Scala analysis: 637_T44
Aristoxenian style tetrachord 5 + 10 + 15, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.333 cents 83.333330 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 83.3333 cents 83.3333 2: 166.6667 cents 166.6667 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.33333 cents 1: 1 166.66667 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 333.33333 cents 2: 1 416.66667 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 : 83.3 250.0 500.0 83.3 : 166.7 416.7 500.0 250.0: 250.0 333.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 250.0000 cents 166.66667 cents 83.33333 cents 2: 250.0000 .. 416.6667 cents 166.66667 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 83.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 2.000000 Largest / Average step : 1.500000 Largest / Smallest step : 3.000000 Median interval of one step : 166.66667 cents, amount: 1 Least squares average step : 148.80952 cents, oct.: 446.42857 cents Scale is proper Scale has trivalence property Scale is a mode of a 6-tone equal temperament with octave 500.000 cents degrees: 1 3 6 Least number of segments generator : 5 of 416.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 5 of 416.667 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 1 1 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.058745 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.333333 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 : 83.33333 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% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 68.0414 c. M: 83.3333 c. 4: 1 1 2 P M ME S SD: 24.0563 c. M:-41.6667 c. 6: 1 2 3 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 x 10:12 S SD: 33.8123 cents 11:12:13:15 SD: 28.7374 cents 12:13:14:16 S SD: 19.2638 cents 13:14:15:17 SD: 19.1263 cents 14:15:16:19 SD: 16.6041 cents 15:16:17:20 SD: 14.6061 cents 17:18:20:23 SD: 14.0283 cents 18:19:21:24 SD: 6.6158 cents 21:22:24:28 S SD: 6.3775 cents 37:39:43:49 SD: 6.2530 cents 38:40:44:51 SD: 3.8396 cents 39:41:45:52 SD: 1.4706 cents 83:87:96:111 SD: 1.3996 cents 84:88:97:112 SD: 1.1750 cents 102:107:118:136 SD: 1.0093 cents 122:128:141:163 SD: 0.5682 cents 161:169:186:215 SD: 0.3220 cents 245:257:283:327 SD: 0.2306 cents 367:385:424:490 SD: 0.1995 cents 406:426:469:542 SD: 0.1111 cents