Scala analysis: 622_T29
Aristoxenian style tetrachord 4 + 8 + 18, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666670 2: 200.000 cents 200.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 300.0000 cents 300.0000 1: 66.6667 cents 66.6667 2: 133.3333 cents 133.3333 3: 300.0000 cents 300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.66667 cents 1: 1 133.33333 cents 1: 1 300.00000 cents 2: 1 200.00000 cents 2: 1 366.66667 cents 2: 1 433.33333 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 : 66.7 200.0 500.0 66.7 : 133.3 433.3 500.0 200.0: 300.0 366.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 300.0000 cents 233.33333 cents 66.66667 cents 2: 200.0000 .. 433.3333 cents 233.33333 cents -100.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66.66667 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 300.00000 cents Average / Smallest step : 2.500000 Largest / Average step : 1.800000 Largest / Smallest step : 4.500000 Median interval of one step : 133.33333 cents, amount: 1 Least squares average step : 140.47619 cents, oct.: 421.42857 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: 2 6 15 Least number of segments generator : 8 of 266.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 13 of 433.333 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 : SML Interval vector is [ 0 1 0 1 0 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.66667 cents Scale diversity : 1.005325 Lumma stability : 0.266667 Lumma impropriety factor : 0.200000 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 : 66.66666 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% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 43.0332 c. M: 66.6667 c. 5: 1 1 3 N M DE S SD: 19.2450 c. M:-33.3333 c. 7: 1 2 4 N T3 SD: 8.6940 c. M:-14.2857 c. 8: 1 2 5 N T3 SD: 7.6073 c. M: 12.5000 c. 13: 2 3 8 N T3 SD: 7.4019 c. M:-10.2564 c. 15: 2 4 9 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 x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 71.0302 cents 6 x 7:8 S SD: 33.4497 cents 7 x 8:9 S SD: 36.0066 cents 8 x 9:11 SD: 25.7333 cents 9 x 10:12 S SD: 8.8523 cents 10 x 11:13 SD: 28.8143 cents 11 x 12:15 S SD: 30.8304 cents 12 x 13:16 SD: 30.7292 cents 13:14:15:17 SD: 28.5639 cents 14:15:16:19 SD: 22.5588 cents 15:16:17:20 SD: 16.0315 cents 17:18:19:23 SD: 13.5059 cents 18:19:20:24 S SD: 10.7446 cents 22:23:25:29 SD: 10.7115 cents 23:24:26:31 SD: 7.3051 cents 24:25:27:32 SD: 1.9764 cents 74:77:83:99 SD: 1.5390 cents 75:78:84:100 SD: 1.4831 cents 98:102:110:131 SD: 1.1902 cents 99:103:111:132 SD: 1.1143 cents 123:128:138:164 SD: 1.0438 cents 131:136:147:175 SD: 0.7724 cents 155:161:174:207 SD: 0.4176 cents 179:186:201:239 SD: 0.2876 cents 254:264:285:339 SD: 0.2373 cents 278:289:312:371 SD: 0.2321 cents 409:425:459:546 SD: 0.1442 cents 433:450:486:578 SD: 0.0341 cents