. M: 21.5063 c. 9: 0 1 8 N G T3 SD: 13.1735 c. M: 21.5063 c. 10: 0 1 9 N G T3 SD: 14.5558 c. M: 21.5063 c. 14: 1 1 12 N M DE S SD: 9.3980 c. M:-14.0684 c. 15: 1 1 13 N M DE S SD: 7.0399 c. M:-11.6967 c. 16: 1 1 14 N M DE S SD: 5.5699 c. M:-9.6215 c. 17: 1 1 15 N M DE S SD: 5.1564 c. M:-7.7905 c. 18: 1 1 16 N M DE S SD: 5.6593 c. M: 7.6226 c. 21: 1 2 18 N T3 SD: 4.8967 c. M:-8.1884 c. 22: 1 2 19 N T3 SD: 2.9341 c. M:-4.9543 c. 23: 1 2 20 N T3 SD: 1.1587 c. M:-2.0015 c. 24: 1 2 21 N T3 SD: 0.5963 c. M: 0.7544 c. 47: 2 4 41 N T3 SD: 0.4006 c. M:-0.6193 c. 71: 3 6 62 N T3 SD: 0.2846 c. M: 0.4621 c. 95: 4 8 83 N T3 SD: 0.3108 c. M: 0.5360 c. 118: 5 10 103 N T3 SD: 0.3080 c. M: 0.4027 c. 159: 7 13 139 N T3 SD: 0.3028 c. M:-0.4202 c. 166: 7 14 145 N T3 SD: 0.2924 c. M: 0.5044 c. 181: 8 15 158 N T3 SD: 0.3481 c. M:-0.5067 c. 182: 8 15 159 N T3 SD: 0.2231 c. M:-0.3858 c. 183: 8 15 160 N T3 SD: 0.2609 c. M: 0.3651 c. 205: 9 17 179 N T3 SD: 0.2390 c. M:-0.3591 c. 206: 9 17 180 N T3 SD: 0.1572 c. M:-0.2530 c. 229: 10 19 200 N T3 SD: 0.1538 c. M:-0.2424 c. 230: 10 19 201 N T3 SD: 0.1274 c. M: 0.1639 c. 253: 11 21 221 N T3 SD: 0.0874 c. M:-0.1478 c. 277: 12 23 242 N T3 SD: 0.0440 c. M:-0.0697 c. 301: 13 25 263 N T3 SD: 0.0490 c. M: 0.0848 c. 324: 14 27 283 N T3 SD: 0.0375 c. M:-0.0633 c. 348: 15 29 304 N T3 SD: 0.0232 c. M: 0.0388 c. 601: 26 50 525 N T3 SD: 0.0256 c. M:-0.0398 c. 625: 27 52 546 N T3 SD: 0.0071 c. M:-0.0093 c. 973: 42 81 850 N T3 SD: 0.0047 c. M: 0.0079 c. 1598: 69 133 1396 N T3 SD: 0.0024 c. M: 0.0040 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: 9.9962 cents 42:43:44:56 SD: 8.6842 cents 44:45:46:59 SD: 8.1297 cents 45:46:47:60 SD: 6.8763 cents 47:48:49:63 SD: 6.5994 cents 48:49:50:64 SD: 5.3835 cents 51:52:53:68 SD: 4.2147 cents 54:55:56:72 SD: 3.4201 cents 57:58:59:76 SD: 3.0663 cents 72:73:75:96 SD: 2.6895 cents 75:76:78:100 SD: 1.7135 cents 78:79:81:104 SD: 0.8129 cents 81:82:84:108 SD: 0.0880 cents