Scala analysis: 602_T9
Aristoxenian style tetrachord 3.5 + 3.5 + 23, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.333 cents 58.333330 2: 116.667 cents 116.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 383.3333 cents 383.3333 1: 58.3333 cents 58.3333 2: 58.3333 cents 58.3333 3: 383.3333 cents 383.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 58.33333 cents 1: 1 383.33333 cents 2: 1 116.66667 cents 2: 2 441.66667 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 : 58.3 116.7 500.0 58.3 : 58.3 441.7 500.0 116.7: 383.3 441.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.3333 .. 383.3333 cents 325.00000 cents 58.33333 cents 2: 116.6667 .. 441.6667 cents 325.00000 cents -266.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 58.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 383.33333 cents Average / Smallest step : 2.857143 Largest / Average step : 2.300000 Largest / Smallest step : 6.571429 Median interval of one step : 58.33333 cents, amount: 2 Most common interval of one step : 58.33333 cents, amount: 2 Least squares average step : 127.97619 cents, oct.: 383.92857 cents Scale is not proper Scale has Myhill's property chromas: 325.00000 cents and 266.66667 cents, ratio: 1.218750 generators: 1 of 58.33333 cents and 441.66667 cents ET pair of linear temperament : 34&86 Scale is distributional even Scale is a mode of a 60-tone equal temperament with octave 500.000 cents degrees: 7 14 60 generators: 7 and 53 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 58.33333 cents Scale diversity : 0.555741 Lumma stability : 0.233333 Lumma impropriety factor : 0.533333 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 : 58.33334 cents Most common intervals : 58.33333 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: 44.3576 c. M: 58.3333 c. 4: 0 1 3 N G T3 SD: 34.0207 c. M: 58.3333 c. 5: 0 1 4 N G T3 SD: 35.0264 c. M: 58.3333 c. 6: 1 0 5 N G T3 SD: 24.0563 c. M: 33.3333 c. 7: 1 1 5 N M DE S SD: 16.9059 c. M:-26.1905 c. 8: 1 1 6 N M DE S SD: 5.3791 c. M:-8.3333 c. 9: 1 1 7 N M DE S SD: 3.5861 c. M: 5.5556 c. 17: 2 2 13 N M DE S SD: 0.6328 c. M:-0.9804 c. 43: 5 5 33 N M DE S SD: 0.2502 c. M: 0.3876 c. 60: 7 7 46 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: 75.1085 cents 7 x 8:9 S SD: 65.8142 cents 8 x 9:11 SD: 50.6086 cents 9 x 10:12 S SD: 32.8831 cents 10 x 11:13 SD: 33.2899 cents 11 x 12:15 S SD: 25.0965 cents 12 x 13:16 SD: 10.9965 cents 13 x 14:17 SD: 18.7128 cents 14 x 15:19 SD: 14.4106 cents 15 x 16:20 S SD: 2.6542 cents 16 x 17:21 SD: 15.7394 cents 17 x 18:23 SD: 14.6415 cents 18 x 19:24 SD: 11.5732 cents 19 x 20:25 S SD: 18.6802 cents 20:21 x 27 SD: 16.3189 cents 21:22 x 28 SD: 11.1448 cents 24:25:26:32 SD: 8.4060 cents 26:27:28:35 S SD: 6.6488 cents 27:28:29:36 SD: 2.8844 cents 30:31:32:40 S SD: 1.8449 cents 57:59:61:76 SD: 0.8342 cents 87:90:93:116 SD: 0.7753 cents 116:120:124:155 S SD: 0.7248 cents 143:148:153:191 SD: 0.5401 cents 173:179:185:231 SD: 0.3484 cents 230:238:246:307 SD: 0.2984 cents 403:417:431:538 SD: 0.2980 cents 442:457:473:590 SD: 0.2943 cents 472:488:505:630 SD: 0.2376 cents 529:547:566:706 SD: 0.2126 cents 558:577:597:745 SD: 0.1990 cents 588:608:629:785 SD: 0.1655 cents