Scala analysis: 154_C4
Chromatic tetrachord 135/128 * 128/125 * 100/81, Daniélou
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/81 364.8074 grave major third 1: 135/128 92.1787 major chroma, major limma 2: 128/125 41.0589 minor diesis, diesis 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 100/81 364.807 cents grave major third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 512/405 405.866 cents narrow diminished fourth 2: 1 125/96 456.986 cents classic augmented 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 : 92.2 133.2 498.0 92.2 : 41.1 405.9 498.0 133.2: 364.8 457.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 364.8074 cents 3125/2592, 323.7486 cents 128/125, 41.0589 cents 2: 133.2376 .. 456.9861 cents 3125/2592, 323.7486 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 4.043342 Largest / Average step : 2.197437 Largest / Smallest step : 8.884987 Median interval of one step : 135/128, 92.1787 cents, amount: 1 Least squares average step : 132.34206 cents, oct.: 397.02619 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1783-tone equal temperament with octave 4/3 degrees: 330 477 1783 Least number of segments generator : 892 of 249.162 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1209 of 337.710 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 41.05886 cents Scale diversity : 0.612594 Lumma stability : 0.164880 Lumma impropriety factor : 0.464958 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 : 128/125, 41.0589 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 135 Scale harmonicity : 0.025729 Average absolute harmonicity : 0.103030 Specific harmonicity : 0.128410 Fundamental : 1/9600, -13.2288 octaves, 0.0273 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 5.184000E+06, 22.30563 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 161.0, average 53.66667 Mersenne's string divisions : 95732 Sum of van Prooijen's expressibility: 4.03882, average 1.34627 Sum of Tenney's harmonic distance : 8.14603, average 2.71534 Vogel's harmonic complexity : 21.66667 Wille's k value : 5062 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 35.93701, average 5.98950 Lattice compactness (without 2's) : 19.36307, average 3.22718 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -1.66667 9 3: -1 .. 3 1.66667 7 1 5: -2 .. 1 -0.33333 3 2 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 12 16| Scale is weakly epimorphic with val: <8 11 15|
FIT/MODE
3: 1 0 2 N G T3 SD: 46.6410 c. M:-73.8363 c. 4: 1 0 3 N G T3 SD: 19.3351 c. M:-32.3325 c. 7: 1 1 5 N M DE S SD: 13.2204 c. M: 21.0294 c. 10: 2 1 7 N T3 SD: 10.2773 c. M:-16.1759 c. 11: 2 1 8 N T3 SD: 1.7667 c. M:-2.5929 c. 37: 7 3 27 N T3 SD: 1.4214 c. M:-2.0460 c. 38: 7 3 28 N T3 SD: 1.2794 c. M: 2.1731 c. 48: 9 4 35 N T3 SD: 1.1793 c. M:-1.6496 c. 49: 9 4 36 N T3 SD: 0.7547 c. M: 1.1032 c. 60: 11 5 44 N T3 SD: 0.5594 c. M: 0.8705 c. 75: 14 6 55 N T3 SD: 0.5179 c. M:-0.7897 c. 86: 16 7 63 N T3 SD: 0.2785 c. M:-0.4808 c. 97: 18 8 71 N T3 SD: 0.2047 c. M:-0.2590 c. 146: 27 12 107 N T3 SD: 0.1222 c. M: 0.1982 c. 157: 29 13 115 N T3 SD: 0.1057 c. M: 0.1831 c. 232: 43 19 170 N T3 SD: 0.1106 c. M: 0.1393 c. 243: 45 20 178 N T3 SD: 0.0313 c. M:-0.0518 c. 400: 74 33 293 N T3 SD: 0.0241 c. M: 0.0404 c. 643: 119 53 471 N T3 SD: 0.0079 c. M: 0.0125 c. 1140: 211 94 835 N T3 SD: 0.0068 c. M:-0.0113 c. 1540: 285 127 1128 N T3 SD: 0.0057 c. M: 0.0081 c. 1783: 330 147 1306 N T3 SD: 0.0016 c. M:-0.0027 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: 100.5060 cents 6 x 7:8 S SD: 66.8167 cents 7 x 8:9 S SD: 58.2143 cents 8 x 9:11 SD: 44.2510 cents 9 x 10:12 S SD: 24.5831 cents 10 x 11:13 SD: 27.0660 cents 11 x 12:15 S SD: 21.3096 cents 12 x 13:16 SD: 2.6675 cents 13 x 14:17 SD: 16.9891 cents 14 x 15:19 SD: 16.8020 cents 15:16 x 20 S SD: 9.7763 cents 16:17 x 21 SD: 15.0547 cents 17:18 x 23 SD: 13.0832 cents 18:19 x 24 SD: 0.7121 cents 28 x 30:37 SD: 10.3848 cents 29 x 31:39 SD: 11.5859 cents 30:32 x 40 S SD: 9.7763 cents 31:33 x 41 SD: 10.6582 cents 32:34:35:43 SD: 9.5711 cents 33:35:36:44 SD: 6.6383 cents 34:36:37:45 SD: 6.5158 cents 35:37:38:47 SD: 5.2863 cents 36:38:39:48 SD: 1.8406 cents 75:79:81:100 SD: 0.7414 cents 111:117:120:148 SD: 0.6735 cents 126:133:136:168 SD: 0.5836 cents 162:171:175:216 SD: 0.4928 cents 201:212:217:268 SD: 0.2138 cents 237:250:256:316 SD: 0.1275 cents 438:462:473:584 SD: 0.0762 cents 513:541:554:684 SD: 0.0717 cents