Scala analysis: 615_T22
Aristoxenian style tetrachord 5 + 5 + 20, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.333 cents 83.333330 2: 166.667 cents 166.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 333.3333 cents 333.3333 1: 83.3333 cents 83.3333 2: 83.3333 cents 83.3333 3: 333.3333 cents 333.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 83.33333 cents 1: 1 333.33333 cents 2: 1 166.66667 cents 2: 2 416.66667 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 : 83.3 166.7 500.0 83.3 : 83.3 416.7 500.0 166.7: 333.3 416.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 333.3333 cents 250.00000 cents 83.33333 cents 2: 166.6667 .. 416.6667 cents 250.00000 cents -166.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 83.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 333.33333 cents Average / Smallest step : 2.000000 Largest / Average step : 2.000000 Largest / Smallest step : 4.000000 Median interval of one step : 83.33333 cents, amount: 2 Most common interval of one step : 83.33333 cents, amount: 2 Least squares average step : 136.90476 cents, oct.: 410.71429 cents Scale is not proper Scale has Myhill's property chromas: 250.00000 cents and 166.66667 cents, ratio: 1.500000 generators: 1 of 83.33333 cents and 416.66667 cents ET pair of linear temperament : 49999994&149999994 Scale is distributional even Scale is a mode of a 6-tone equal temperament with octave 500.000 cents degrees: 1 2 6 generators: 1 and 5 Number of contiguous 1-step segments: 1 Scale is a Winograd/Gamer deep scale Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 2 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 83.33333 cents Scale diversity : 0.909804 Lumma stability : 0.333333 Lumma impropriety factor : 0.333333 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 : 83.33334 cents Most common intervals : 83.33333 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 1 2 N G T3 SD: 48.1125 c. M: 83.3333 c. 4: 0 1 3 N G T3 SD: 53.7914 c. M: 83.3333 c. 5: 1 1 3 N M DE S SD: 21.5166 c. M:-33.3333 c. 6: 1 1 4 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: 85.1494 cents 6 x 7:8 S SD: 50.1117 cents 7 x 8:9 S SD: 45.7583 cents 8 x 9:11 SD: 31.7041 cents 9 x 10:12 S SD: 7.9290 cents 10 x 11:13 SD: 22.9081 cents 11 x 12:15 S SD: 20.1389 cents 12 x 13:16 SD: 14.0810 cents 13 x 14:17 SD: 26.1607 cents 14:15 x 19 SD: 23.0589 cents 15:16:17:20 SD: 19.1841 cents 16:17:18:21 S SD: 17.3472 cents 17:18:19:23 SD: 12.7285 cents 18:19:20:24 S SD: 6.2976 cents 21:22:23:28 SD: 3.2624 cents 39:41:43:52 SD: 1.4896 cents 60:63:66:80 SD: 0.9352 cents 99:104:109:132 SD: 0.9246 cents 119:125:131:159 SD: 0.8346 cents 140:147:154:187 SD: 0.7699 cents 179:188:197:239 SD: 0.6118 cents 227:238:250:303 SD: 0.4904 cents 266:279:293:355 SD: 0.3543 cents 287:301:316:383 SD: 0.3286 cents 326:342:359:435 SD: 0.2611 cents 346:363:381:462 SD: 0.2132 cents 385:404:424:514 SD: 0.1612 cents 406:426:447:542 SD: 0.0751 cents