Scala analysis: 594_T1
Aristoxenian style tetrachord 2 + 2 + 26, 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: 66.667 cents 66.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 433.3333 cents 433.3333 1: 33.3333 cents 33.3333 2: 33.3333 cents 33.3333 3: 433.3333 cents 433.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33.33333 cents 1: 1 433.33333 cents 2: 1 66.66667 cents 2: 2 466.66667 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 : 33.3 66.7 500.0 33.3 : 33.3 466.7 500.0 66.7 : 433.3 466.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 433.3333 cents 400.00000 cents 33.33333 cents 2: 66.6667 .. 466.6667 cents 400.00000 cents -366.66666 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 : 433.33333 cents Average / Smallest step : 5.000001 Largest / Average step : 2.600000 Largest / Smallest step : 13.000001 Median interval of one step : 33.33333 cents, amount: 2 Most common interval of one step : 33.33333 cents, amount: 2 Least squares average step : 119.04762 cents, oct.: 357.14286 cents Scale is not proper Scale has Myhill's property chromas: 400.00000 cents and 366.66667 cents, ratio: 1.090909 generators: 1 of 33.33333 cents and 466.66667 cents ET pair of linear temperament : 30&19999982 Scale is distributional even Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 1 2 15 generators: 1 and 14 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 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 0.182799 Lumma stability : 0.133333 Lumma impropriety factor : 0.733333 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 : 33.33334 cents Most common intervals : 33.33333 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: 43.0331 c. M: 66.6667 c. 5: 0 1 4 N G T3 SD: 27.2165 c. M:-33.3333 c. 6: 0 1 5 N G T3 SD: 21.5166 c. M: 33.3333 c. 7: 0 1 6 N G T3 SD: 19.4404 c. M: 33.3333 c. 8: 0 1 7 N G T3 SD: 19.3948 c. M: 33.3333 c. 9: 0 1 8 N G T3 SD: 20.2860 c. M: 33.3333 c. 10: 0 1 9 N G T3 SD: 21.5166 c. M: 33.3333 c. 11: 1 1 9 N M DE S SD: 15.6484 c. M:-24.2424 c. 12: 1 1 10 N M DE S SD: 10.7583 c. M:-16.6667 c. 13: 1 1 11 N M DE S SD: 6.6205 c. M:-10.2564 c. 14: 1 1 12 N M DE S SD: 3.0738 c. M:-4.7619 c. 15: 1 1 13 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: 100.1069 cents 7 x 8:9 S SD: 88.4262 cents 8 x 9:11 SD: 73.2620 cents 9 x 10:12 S SD: 57.8768 cents 10 x 11:13 SD: 54.2371 cents 11 x 12:15 S SD: 45.8704 cents 12 x 13:16 SD: 35.9663 cents 13 x 14:17 SD: 35.5803 cents 14 x 15:19 SD: 30.0344 cents 15 x 16:20 S SD: 22.5535 cents 16 x 17:21 SD: 24.0821 cents 17 x 18:23 SD: 19.9141 cents 18 x 19:24 SD: 13.5036 cents 19 x 20:25 S SD: 16.6524 cents 20 x 21:27 SD: 13.2204 cents 21 x 22:28 SD: 7.0037 cents 22 x 23:29 SD: 12.0264 cents 23 x 24:31 SD: 9.0848 cents 24 x 25:32 SD: 2.2287 cents 25 x 26:33 SD: 9.6969 cents 26 x 27:35 SD: 7.3362 cents 27 x 28:36 SD: 2.0949 cents 28 x 29:37 SD: 9.2278 cents 29 x 30:39 SD: 7.5854 cents 30 x 31:40 SD: 5.0455 cents 31 x 32:41 SD: 9.9006 cents 32 x 33:43 SD: 8.8325 cents 33 x 34:44 SD: 7.5556 cents 34 x 35:45 SD: 11.0532 cents 35:36 x 47 SD: 9.2975 cents 36:37 x 48 SD: 7.1178 cents 37:38 x 49 SD: 9.3839 cents 38:39 x 51 SD: 7.4786 cents 41:42:43:55 SD: 6.6083 cents 42:43:44:56 SD: 5.2812 cents 44:45:46:59 SD: 4.6977 cents 45:46:47:60 SD: 3.3386 cents 47:48:49:63 SD: 3.1969 cents 48:49:50:64 SD: 1.6817 cents 51:52:53:68 SD: 0.6589 cents 152:155:158:203 SD: 0.3610 cents 203:207:211:271 SD: 0.1806 cents 254:259:264:339 SD: 0.1731 cents 409:417:425:546 SD: 0.1158 cents 460:469:478:614 SD: 0.1034 cents