Scala analysis: 139_C3
Chromatic tetrachord 136/131 * 131/126 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 136/131 64.847808 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 136/131 64.8478 2: 131/126 67.3717 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 136/131 64.848 cents 1: 1 131/126 67.372 cents 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 168/131 430.673 cents 2: 1 131/102 433.197 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 : 64.8 132.2 498.0 64.8 : 67.4 433.2 498.0 132.2: 365.8 430.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.8478 .. 365.8255 cents 2751/2312, 300.9777 cents 136/131, 64.8478 cents 2: 132.2195 .. 433.1972 cents 2751/2312, 300.9777 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 136/131, 64.8478 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 2.560071 Largest / Average step : 2.203569 Largest / Smallest step : 5.641293 Median interval of one step : 131/126, 67.3717 cents, amount: 1 Least squares average step : 130.24441 cents, oct.: 390.73324 cents Scale is not proper Scale has trivalence property Scale is a mode of a 791-tone equal temperament with octave 4/3 degrees: 103 210 791 Least number of segments generator : 396 of 249.337 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 688 of 433.192 cents and inv. generated superset size: 23 = 20 more = 766.667% 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 64.84781 cents Scale diversity : 0.672422 Lumma stability : 0.260409 Lumma impropriety factor : 0.469046 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 : 17161/17136, 2.5239 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 298.4538 cents: 2 -- Rational properties -- Prime limit : 131 Odd number limit : 131 (O: 131 U: 131) Highest odd numerator or denominator: 131 Scale harmonicity : 0.020518 Fundamental : 1/8253, -13.0107 octaves, 0.0317 Hz. Guide tone : 136, 7.0875 octaves, 35581.077 Hz. Exponens Consonantiae : 1.122408E+06, 20.09817 octaves Euler's gradus suavitatis : 160 Sum of Mann's harmonic distance : 202.5, average 67.50000 Mersenne's string divisions : 244839 Sum of van Prooijen's expressibility: 4.39373, average 1.46458 Sum of Tenney's harmonic distance : 8.96184, average 2.98728 Vogel's harmonic complexity : 108.66667 Wille's k value : 1375 Wilson's harmonic complexity : 161 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.47421, average 2.41237 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 131: -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 18 29 52| Scale is weakly epimorphic with val: <6 10 19 30 50| Scale is weakly epimorphic with val: <6 10 20 31 51| Scale is weakly epimorphic with val: <6 10 21 32 52| Scale is weakly epimorphic with val: <6 10 22 33 50| Scale is weakly epimorphic with val: <6 11 18 31 50| Scale is weakly epimorphic with val: <6 11 19 32 51| Scale is weakly epimorphic with val: <6 11 20 33 52| Scale is weakly epimorphic with val: <7 10 18 27 52| Scale is weakly epimorphic with val: <7 10 18 32 50| Scale is weakly epimorphic with val: <7 10 19 28 50| Scale is weakly epimorphic with val: <7 10 19 33 51| Scale is weakly epimorphic with val: <7 10 20 29 51| Scale is weakly epimorphic with val: <7 10 21 30 52| Scale is weakly epimorphic with val: <7 10 21 32 50| Scale is weakly epimorphic with val: <7 10 22 31 50| Scale is weakly epimorphic with val: <7 10 22 33 51| Scale is weakly epimorphic with val: <7 11 18 27 52| Scale is weakly epimorphic with val: <7 11 18 28 51| Scale is weakly epimorphic with val: <7 11 18 30 52| Scale is weakly epimorphic with val: <7 11 18 31 51| Scale is weakly epimorphic with val: <7 11 18 33 52| Scale is weakly epimorphic with val: <7 11 19 28 50| Scale is weakly epimorphic with val: <7 11 19 29 52| Scale is weakly epimorphic with val: <7 11 19 31 50| Scale is weakly epimorphic with val: <7 11 19 32 52| Scale is weakly epimorphic with val: <7 11 20 27 50| Scale is weakly epimorphic with val: <7 11 20 29 51| Scale is JI-epimorphic with val: <7 11 20 30 50| Scale is weakly epimorphic with val: <7 11 20 32 51| Scale is weakly epimorphic with val: <7 11 20 33 50| Scale is weakly epimorphic with val: <7 11 21 27 52| Scale is weakly epimorphic with val: <7 11 21 28 51| Scale is weakly epimorphic with val: <7 11 21 30 52| Scale is JI-epimorphic with val: <7 11 21 31 51| Scale is weakly epimorphic with val: <7 11 21 33 52| Scale is weakly epimorphic with val: <7 11 22 28 50| Scale is weakly epimorphic with val: <7 11 22 29 52| Scale is weakly epimorphic with val: <7 11 22 31 50| Scale is JI-epimorphic with val: <7 11 22 32 52| Scale is weakly epimorphic with val: <7 12 18 31 51| Scale is weakly epimorphic with val: <7 12 18 32 50| Scale is weakly epimorphic with val: <7 12 19 32 52| Scale is weakly epimorphic with val: <7 12 19 33 51| Scale is weakly epimorphic with val: <7 12 20 33 50| Scale is weakly epimorphic with val: <7 12 21 32 50| Scale is weakly epimorphic with val: <7 12 22 33 51| Scale is weakly epimorphic with val: <8 11 18 27 50| Scale is weakly epimorphic with val: <8 11 18 31 52| Scale is weakly epimorphic with val: <8 11 19 28 51| Scale is weakly epimorphic with val: <8 11 19 29 50| Scale is weakly epimorphic with val: <8 11 20 29 52| Scale is weakly epimorphic with val: <8 11 20 30 51| Scale is weakly epimorphic with val: <8 11 21 30 50| Scale is weakly epimorphic with val: <8 11 21 31 52| Scale is weakly epimorphic with val: <8 11 22 29 50| Scale is weakly epimorphic with val: <8 11 22 31 51| Scale is weakly epimorphic with val: <8 12 18 29 51| Scale is weakly epimorphic with val: <8 12 18 31 52| Scale is weakly epimorphic with val: <8 12 19 29 50| Scale is weakly epimorphic with val: <8 12 19 30 52| Scale is weakly epimorphic with val: <8 12 20 30 51| Scale is weakly epimorphic with val: <8 12 20 31 50| Scale is weakly epimorphic with val: <8 12 21 31 52| Scale is weakly epimorphic with val: <8 12 21 32 51| Scale is weakly epimorphic with val: <8 12 22 29 50| Scale is weakly epimorphic with val: <8 12 22 33 52|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.2192 c. M: 64.8478 c. 4: 0 1 3 N G T3 SD: 37.7035 c. M: 64.8478 c. 5: 0 1 4 N G T3 SD: 41.9074 c. M: 64.8478 c. 6: 1 1 4 N M DE S SD: 22.1503 c. M:-33.7955 c. 7: 1 1 5 N M DE S SD: 6.8629 c. M:-10.0791 c. 8: 1 1 6 N M DE S SD: 4.6953 c. M: 7.7083 c. 15: 2 2 11 N M DE S SD: 0.9625 c. M:-1.5582 c. 38: 5 5 28 N M DE S SD: 0.7751 c. M: 1.1550 c. 53: 7 7 39 N M DE S SD: 0.6594 c. M:-0.9317 c. 68: 9 9 50 N M DE S SD: 0.6563 c. M:-1.0699 c. 83: 11 11 61 N M DE S SD: 0.6793 c. M:-1.1582 c. 91: 12 12 67 N M DE S SD: 0.6923 c. M: 0.8670 c. 98: 13 13 72 N M DE S SD: 0.7057 c. M:-1.2194 c. 101: 13 14 74 N T3 SD: 0.6833 c. M:-0.9212 c. 109: 14 15 80 N T3 SD: 0.5339 c. M: 0.8787 c. 117: 15 16 86 N T3 SD: 0.5941 c. M: 0.9959 c. 124: 16 17 91 N T3 SD: 0.3858 c. M: 0.5839 c. 132: 17 18 97 N T3 SD: 0.4180 c. M: 0.7056 c. 139: 18 19 102 N T3 SD: 0.2884 c. M:-0.3536 c. 147: 19 20 108 N T3 SD: 0.2784 c. M: 0.4746 c. 154: 20 21 113 N T3 SD: 0.2379 c. M:-0.3769 c. 162: 21 22 119 N T3 SD: 0.1659 c. M: 0.2864 c. 177: 23 24 130 N T3 SD: 0.0770 c. M: 0.1301 c. 192: 25 26 141 N T3 SD: 0.0426 c. M:-0.0737 c. 369: 48 50 271 N T3 SD: 0.0467 c. M: 0.0615 c. 407: 53 55 299 N T3 SD: 0.0350 c. M: 0.0601 c. 561: 73 76 412 N T3 SD: 0.0415 c. M:-0.0598 c. 584: 76 79 429 N T3 SD: 0.0272 c. M: 0.0337 c. 599: 78 81 440 N T3 SD: 0.0106 c. M: 0.0172 c. 791: 103 107 581 N T3 SD: 0.0040 c. M:-0.0051 c. 2181: 284 295 1602 N T3 SD: 0.0032 c. M:-0.0054 c. 2358: 307 319 1732 N T3 SD: 0.0028 c. M: 0.0048 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: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16 x 17:21 SD: 19.2786 cents 17 x 18:23 SD: 20.8886 cents 18:19 x 24 SD: 14.3776 cents 21:22:23:28 SD: 9.9159 cents 22:23:24:29 SD: 9.8731 cents 23:24:25:31 SD: 7.9968 cents 24:25:26:32 SD: 2.8730 cents 51:53:55:68 SD: 0.7670 cents 186:193:201:248 SD: 0.7455 cents 189:196:204:252 SD: 0.6290 cents 213:221:230:284 SD: 0.4146 cents 240:249:259:320 SD: 0.3863 cents 264:274:285:352 SD: 0.1875 cents 315:327:340:420 SD: 0.0404 cents