Scala analysis: 629_T36
Aristoxenian style tetrachord 2 + 16 + 12, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.333 cents 33.333330 2: 300.000 cents 300.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 200.0000 cents 200.0000 1: 33.3333 cents 33.3333 2: 266.6667 cents 266.6667 3: 200.0000 cents 200.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 200.00000 cents 1: 1 266.66667 cents 2: 1 233.33333 cents 2: 1 300.00000 cents 2: 1 466.66667 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 : 33.3 300.0 500.0 33.3 : 266.7 466.7 500.0 300.0: 200.0 233.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 266.6667 cents 233.33334 cents 33.33333 cents 2: 233.3333 .. 466.6667 cents 233.33334 cents -33.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 266.66667 cents Average / Smallest step : 5.000001 Largest / Average step : 1.600000 Largest / Smallest step : 8.000001 Median interval of one step : 200.00000 cents, amount: 1 Least squares average step : 152.38095 cents, oct.: 457.14286 cents Scale is not proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 1 9 15 Least number of segments generator : 11 of 366.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 8 of 266.667 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 : SLM Interval vector is [ 1 0 0 0 0 1 1 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 0.618375 Lumma stability : 0.133333 Lumma impropriety factor : 0.066667 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 : 33.33333 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 --
FIT/MODE
3: 0 2 1 N G T3 SD: 27.2166 c. M:-33.3333 c. 5: 0 3 2 N G T3 SD: 19.2450 c. M: 33.3333 c. 7: 0 4 3 N G T3 SD: 20.9379 c. M: 33.3333 c. 8: 1 4 3 P T3 SD: 18.3207 c. M:-29.1667 c. 10: 1 5 4 P T3 SD: 9.6225 c. M:-16.6667 c. 12: 1 6 5 P T3 SD: 6.8041 c. M:-8.3333 c. 13: 1 7 5 N T3 SD: 5.3376 c. M:-7.6923 c. 15: 1 8 6 N 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 5 x S SD: 86.3137 cents 5 x 6:7 S SD: 41.9908 cents 6 x 7:8 S SD: 16.5934 cents 7 x 8:9 S SD: 47.3051 cents 8 x 10:11 S SD: 50.2085 cents 9 x 11:12 SD: 23.7241 cents 18:19:21:24 SD: 22.9342 cents 19:20:23:25 SD: 22.7112 cents 20:21:24:27 S SD: 18.9783 cents 21:22:25:28 SD: 15.7601 cents 24:25:29:32 SD: 15.4956 cents 25:26:30:33 SD: 14.1975 cents 26:27:31:35 SD: 11.8232 cents 27:28:32:36 S SD: 10.0886 cents 30:31:36:40 SD: 9.4140 cents 31:32:37:41 SD: 9.2065 cents 32:33:38:43 SD: 7.7203 cents 33:34:39:44 SD: 7.1254 cents 36:37:43:48 SD: 5.3803 cents 41:42:49:55 SD: 4.9162 cents 42:43:50:56 SD: 2.6256 cents 48:49:57:64 SD: 1.3163 cents 95:97:113:127 SD: 1.2634 cents 101:103:120:135 SD: 0.9600 cents 105:107:125:140 SD: 0.9236 cents 149:152:177:199 SD: 0.8029 cents 153:156:182:204 SD: 0.6783 cents 158:161:188:211 SD: 0.4882 cents 206:210:245:275 SD: 0.0743 cents