Scala analysis: 536_M44
Miscellaneous tetrachord 19/18 * 24/23 * 23/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 76/69 167.283668 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/19 330.7613 1: 19/18 93.6030 undevicesimal semitone 2: 24/23 73.6807 vicesimotertial minor semitone 3: 23/19 330.7613
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 23/19 330.761 cents 2: 1 76/69 167.284 cents 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 93.6 167.3 498.0 93.6 : 73.7 404.4 498.0 167.3: 330.8 424.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 330.7613 cents 529/456, 257.0807 cents 24/23, 73.6807 cents 2: 167.2837 .. 424.3643 cents 529/456, 257.0807 cents 1444/1587,-163.4777 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/19, 330.7613 cents Average / Smallest step : 2.253169 Largest / Average step : 1.992358 Largest / Smallest step : 4.489120 Median interval of one step : 19/18, 93.6030 cents, amount: 1 Least squares average step : 137.30752 cents, oct.: 411.92257 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1575-tone equal temperament with octave 4/3 degrees: 296 529 1575 Least number of segments generator : 788 of 249.181 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1376 of 435.117 cents and inv. generated superset size: 47 = 44 more = 1566.667% Number of contiguous 1-step segments: 0 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 73.68065 cents Scale diversity : 0.910960 Lumma stability : 0.295880 Lumma impropriety factor : 0.328239 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 : 437/432, 19.9224 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 257.0807 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 69 Scale harmonicity : 0.011831 Average absolute harmonicity : 0.083793 Specific harmonicity : 0.055233 Fundamental : 1/414, -8.6935 octaves, 0.6319 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 3.146400E+04, 14.94141 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 94.5, average 31.50000 Mersenne's string divisions : 37555 Sum of van Prooijen's expressibility: 3.59472, average 1.19824 Sum of Tenney's harmonic distance : 7.33287, average 2.44429 Vogel's harmonic complexity : 32.00000 Wille's k value : 218 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 15.37877, average 2.56313 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -2 ..-1 -1.33333 4 1 19: 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: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 29 30| Scale is weakly epimorphic with val: <6 10 29 33| Scale is weakly epimorphic with val: <6 10 29 36| Scale is weakly epimorphic with val: <6 11 31 33| Scale is weakly epimorphic with val: <6 11 31 36| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 10 30 32| Scale is weakly epimorphic with val: <7 10 30 35| Scale is weakly epimorphic with val: <7 10 32 33| Scale is weakly epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 28 36| Scale is JI-epimorphic with val: <7 11 30 31| Scale is weakly epimorphic with val: <7 11 30 34| Scale is weakly epimorphic with val: <7 11 31 33| = patent Scale is weakly epimorphic with val: <7 11 31 36| Scale is weakly epimorphic with val: <7 11 33 34| Scale is weakly epimorphic with val: <7 11 34 36| Scale is weakly epimorphic with val: <7 12 34 35| Scale is weakly epimorphic with val: <8 11 28 30| Scale is weakly epimorphic with val: <8 11 31 33| Scale is weakly epimorphic with val: <8 11 33 34| Scale is weakly epimorphic with val: <8 11 34 36| Scale is weakly epimorphic with val: <8 12 31 32| Scale is weakly epimorphic with val: <8 12 34 35|
FIT/MODE
3: 1 0 2 N G T3 SD: 41.8135 c. M:-72.4120 c. 4: 1 0 3 N G T3 SD: 30.4675 c. M: 42.7724 c. 5: 1 1 3 N M DE S SD: 18.7605 c. M:-31.9343 c. 6: 1 1 4 N M DE S SD: 6.1610 c. M: 10.5955 c. 15: 3 2 10 N T3 SD: 3.5441 c. M:-6.0060 c. 21: 4 3 14 N T3 SD: 1.0334 c. M: 1.2687 c. 27: 5 4 18 N T3 SD: 1.0791 c. M: 1.3725 c. 48: 9 7 32 N T3 SD: 0.7434 c. M: 1.2687 c. 74: 14 11 49 N T3 SD: 0.6675 c. M:-0.9748 c. 80: 15 12 53 N T3 SD: 0.4826 c. M:-0.8065 c. 95: 18 14 63 N T3 SD: 0.5203 c. M:-0.7634 c. 101: 19 15 67 N T3 SD: 0.2225 c. M:-0.3750 c. 122: 23 18 81 N T3 SD: 0.1761 c. M:-0.2907 c. 128: 24 19 85 N T3 SD: 0.1278 c. M: 0.2196 c. 149: 28 22 99 N T3 SD: 0.0894 c. M: 0.1545 c. 250: 47 37 166 N T3 SD: 0.0383 c. M:-0.0595 c. 378: 71 56 251 N T3 SD: 0.0424 c. M: 0.0549 c. 399: 75 59 265 N T3 SD: 0.0145 c. M: 0.0204 c. 649: 122 96 431 N T3 SD: 0.0131 c. M:-0.0202 c. 777: 146 115 516 N T3 SD: 0.0135 c. M: 0.0193 c. 926: 174 137 615 N T3 SD: 0.0130 c. M: 0.0179 c. 1048: 197 155 696 N T3 SD: 0.0104 c. M:-0.0180 c. 1176: 221 174 781 N T3 SD: 0.0046 c. M: 0.0078 c. 1575: 296 233 1046 N T3 SD: 0.0025 c. M: 0.0038 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 6:7 S SD: 85.3591 cents 6 x 7:8 S SD: 49.7936 cents 7 x 8:9 S SD: 44.8499 cents 8 x 9:11 SD: 32.3245 cents 9 x 10:12 S SD: 7.5600 cents 10 x 11:13 SD: 21.9451 cents 11 x 12:15 S SD: 21.1587 cents 12 x 13:16 SD: 14.3555 cents 13:14 x 17 SD: 24.1551 cents 14:15 x 19 SD: 20.0414 cents 15:16:17:20 SD: 17.5414 cents 16:17:18:21 S SD: 15.6833 cents 17:18:19:23 SD: 12.0471 cents 18:19:20:24 S SD: 5.0400 cents 38:40:42:51 SD: 4.5674 cents 39:41:43:52 SD: 2.4128 cents 69:73:76:92 SD: 1.3190 cents 90:95:99:120 SD: 0.7598 cents 108:114:119:144 SD: 0.2109 cents 306:323:337:408 SD: 0.0744 cents 414:437:456:552 SD: 0.0000 cents