Scala analysis: 610_T17
Aristoxenian style tetrachord 4.5 + 4.5 + 21, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 150.000 cents 150.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 350.0000 cents 350.0000 1: 75.0000 cents 75.0000 2: 75.0000 cents 75.0000 3: 350.0000 cents 350.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 75.00000 cents 1: 1 350.00000 cents 2: 1 150.00000 cents 2: 2 425.00000 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 : 75.0 150.0 500.0 75.0 : 75.0 425.0 500.0 150.0: 350.0 425.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 350.0000 cents 275.00000 cents 75.00000 cents 2: 150.0000 .. 425.0000 cents 275.00000 cents -200.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 350.00000 cents Average / Smallest step : 2.222222 Largest / Average step : 2.100000 Largest / Smallest step : 4.666667 Median interval of one step : 75.00000 cents, amount: 2 Most common interval of one step : 75.00000 cents, amount: 2 Least squares average step : 133.92857 cents, oct.: 401.78571 cents Scale is not proper Scale has Myhill's property chromas: 275.00000 cents and 200.00000 cents, ratio: 1.375000 generators: 1 of 75.00000 cents and 425.00000 cents ET pair of linear temperament : 40&40 Scale is distributional even Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 3 6 20 generators: 3 and 17 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 0 0 2 0 0 1 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 75.00000 cents Scale diversity : 0.799925 Lumma stability : 0.300000 Lumma impropriety factor : 0.400000 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 : 75.00000 cents Most common intervals : 75.00000 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 1 2 N G T3 SD: 44.3576 c. M: 75.0000 c. 4: 0 1 3 N G T3 SD: 45.6435 c. M: 75.0000 c. 6: 1 1 4 N M DE S SD: 10.7583 c. M:-16.6667 c. 7: 1 1 5 N M DE S SD: 4.6107 c. M: 7.1429 c. 13: 2 2 9 N M DE S SD: 2.4827 c. M:-3.8462 c. 20: 3 3 14 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 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 15:16 x 20 S SD: 18.3916 cents 16:17 x 21 SD: 20.9230 cents 17:18:19:23 SD: 18.0393 cents 18:19:20:24 S SD: 12.4717 cents 19:20:21:25 SD: 12.2526 cents 20:21:22:27 SD: 8.8003 cents 21:22:23:28 SD: 3.1734 cents 44:46:48:59 SD: 2.7063 cents 45:47:49:60 SD: 1.0810 cents 66:69:72:88 SD: 0.9461 cents 111:116:121:148 SD: 0.8094 cents 134:140:146:179 SD: 0.7160 cents 155:162:169:207 SD: 0.5722 cents 200:209:218:267 SD: 0.4878 cents 275:287:300:367 SD: 0.4306 cents 319:333:348:426 SD: 0.3929 cents 320:334:349:427 SD: 0.3579 cents 341:356:372:455 SD: 0.3497 cents 364:380:397:486 SD: 0.2388 cents 409:427:446:546 SD: 0.1570 cents 430:449:469:574 SD: 0.1132 cents 475:496:518:634 SD: 0.0575 cents