Scala analysis: 633_T40
Aristoxenian style tetrachord 7 + 16 + 7, Xenakis; Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666670 2: 383.333 cents 383.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 266.6667 cents 266.6667 3: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 116.66667 cents 1: 1 266.66666 cents 2: 1 233.33334 cents 2: 2 383.33333 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 : 116.7 383.3 500.0 116.7: 266.7 383.3 500.0 383.3: 116.7 233.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.6667 .. 266.6667 cents 149.99999 cents 116.66667 cents 2: 233.3333 .. 383.3333 cents 149.99999 cents -33.33332 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 116.66667 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 266.66666 cents Average / Smallest step : 1.428571 Largest / Average step : 1.600000 Largest / Smallest step : 2.285714 Median interval of one step : 116.66667 cents, amount: 2 Most common interval of one step : 116.66667 cents, amount: 2 Least squares average step : 170.23809 cents, oct.: 510.71428 cents Scale is not proper Scale has Myhill's property chromas: 149.99999 cents and 33.33332 cents, ratio: 4.500002 generators: 1 of 116.66667 cents and 2 of 383.33333 cents ET pair of linear temperament : 26&34 Scale is distributional even Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 7 23 30 generators: 7 and 23 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Interval vector is [ 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 ] Scale is a Constant Structure, by a margin of 33.33332 cents Scale diversity : 1.125890 Lumma stability : 0.466667 Lumma impropriety factor : 0.066667 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 : 33.33332 cents Most common intervals : 116.66667 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 40.8248 c. M:-50.0000 c. 4: 1 2 1 P M ME I SD: 6.8041 c. M:-8.3333 c. 9: 2 5 2 N M DE I SD: 4.5361 c. M:-5.5556 c. 13: 3 7 3 N M DE I SD: 1.0468 c. M:-1.2821 c. 17: 4 9 4 N M DE I SD: 0.8005 c. M:-0.9804 c. 30: 7 16 7 N M DE I 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 5 x S SD: 2.9804 cents 5 x 6:7 S SD: 53.3631 cents 6 x x 8 S SD: 1.9550 cents 7:8:9 x S SD: 62.8293 cents 8:9:10:11 H SD: 33.7537 cents 9:10:11:12 H SD: 24.9796 cents 11:12:14:15 S SD: 20.2409 cents 12:13:15:16 SD: 7.3980 cents 27:29:34:36 SD: 5.7903 cents 29:31:36:39 SD: 5.2601 cents 40:43:50:53 SD: 5.2265 cents 41:44:51:55 SD: 3.8695 cents 44:47:55:59 SD: 2.9194 cents 45:48:56:60 S SD: 2.3703 cents 56:60:70:75 S SD: 2.3506 cents 57:61:71:76 SD: 1.2483 cents 72:77:90:96 SD: 1.1969 cents 101:108:126:135 SD: 0.8191 cents 129:138:161:172 SD: 0.6597 cents 158:169:197:211 SD: 0.5392 cents 173:185:216:231 SD: 0.4176 cents 230:246:287:307 SD: 0.0836 cents