Scala analysis: 030_H8
Hyperenharmonic tetrachord 70/69 * 46/45 * 9/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70/69 24.910272 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: 70/69 24.9103 2: 46/45 38.0506 23rd-partial chroma 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 70/69 24.910 cents 1: 1 46/45 38.051 cents 23rd-partial chroma 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 30/23 459.994 cents 2: 1 46/35 473.135 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 : 24.9 63.0 498.0 24.9 : 38.1 473.1 498.0 63.0 : 435.1 460.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.9103 .. 435.0841 cents 621/490, 410.1738 cents 70/69, 24.9103 cents 2: 62.9609 .. 473.1347 cents 621/490, 410.1738 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 70/69, 24.9103 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 6.664520 Largest / Average step : 2.620752 Largest / Smallest step : 17.466051 Median interval of one step : 46/45, 38.0506 cents, amount: 1 Least squares average step : 117.49765 cents, oct.: 352.49295 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1859-tone equal temperament with octave 4/3 degrees: 93 235 1859 Least number of segments generator : 930 of 249.156 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1087 of 291.218 cents and inv. generated superset size: 37 = 34 more = 1233.333% 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 24.91027 cents Scale diversity : 0.144378 Lumma stability : 0.100032 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 : 529/525, 13.1404 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 397.0335 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 35 U: 69) Highest odd numerator or denominator: 69 Scale harmonicity : 0.014541 Average absolute harmonicity : 0.093199 Specific harmonicity : 0.073528 Fundamental : 1/621, -9.2784 octaves, 0.4213 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 8.694000E+04, 16.40773 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 100.5, average 33.50000 Mersenne's string divisions : 53515 Sum of van Prooijen's expressibility: 3.74733, average 1.24911 Sum of Tenney's harmonic distance : 7.64165, average 2.54722 Vogel's harmonic complexity : 27.33333 Wille's k value : 157 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.09561, average 2.51594 Lattice compactness (without 2's) : 12.57989, average 2.09665 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 ..-1 -1.66667 5 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.66667 2 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 21 31| Scale is weakly epimorphic with val: <6 10 15 21 34| Scale is weakly epimorphic with val: <6 10 15 22 30| Scale is weakly epimorphic with val: <6 10 16 21 32| Scale is weakly epimorphic with val: <6 10 16 21 35| Scale is weakly epimorphic with val: <6 10 16 22 31| Scale is weakly epimorphic with val: <6 10 17 21 30| Scale is weakly epimorphic with val: <6 10 17 21 33| Scale is weakly epimorphic with val: <6 10 17 21 36| Scale is weakly epimorphic with val: <6 10 17 22 32| Scale is weakly epimorphic with val: <6 10 18 19 30| Scale is weakly epimorphic with val: <6 10 18 21 31| Scale is weakly epimorphic with val: <6 10 18 21 34| Scale is weakly epimorphic with val: <6 10 18 22 33| Scale is weakly epimorphic with val: <6 10 19 19 31| Scale is weakly epimorphic with val: <6 10 19 21 32| Scale is weakly epimorphic with val: <6 10 19 21 35| Scale is weakly epimorphic with val: <6 10 19 22 34| Scale is weakly epimorphic with val: <6 11 18 20 30| Scale is weakly epimorphic with val: <6 11 19 20 31| Scale is weakly epimorphic with val: <7 10 15 19 32| Scale is weakly epimorphic with val: <7 10 15 19 35| Scale is weakly epimorphic with val: <7 10 15 21 30| Scale is weakly epimorphic with val: <7 10 16 19 30| Scale is weakly epimorphic with val: <7 10 16 19 33| Scale is weakly epimorphic with val: <7 10 16 19 36| Scale is weakly epimorphic with val: <7 10 16 21 31| Scale is weakly epimorphic with val: <7 10 17 19 31| Scale is weakly epimorphic with val: <7 10 17 19 34| Scale is weakly epimorphic with val: <7 10 17 21 32| Scale is weakly epimorphic with val: <7 10 18 18 30| Scale is weakly epimorphic with val: <7 10 18 19 32| Scale is weakly epimorphic with val: <7 10 18 19 35| Scale is weakly epimorphic with val: <7 10 18 21 33| Scale is weakly epimorphic with val: <7 10 19 19 30| Scale is weakly epimorphic with val: <7 10 19 19 33| Scale is weakly epimorphic with val: <7 10 19 19 36| Scale is weakly epimorphic with val: <7 10 19 21 34| Scale is weakly epimorphic with val: <7 11 15 18 31| Scale is weakly epimorphic with val: <7 11 15 18 34| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 20 35| Scale is JI-epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is weakly epimorphic with val: <7 11 16 18 35| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 20 33| Scale is weakly epimorphic with val: <7 11 16 20 36| Scale is JI-epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 16 21 35| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 18 36| Scale is weakly epimorphic with val: <7 11 17 20 31| Scale is weakly epimorphic with val: <7 11 17 20 34| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is JI-epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 17 21 36| Scale is weakly epimorphic with val: <7 11 18 18 31| Scale is weakly epimorphic with val: <7 11 18 18 34| Scale is weakly epimorphic with val: <7 11 18 20 32| Scale is weakly epimorphic with val: <7 11 18 20 35| Scale is weakly epimorphic with val: <7 11 18 21 31| Scale is JI-epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is weakly epimorphic with val: <7 11 19 20 33| Scale is weakly epimorphic with val: <7 11 19 20 36| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is JI-epimorphic with val: <7 11 19 21 35| Scale is weakly epimorphic with val: <7 12 18 20 30| Scale is weakly epimorphic with val: <7 12 19 20 31| Scale is weakly epimorphic with val: <8 11 15 20 31| Scale is weakly epimorphic with val: <8 11 15 20 34| Scale is weakly epimorphic with val: <8 11 15 21 30| Scale is weakly epimorphic with val: <8 11 16 20 32| Scale is weakly epimorphic with val: <8 11 16 20 35| Scale is weakly epimorphic with val: <8 11 16 21 31| Scale is weakly epimorphic with val: <8 11 17 20 30| Scale is weakly epimorphic with val: <8 11 17 20 33| Scale is weakly epimorphic with val: <8 11 17 20 36| Scale is weakly epimorphic with val: <8 11 17 21 32| Scale is weakly epimorphic with val: <8 11 18 18 30| Scale is weakly epimorphic with val: <8 11 18 20 31| Scale is weakly epimorphic with val: <8 11 18 20 34| Scale is weakly epimorphic with val: <8 11 18 21 33| Scale is weakly epimorphic with val: <8 11 19 20 32| Scale is weakly epimorphic with val: <8 11 19 20 35| Scale is weakly epimorphic with val: <8 11 19 21 34| Scale is weakly epimorphic with val: <8 12 15 22 30| Scale is weakly epimorphic with val: <8 12 16 22 31| Scale is weakly epimorphic with val: <8 12 17 22 32| Scale is weakly epimorphic with val: <8 12 18 19 30| Scale is weakly epimorphic with val: <8 12 18 22 33| Scale is weakly epimorphic with val: <8 12 19 19 31| Scale is weakly epimorphic with val: <8 12 19 22 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 39.0922 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 25.5839 c. M:-36.6481 c. 6: 0 1 5 N G T3 SD: 18.4607 c. M: 24.9103 c. 7: 0 1 6 N G T3 SD: 15.1390 c. M: 24.9103 c. 8: 0 1 7 N G T3 SD: 14.3877 c. M: 24.9103 c. 9: 0 1 8 N G T3 SD: 15.0402 c. M: 24.9103 c. 10: 0 1 9 N G T3 SD: 16.2646 c. M: 24.9103 c. 13: 1 1 11 N M DE S SD: 11.0486 c. M:-13.6614 c. 14: 1 1 12 N M DE S SD: 7.7627 c. M:-10.6644 c. 15: 1 1 13 N M DE S SD: 5.1845 c. M:-8.2927 c. 16: 1 1 14 N M DE S SD: 3.6127 c. M:-6.2175 c. 17: 1 1 15 N M DE S SD: 3.5738 c. M:-4.3865 c. 22: 1 2 19 N T3 SD: 3.1468 c. M:-4.9543 c. 23: 1 2 20 N T3 SD: 2.2067 c. M: 3.2561 c. 24: 1 2 21 N T3 SD: 2.4351 c. M: 4.1584 c. 37: 2 3 32 N T3 SD: 2.7629 c. M:-4.3425 c. 38: 2 3 33 N T3 SD: 1.6642 c. M:-2.5713 c. 39: 2 3 34 N T3 SD: 0.6302 c. M:-0.8910 c. 40: 2 3 35 N T3 SD: 0.4072 c. M: 0.7053 c. 79: 4 6 69 N T3 SD: 0.1837 c. M:-0.3072 c. 119: 6 9 104 N T3 SD: 0.1567 c. M:-0.2012 c. 182: 9 14 159 N T3 SD: 0.1631 c. M: 0.2817 c. 198: 10 15 173 N T3 SD: 0.1474 c. M:-0.2435 c. 221: 11 17 193 N T3 SD: 0.1066 c. M:-0.1398 c. 261: 13 20 228 N T3 SD: 0.0600 c. M: 0.1034 c. 301: 15 23 263 N T3 SD: 0.0717 c. M: 0.0908 c. 340: 17 26 297 N T3 SD: 0.0163 c. M:-0.0271 c. 720: 36 55 629 N T3 SD: 0.0091 c. M: 0.0135 c. 1060: 53 81 926 N T3 SD: 0.0046 c. M: 0.0080 c. 1400: 70 107 1223 N T3 SD: 0.0059 c. M: 0.0080 c. 1780: 89 136 1555 N T3 SD: 0.0057 c. M: 0.0080 c. 1859: 93 142 1624 N T3 SD: 0.0033 c. M:-0.0054 c. 2199: 110 168 1921 N T3 SD: 0.0024 c. M:-0.0033 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 39:40 x 52 SD: 9.4604 cents 40:41 x 53 SD: 10.4406 cents 41:42:43:55 SD: 9.2695 cents 42:43:44:56 SD: 7.8839 cents 44:45:46:59 SD: 7.3633 cents 45:46:47:60 SD: 6.0046 cents 47:48:49:63 SD: 5.7911 cents 48:49:50:64 SD: 4.4199 cents 51:52:53:68 SD: 3.1449 cents 54:55:56:72 SD: 2.2855 cents 57:58:59:76 SD: 2.0450 cents 75:76:78:100 SD: 1.7738 cents 78:79:81:104 SD: 1.2385 cents 81:82:84:108 SD: 1.2226 cents 129:131:134:172 SD: 1.1171 cents 132:134:137:176 SD: 0.5996 cents 135:137:140:180 SD: 0.1832 cents 351:356:364:468 SD: 0.1409 cents 483:490:501:644 SD: 0.1280 cents 486:493:504:648 SD: 0.0509 cents