Scala analysis: 596_T3
Aristoxenian style tetrachord 2 + 3 + 25, 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: 83.333 cents 83.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 416.6667 cents 416.6667 1: 33.3333 cents 33.3333 2: 50.0000 cents 50.0000 3: 416.6667 cents 416.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 50.00000 cents 1: 1 416.66667 cents 2: 1 83.33333 cents 2: 1 450.00000 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 83.3 500.0 33.3 : 50.0 466.7 500.0 83.3 : 416.7 450.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 416.6667 cents 383.33334 cents 33.33333 cents 2: 83.3333 .. 466.6667 cents 383.33334 cents -333.33334 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 : 416.66667 cents Average / Smallest step : 5.000001 Largest / Average step : 2.500000 Largest / Smallest step : 12.500001 Median interval of one step : 50.00000 cents, amount: 1 Least squares average step : 121.42857 cents, oct.: 364.28571 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 5 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 29 of 483.333 cents and inv. generated superset size: 6 = 3 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 1 1 0 1 0 0 0 0 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 : 0.290280 Lumma stability : 0.133333 Lumma impropriety factor : 0.666667 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 : 16.66667 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% Limited inverse transpositions with margin 366.6667 cents: 2 -- Rational properties --
FIT/MODE
3: 0 0 3 N M DE S SD: 51.8188 c. M: 83.3333 c. 4: 0 1 3 N G T3 SD: 30.8070 c. M:-41.6667 c. 5: 0 1 4 N G T3 SD: 21.5166 c. M: 33.3333 c. 6: 0 1 5 N G T3 SD: 19.2450 c. M: 33.3333 c. 7: 0 1 6 N G T3 SD: 20.4355 c. M: 33.3333 c. 8: 0 1 7 N G T3 SD: 22.6946 c. M: 33.3333 c. 10: 1 1 8 N M DE S SD: 13.6083 c. M:-16.6667 c. 11: 1 1 9 N M DE S SD: 8.2526 c. M:-12.1212 c. 12: 1 1 10 N M DE S SD: 4.8113 c. M:-8.3333 c. 13: 1 1 11 N M DE S SD: 4.7395 c. M: 6.4103 c. 17: 1 2 14 N T3 SD: 3.6244 c. M:-4.9020 c. 18: 1 2 15 N T3 SD: 3.2075 c. M: 5.5556 c. 28: 2 3 23 N T3 SD: 3.7013 c. M:-5.9524 c. 29: 2 3 24 N T3 SD: 1.7869 c. M:-2.8736 c. 30: 2 3 25 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 x 7 SD: 82.5122 cents 6 x 7:8 S SD: 91.7740 cents 7 x 8:9 S SD: 80.7325 cents 8 x 9:11 SD: 65.5215 cents 9 x 10:12 S SD: 49.5448 cents 10 x 11:13 SD: 46.8148 cents 11 x 12:15 S SD: 38.3899 cents 12 x 13:16 SD: 27.6370 cents 13 x 14:17 SD: 28.6672 cents 14 x 15:19 SD: 23.0589 cents 15 x 16:20 S SD: 14.2326 cents 16 x 17:21 SD: 18.1746 cents 17 x 18:23 SD: 14.0339 cents 18 x 19:24 SD: 5.2271 cents 19 x 20:25 S SD: 12.7396 cents 20 x 21:27 SD: 9.7921 cents 21 x 22:28 SD: 1.7060 cents 22 x 23:29 SD: 11.3283 cents 23 x 24:31 SD: 9.6710 cents 24 x 25:32 SD: 6.4055 cents 25 x 26:33 SD: 12.3772 cents 26 x 27:35 SD: 11.5906 cents 27 x 28:36 SD: 10.2330 cents 28 x 29:37 SD: 14.2790 cents 29 x 30:39 SD: 13.9084 cents 30:31 x 40 SD: 11.7575 cents 32:33:34:43 SD: 10.5291 cents 33:34:35:44 SD: 8.7178 cents 35:36:37:47 SD: 7.5384 cents 36:37:38:48 SD: 5.8511 cents 38:39:40:51 SD: 5.3083 cents 39:40:41:52 SD: 3.7203 cents 42:43:44:56 SD: 2.7173 cents 57:58:60:76 SD: 2.2138 cents 60:61:63:80 SD: 1.7436 cents 98:100:103:131 SD: 1.3604 cents 99:101:104:132 SD: 1.0198 cents 101:103:106:135 SD: 0.8085 cents 102:104:107:136 SD: 0.6779 cents 161:164:169:215 SD: 0.5579 cents 200:204:210:267 SD: 0.4978 cents 203:207:213:271 SD: 0.1629 cents 466:475:489:622 SD: 0.0828 cents