Scala analysis: 604_T11
Aristoxenian style tetrachord 4 + 4 + 22, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666670 2: 133.333 cents 133.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 366.6667 cents 366.6667 1: 66.6667 cents 66.6667 2: 66.6667 cents 66.6667 3: 366.6667 cents 366.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 66.66667 cents 1: 1 366.66667 cents 2: 1 133.33333 cents 2: 2 433.33333 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 : 66.7 133.3 500.0 66.7 : 66.7 433.3 500.0 133.3: 366.7 433.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 366.6667 cents 300.00000 cents 66.66667 cents 2: 133.3333 .. 433.3333 cents 300.00000 cents -233.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66.66666 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 366.66667 cents Average / Smallest step : 2.500000 Largest / Average step : 2.200000 Largest / Smallest step : 5.500001 Median interval of one step : 66.66667 cents, amount: 2 Most common interval of one step : 66.66667 cents, amount: 2 Least squares average step : 130.95238 cents, oct.: 392.85714 cents Scale is not proper Scale has Myhill's property chromas: 300.00000 cents and 233.33333 cents, ratio: 1.285714 generators: 1 of 66.66667 cents and 433.33333 cents ET pair of linear temperament : 30&19999994 Scale is distributional even Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 2 4 15 generators: 2 and 13 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 0 2 0 1 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.66666 cents Scale diversity : 0.680284 Lumma stability : 0.266667 Lumma impropriety factor : 0.466667 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 : 66.66666 cents Most common intervals : 66.66667 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 1 2 N G T3 SD: 43.0332 c. M: 66.6667 c. 4: 0 1 3 N G T3 SD: 38.7896 c. M: 66.6667 c. 5: 1 0 4 N G T3 SD: 27.2165 c. M:-33.3333 c. 6: 1 1 4 N M DE S SD: 21.5166 c. M:-33.3333 c. 7: 1 1 5 N M DE S SD: 6.1476 c. M:-9.5238 c. 8: 1 1 6 N M DE S SD: 5.3791 c. M: 8.3333 c. 15: 2 2 11 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: 100.0556 cents 6 x 7:8 S SD: 66.7759 cents 7 x 8:9 S SD: 58.7088 cents 8 x 9:11 SD: 43.6308 cents 9 x 10:12 S SD: 24.5547 cents 10 x 11:13 SD: 27.8362 cents 11 x 12:15 S SD: 20.4008 cents 12 x 13:16 SD: 2.7961 cents 13 x 14:17 SD: 17.9634 cents 14 x 15:19 SD: 15.9366 cents 15 x 16:20 S SD: 10.8452 cents 16 x 17:21 SD: 20.3658 cents 17:18 x 23 SD: 19.9141 cents 18:19 x 24 SD: 13.5036 cents 21:22:23:28 SD: 9.3090 cents 23:24:25:31 SD: 7.0834 cents 24:25:26:32 SD: 2.2930 cents 50:52:54:67 SD: 2.2644 cents 51:53:55:68 SD: 1.0878 cents 75:78:81:100 SD: 0.7712 cents 125:130:135:167 SD: 0.6492 cents 176:183:190:235 SD: 0.4299 cents 200:208:216:267 SD: 0.4182 cents 251:261:271:335 SD: 0.3886 cents 361:375:390:482 SD: 0.3367 cents 385:400:416:514 SD: 0.3118 cents 412:428:445:550 SD: 0.2414 cents 436:453:471:582 SD: 0.1886 cents 487:506:526:650 SD: 0.1489 cents 511:531:552:682 SD: 0.1443 cents 588:611:635:785 SD: 0.1344 cents