Scala analysis: 639_T46
Aristoxenian style tetrachord 7 + 8 + 15, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666670 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 116.6667 cents 116.6667 2: 133.3333 cents 133.3333 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 116.66667 cents 1: 1 133.33333 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 366.66667 cents 2: 1 383.33333 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 : 116.7 250.0 500.0 116.7: 133.3 383.3 500.0 250.0: 250.0 366.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.6667 .. 250.0000 cents 133.33333 cents 116.66667 cents 2: 250.0000 .. 383.3333 cents 133.33333 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 116.66667 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.428571 Largest / Average step : 1.500000 Largest / Smallest step : 2.142857 Median interval of one step : 133.33333 cents, amount: 1 Least squares average step : 151.19048 cents, oct.: 453.57143 cents Scale is proper Scale has trivalence property Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 7 15 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 283.333 cents and inv. generated superset size: 16 = 13 more = 533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.132885 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.466667 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 : 16.66666 cents Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 116.6667 cents: 2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 56.1084 c. M:-83.3333 c. 4: 1 1 2 P M ME S SD: 4.8113 c. M:-8.3333 c. 18: 4 5 9 P T3 SD: 3.2075 c. M: 5.5556 c. 22: 5 6 11 P T3 SD: 1.7495 c. M: 3.0303 c. 26: 6 7 13 P T3 SD: 0.7402 c. M: 1.2821 c. 30: 7 8 15 P T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7 x 8:9 S SD: 33.7953 cents 8 x 9:11 SD: 34.4885 cents 9:10 x 12 S SD: 32.8831 cents 10:11:12:13 H SD: 31.1656 cents 11:12:13:15 SD: 21.2309 cents 12:13:14:16 S SD: 9.2395 cents 25:27:29:33 SD: 8.8033 cents 26:28:30:35 S SD: 6.2708 cents 27:29:31:36 SD: 4.3556 cents 39:42:45:52 SD: 4.0030 cents 44:47:51:59 SD: 3.3182 cents 45:48:52:60 SD: 1.7724 cents 57:61:66:76 SD: 1.4477 cents 71:76:82:95 SD: 1.4446 cents 84:90:97:112 SD: 1.1697 cents 102:109:118:136 SD: 1.1556 cents 116:124:134:155 SD: 0.7206 cents 129:138:149:172 SD: 0.6709 cents 173:185:200:231 SD: 0.4430 cents 200:214:231:267 SD: 0.2449 cents 245:262:283:327 SD: 0.2241 cents 373:399:431:498 SD: 0.1410 cents 502:537:580:670 SD: 0.0784 cents