Scala analysis: 595_T2
Aristoxenian style tetrachord 2.5 + 2.5 + 25, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 41.667 cents 41.666670 2: 83.333 cents 83.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 416.6667 cents 416.6667 1: 41.6667 cents 41.6667 2: 41.6667 cents 41.6667 3: 416.6667 cents 416.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 41.66667 cents 1: 1 416.66667 cents 2: 1 83.33333 cents 2: 2 458.33333 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 41.7 83.3 500.0 41.7 : 41.7 458.3 500.0 83.3 : 416.7 458.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.6667 .. 416.6667 cents 375.00000 cents 41.66667 cents 2: 83.3333 .. 458.3333 cents 375.00000 cents -333.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 41.66666 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 416.66667 cents Average / Smallest step : 4.000001 Largest / Average step : 2.500000 Largest / Smallest step : 10.000002 Median interval of one step : 41.66667 cents, amount: 2 Most common interval of one step : 41.66667 cents, amount: 2 Least squares average step : 122.02381 cents, oct.: 366.07143 cents Scale is not proper Scale has Myhill's property chromas: 375.00000 cents and 333.33333 cents, ratio: 1.125000 generators: 1 of 41.66667 cents and 458.33333 cents ET pair of linear temperament : 22&24 Scale is distributional even Scale is a mode of a 12-tone equal temperament with octave 500.000 cents degrees: 1 2 12 generators: 1 and 11 Number of contiguous 1-step segments: 1 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 2 1 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 41.66666 cents Scale diversity : 0.305007 Lumma stability : 0.166667 Lumma impropriety factor : 0.666667 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 41.66666 cents Most common intervals : 41.66667 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
3: 0 0 3 N M DE S SD: 53.7914 c. M: 83.3333 c. 5: 0 1 4 N G T3 SD: 25.9094 c. M: 41.6667 c. 6: 0 1 5 N G T3 SD: 24.0563 c. M: 41.6667 c. 7: 0 1 6 N G T3 SD: 25.0189 c. M: 41.6667 c. 8: 1 0 7 N G T3 SD: 17.0103 c. M:-20.8333 c. 9: 1 1 7 N M DE S SD: 17.9305 c. M:-27.7778 c. 10: 1 1 8 N M DE S SD: 10.7583 c. M:-16.6667 c. 11: 1 1 9 N M DE S SD: 4.8901 c. M:-7.5758 c. 12: 1 1 10 N M DE S 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 28:29 x 37 SD: 12.9406 cents 29:30 x 39 SD: 10.6817 cents 30:31 x 40 SD: 7.6131 cents 33:34:35:44 SD: 7.0524 cents 35:36:37:47 SD: 5.9963 cents 36:37:38:48 SD: 3.9798 cents 38:39:40:51 SD: 3.7876 cents 39:40:41:52 SD: 1.4547 cents 42:43:44:56 SD: 1.1788 cents 81:83:85:108 SD: 0.6790 cents 122:125:128:163 SD: 0.5502 cents 161:165:169:215 SD: 0.4207 cents 164:168:172:219 SD: 0.3710 cents 203:208:213:271 SD: 0.1659 cents 448:459:470:598 SD: 0.1574 cents