Scala analysis: 524_M32
Miscellaneous tetrachord 36/35 * 256/243 * 315/256
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 1024/945 138.995377 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 315/256 359.0496 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 256/243 90.2250 limma, Pythagorean minor second 3: 315/256 359.0496
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 315/256 359.050 cents 2: 1 1024/945 138.995 cents 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 139.0 498.0 48.8 : 90.2 449.3 498.0 139.0: 359.0 407.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 359.0496 cents 1225/1024, 310.2792 cents 36/35, 48.7704 cents 2: 138.9954 .. 449.2746 cents 1225/1024, 310.2792 cents 262144/297675,-220.0542 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 315/256, 359.0496 cents Average / Smallest step : 3.404013 Largest / Average step : 2.162754 Largest / Smallest step : 7.362043 Median interval of one step : 256/243, 90.2250 cents, amount: 1 Least squares average step : 130.06401 cents, oct.: 390.19203 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2114-tone equal temperament with octave 4/3 degrees: 207 590 2114 Least number of segments generator : 1059 of 249.494 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1907 of 449.277 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 48.77038 cents Scale diversity : 0.677525 Lumma stability : 0.195847 Lumma impropriety factor : 0.441836 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 : 2240/2187, 41.4546 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% -- Rational properties -- Prime limit : 7 Odd number limit : 945 (O: 315 U: 945) Highest odd numerator or denominator: 945 Scale harmonicity : 0.024988 Average absolute harmonicity : 0.094916 Specific harmonicity : 0.114769 Fundamental : 1/945, -9.8842 octaves, 0.2769 Hz. Guide tone : 9216, 13.1699 octaves, 2411141.210 Hz. Exponens Consonantiae : 8.709120E+06, 23.05410 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 1023.5, average 341.16667 Mersenne's string divisions : 978593 Sum of van Prooijen's expressibility: 4.99662, average 1.66554 Sum of Tenney's harmonic distance : 10.16528, average 3.38843 Vogel's harmonic complexity : 15.66667 Wille's k value : 157 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 37.05121, average 6.17520 Lattice compactness (without 2's) : 17.53223, average 2.92204 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 10 4.66667 14 3: -3 .. 2 -0.66667 6 1 5: -1 .. 0 -0.66667 2 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is JI-epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.1901 c. M: 48.7704 c. 4: 0 1 3 N G T3 SD: 29.3731 c. M: 48.7704 c. 7: 1 1 5 N M DE S SD: 13.0605 c. M:-22.3789 c. 8: 1 1 6 N M DE S SD: 11.4257 c. M: 14.4841 c. 10: 1 2 7 N T3 SD: 6.0445 c. M:-10.4181 c. 11: 1 2 8 N T3 SD: 2.7216 c. M: 3.4936 c. 21: 2 4 15 N T3 SD: 2.0575 c. M:-3.3032 c. 29: 3 5 21 N T3 SD: 1.8387 c. M:-2.7515 c. 32: 3 6 23 N T3 SD: 1.3524 c. M: 2.0787 c. 39: 4 7 28 N T3 SD: 1.5841 c. M:-2.3112 c. 40: 4 7 29 N T3 SD: 1.3169 c. M: 2.0330 c. 50: 5 9 36 N T3 SD: 0.6528 c. M:-1.0341 c. 61: 6 11 44 N T3 SD: 0.1691 c. M:-0.2177 c. 143: 14 26 103 N T3 SD: 0.1836 c. M:-0.3179 c. 154: 15 28 111 N T3 SD: 0.1551 c. M: 0.2595 c. 204: 20 37 147 N T3 SD: 0.1005 c. M:-0.1643 c. 215: 21 39 155 N T3 SD: 0.0717 c. M: 0.1241 c. 265: 26 48 191 N T3 SD: 0.0719 c. M:-0.0944 c. 276: 27 50 199 N T3 SD: 0.0394 c. M: 0.0486 c. 480: 47 87 346 N T3 SD: 0.0244 c. M:-0.0422 c. 541: 53 98 390 N T3 SD: 0.0152 c. M:-0.0215 c. 756: 74 137 545 N T3 SD: 0.0127 c. M: 0.0199 c. 817: 80 148 589 N T3 SD: 0.0037 c. M: 0.0061 c. 2114: 207 383 1524 N T3 SD: 0.0032 c. M:-0.0049 c. 2175: 213 394 1568 N T3 SD: 0.0022 c. M:-0.0037 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: 97.9011 cents 6 x 7:8 S SD: 63.9378 cents 7 x 8:9 S SD: 55.8144 cents 8 x 9:11 SD: 41.9878 cents 9 x 10:12 S SD: 21.7042 cents 10 x 11:13 SD: 25.4834 cents 11 x 12:15 S SD: 20.3051 cents 12 x 13:16 SD: 0.2114 cents 13 x 14:17 SD: 17.6391 cents 14 x 15:19 SD: 18.1744 cents 15 x 16:20 S SD: 13.6320 cents 16 x 17:21 SD: 21.8062 cents 17 x 18:23 SD: 23.6751 cents 18:19:20:24 S SD: 20.8013 cents 19:20:21:25 SD: 19.1568 cents 20:21:22:27 SD: 16.3749 cents 21:22:23:28 SD: 12.2533 cents 22:23:24:29 SD: 12.1173 cents 23:24:25:31 SD: 10.5384 cents 24:25:26:32 SD: 7.3020 cents 27:28:29:36 SD: 6.9518 cents 33:34:36:44 SD: 4.0001 cents 36:37:39:48 SD: 0.4672 cents 240:247:260:320 SD: 0.3624 cents 276:284:299:368 SD: 0.2717 cents 312:321:338:416 SD: 0.2088 cents 348:358:377:464 SD: 0.1683 cents 384:395:416:512 SD: 0.1470 cents 420:432:455:560 SD: 0.1409 cents 489:503:530:652 SD: 0.1354 cents 525:540:569:700 SD: 0.1127 cents 561:577:608:748 SD: 0.1006 cents 597:614:647:796 SD: 0.0981 cents