Scala analysis: 632_T39
Aristoxenian style tetrachord 8 + 16 + 6, Savas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 133.333 cents 133.333330 2: 400.000 cents 400.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 100.0000 cents 100.0000 1: 133.3333 cents 133.3333 2: 266.6667 cents 266.6667 3: 100.0000 cents 100.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.00000 cents 1: 1 133.33333 cents 1: 1 266.66667 cents 2: 1 233.33333 cents 2: 1 366.66667 cents 2: 1 400.00000 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 : 133.3 400.0 500.0 133.3: 266.7 366.7 500.0 400.0: 100.0 233.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 266.6667 cents 166.66667 cents 100.00000 cents 2: 233.3333 .. 400.0000 cents 166.66667 cents -33.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 266.66667 cents Average / Smallest step : 1.666667 Largest / Average step : 1.600000 Largest / Smallest step : 2.666667 Median interval of one step : 133.33333 cents, amount: 1 Least squares average step : 173.80952 cents, oct.: 521.42857 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: 4 12 15 Least number of segments generator : 8 of 266.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 11 of 366.667 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Interval vector is [ 0 0 1 1 0 0 1 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33334 cents Scale diversity : 1.157801 Lumma stability : 0.400000 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: 1 1 1 SP B ME I SD: 43.0331 c. M: 66.6667 c. 4: 1 2 1 P M ME I SD: 15.2145 c. M: 25.0000 c. 9: 2 5 2 N M DE I SD: 14.3444 c. M: 22.2222 c. 10: 3 5 2 P T3 SD: 9.6225 c. M:-16.6667 c. 11: 3 6 2 N T3 SD: 5.5326 c. M:-9.0909 c. 15: 4 8 3 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: 13.6863 cents 5 x 6:7 S SD: 59.0014 cents 6 x x 8 S SD: 1.9550 cents 7:8:9 x S SD: 51.9704 cents 8:9:10:11 H SD: 29.4428 cents 9:10:11:12 H SD: 23.9853 cents 10:11 x 13 SD: 27.8362 cents 11:12:14:15 S SD: 14.7998 cents 12:13:15:16 SD: 4.9282 cents 27:29:34:36 SD: 3.2866 cents 39:42:49:52 SD: 2.4155 cents 50:54:63:67 SD: 2.2271 cents 62:67:78:83 SD: 1.9007 cents 77:83:97:103 SD: 1.6732 cents 89:96:112:119 SD: 1.4039 cents 111:120:140:148 SD: 1.0481 cents 123:133:155:164 SD: 0.9360 cents 138:149:174:184 SD: 0.8051 cents 150:162:189:200 SD: 0.6534 cents 161:174:203:215 SD: 0.6181 cents 173:187:218:231 SD: 0.5044 cents 188:203:237:251 SD: 0.3773 cents 200:216:252:267 SD: 0.0844 cents