Scala analysis: 150_C4
Chromatic tetrachord 81/80 * 16/15 * 100/81
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: 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: 81/80 21.5063 syntonic comma, Didymus comma 2: 16/15 111.7313 minor diatonic semitone 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 16/15 111.731 cents minor diatonic semitone 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 5/4 386.314 cents major third 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 : 21.5 133.2 498.0 21.5 : 111.7 476.5 498.0 133.2: 364.8 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 364.8074 cents 8000/6561, 343.3011 cents 81/80, 21.5063 cents 2: 133.2376 .. 476.5387 cents 8000/6561, 343.3011 cents 2187/2500,-231.5698 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 : 100/81, 364.8074 cents Average / Smallest step : 7.719370 Largest / Average step : 2.197437 Largest / Smallest step : 16.962825 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 127.29403 cents, oct.: 381.88209 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1413-tone equal temperament with octave 4/3 degrees: 61 378 1413 Least number of segments generator : 707 of 249.199 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 928 of 327.095 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 : 0.494353 Lumma stability : 0.086363 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 : 81/80, 21.5063 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 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.031120 Average absolute harmonicity : 0.103277 Specific harmonicity : 0.144404 Fundamental : 1/1200, -10.2288 octaves, 0.2180 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 3.888000E+05, 18.56867 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 110.0, average 36.66667 Mersenne's string divisions : 8372 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.72006, average 2.57335 Vogel's harmonic complexity : 17.33333 Wille's k value : 607 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 28.60181, average 4.76697 Lattice compactness (without 2's) : 19.71403, average 3.28567 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.66667 6 3: -1 .. 4 2.00000 8 1 5: -2 .. 0 -1.00000 3 2 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 11 15| Scale is weakly epimorphic with val: <6 11 17|
FIT/MODE
3: 0 1 2 N G T3 SD: 22.6339 c. M:-32.7774 c. 4: 0 1 3 N G T3 SD: 13.3999 c. M: 21.5063 c. 11: 0 3 8 N G T3 SD: 12.5066 c. M: 21.5063 c. 14: 1 3 10 N T3 SD: 9.6613 c. M:-14.0684 c. 15: 1 3 11 N T3 SD: 6.7576 c. M:-11.6967 c. 16: 1 3 12 N T3 SD: 7.4994 c. M:-9.6215 c. 17: 1 4 12 N T3 SD: 8.8723 c. M:-13.2462 c. 18: 1 4 13 N T3 SD: 4.6215 c. M:-6.1629 c. 19: 1 4 14 N T3 SD: 2.9930 c. M:-4.7066 c. 22: 1 5 16 N T3 SD: 1.6335 c. M:-2.5929 c. 26: 1 6 19 N T3 SD: 1.4435 c. M: 2.3507 c. 45: 2 10 33 N T3 SD: 0.4385 c. M:-0.6290 c. 71: 3 16 52 N T3 SD: 0.2679 c. M: 0.4621 c. 116: 5 26 85 N T3 SD: 0.0835 c. M: 0.1393 c. 254: 11 57 186 N T3 SD: 0.0668 c. M:-0.0973 c. 325: 14 73 238 N T3 SD: 0.0577 c. M:-0.0852 c. 370: 16 83 271 N T3 SD: 0.0222 c. M:-0.0308 c. 486: 21 109 356 N T3 SD: 0.0122 c. M: 0.0157 c. 856: 37 192 627 N T3 SD: 0.0123 c. M:-0.0214 c. 927: 40 208 679 N T3 SD: 0.0094 c. M: 0.0157 c. 1297: 56 291 950 N T3 SD: 0.0057 c. M:-0.0096 c. 1413: 61 317 1035 N T3 SD: 0.0035 c. M: 0.0054 c. 1783: 77 400 1306 N T3 SD: 0.0020 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 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 19.6419 cents 17 x 18:23 SD: 21.2961 cents 18 x 19:24 SD: 19.8173 cents 19 x 21:25 SD: 23.0664 cents 20 x 22:27 SD: 19.1810 cents 21 x 23:28 SD: 12.1279 cents 33:34:36:44 SD: 11.6110 cents 34:35:37:45 SD: 11.3462 cents 35:36:38:47 SD: 10.4277 cents 36:37:39:48 SD: 8.8237 cents 38:39:41:51 SD: 8.7067 cents 39:40:42:52 SD: 7.6215 cents 45:46:49:60 SD: 7.2655 cents 46:47:50:61 SD: 7.1482 cents 47:48:51:63 SD: 6.4490 cents 48:49:52:64 SD: 5.0534 cents 51:52:55:68 SD: 4.1232 cents 60:61:65:80 SD: 2.9630 cents 63:64:68:84 SD: 1.9490 cents 72:73:78:96 SD: 1.9464 cents 75:76:81:100 SD: 0.4748 cents 162:164:175:216 SD: 0.1586 cents 237:240:256:316 SD: 0.1275 cents 399:404:431:532 SD: 0.1086 cents