Scala analysis: 608_T15
Aristoxenian style tetrachord 2 + 7 + 21, 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: 150.000 cents 150.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 350.0000 cents 350.0000 1: 33.3333 cents 33.3333 2: 116.6667 cents 116.6667 3: 350.0000 cents 350.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 116.66667 cents 1: 1 350.00000 cents 2: 1 150.00000 cents 2: 1 383.33333 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 : 33.3 150.0 500.0 33.3 : 116.7 466.7 500.0 150.0: 350.0 383.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 350.0000 cents 316.66667 cents 33.33333 cents 2: 150.0000 .. 466.6667 cents 316.66667 cents -200.00000 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 : 350.00000 cents Average / Smallest step : 5.000001 Largest / Average step : 2.100000 Largest / Smallest step : 10.500001 Median interval of one step : 116.66667 cents, amount: 1 Least squares average step : 130.95238 cents, oct.: 392.85714 cents Scale is not proper Scale has trivalence property Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 2 9 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 23 of 383.333 cents and inv. generated superset size: 5 = 2 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 0.638547 Lumma stability : 0.133333 Lumma impropriety factor : 0.400000 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 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: 21.5166 c. M: 33.3333 c. 4: 0 1 3 N G T3 SD: 24.0563 c. M: 33.3333 c. 6: 0 2 4 N G T3 SD: 21.5166 c. M: 33.3333 c. 7: 0 2 5 N G T3 SD: 19.6819 c. M: 33.3333 c. 9: 1 2 6 N T3 SD: 16.0375 c. M:-22.2222 c. 10: 1 2 7 N T3 SD: 9.6225 c. M:-16.6667 c. 11: 1 2 8 N T3 SD: 10.5337 c. M: 13.6364 c. 12: 1 3 8 N T3 SD: 10.7583 c. M:-16.6667 c. 13: 1 3 9 N T3 SD: 3.7010 c. M:-5.1282 c. 17: 1 4 12 N T3 SD: 2.8301 c. M: 3.9216 c. 27: 2 6 19 N T3 SD: 2.3907 c. M:-3.7037 c. 30: 2 7 21 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: 92.5274 cents 6 x 7:8 S SD: 58.4436 cents 7 x 8:9 S SD: 51.9695 cents 8 x 9:11 SD: 37.2150 cents 9 x 10:12 S SD: 16.2313 cents 10 x 11:13 SD: 24.0909 cents 11 x 12:15 S SD: 18.4781 cents 12 x 13:16 SD: 5.7967 cents 13 x 14:17 SD: 20.8348 cents 14 x 15:19 SD: 20.9565 cents 15 x 16:20 S SD: 19.1593 cents 16 x 17:21 SD: 26.8457 cents 17 x 19:23 SD: 24.2638 cents 18 x 20:24 S SD: 16.2313 cents 21:22:23:28 SD: 15.9449 cents 23:24:25:31 SD: 14.6846 cents 24:25:26:32 SD: 13.0325 cents 29:30:32:39 SD: 11.6747 cents 30:31:33:40 SD: 9.2980 cents 32:33:35:43 SD: 7.8646 cents 33:34:36:44 SD: 6.1547 cents 36:37:39:48 SD: 6.0849 cents 41:42:45:55 SD: 5.4601 cents 42:43:46:56 SD: 3.5713 cents 44:45:48:59 SD: 3.2169 cents 45:46:49:60 SD: 1.9058 cents 54:55:59:72 SD: 1.3829 cents 98:100:107:131 SD: 1.2099 cents 99:101:108:132 SD: 0.8096 cents 155:158:169:207 SD: 0.2991 cents 209:213:228:279 SD: 0.2753 cents 254:259:277:339 SD: 0.1634 cents 409:417:446:546 SD: 0.0890 cents