Scala analysis: 659_T66
Aristoxenian style tetrachord 12 + 13 + 3, Tiby
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 211.714 cents 211.714290 2: 441.071 cents 441.071430 3: 494.000 cents 494.000000
SHOW/INTERVAL
0: 52.9286 cents 52.9286 1: 211.7143 cents 211.7143 2: 229.3571 cents 229.3571 3: 52.9286 cents 52.9286
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52.92857 cents 1: 1 211.71429 cents 1: 1 229.35714 cents 2: 1 264.64286 cents 2: 1 282.28571 cents 2: 1 441.07143 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 211.7 441.1 494.0 211.7: 229.4 282.3 494.0 441.1: 52.9 264.6 494.0 494.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.9286 .. 229.3571 cents 176.42857 cents 52.92857 cents 2: 264.6429 .. 441.0714 cents 176.42857 cents 35.28572 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52.92857 cents, class 1 Average step (divided formal octave): 164.6667 cents Largest one step interval : 229.35714 cents Average / Smallest step : 3.111111 Largest / Average step : 1.392857 Largest / Smallest step : 4.333333 Median interval of one step : 211.71429 cents, amount: 1 Least squares average step : 183.98980 cents, oct.: 551.96939 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 28-tone equal temperament with octave 494.000 cents degrees: 12 25 28 Least number of segments generator : 15 of 264.643 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 25 of 441.071 cents and inv. generated superset size: 6 = 3 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Interval vector is [ 0 0 1 0 0 0 0 0 0 0 0 1 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.28572 cents Scale diversity : 0.712166 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.285714 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 17.64285 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 176.4286 cents: 2 -- Rational properties --
FIT/MODE
3: 1 2 0 N G T3 SD: 40.8857 c. M:-52.9286 c. 4: 2 2 0 P M DE S SD: 36.7265 c. M:-52.9286 c. 5: 2 2 1 SP M ME S SD: 27.7092 c. M: 45.8714 c. 7: 3 3 1 SP M DE S SD: 10.1861 c. M: 17.6429 c. 9: 4 4 1 SP M DE S SD: 4.6665 c. M:-7.8413 c. 19: 8 9 2 SP T3 SD: 2.2104 c. M: 3.7143 c. 28: 12 13 3 SP T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 706.0000 cents 2 x x 3 S SD: 207.9550 cents 3 x x 4 S SD: 4.0450 cents 4 x 5 x S SD: 54.7577 cents 5:6 x 7 S SD: 68.2555 cents 6:7 x 8 S SD: 27.6524 cents 7:8:9 x S SD: 10.1800 cents 9:10 x 12 S SD: 14.7942 cents 10:11:13 x SD: 24.2619 cents 13:15:17 x SD: 21.4677 cents 14:16:18:19 S SD: 13.4070 cents 15:17:19:20 SD: 10.8221 cents 16:18 x 21 S SD: 12.2478 cents 17:19:22:23 SD: 11.8067 cents 18:20:23:24 SD: 11.3265 cents 19:21 x 25 SD: 21.4172 cents 20:23:26:27 SD: 13.9062 cents 21:24:27:28 S SD: 6.9193 cents 24:27:31:32 SD: 3.0057 cents 45:51:58:60 SD: 2.2120 cents 55:62:71:73 SD: 1.9530 cents 69:78:89:92 SD: 1.3675 cents 76:86:98:101 SD: 0.9927 cents 100:113:129:133 SD: 0.1293 cents 569:643:734:757 SD: 0.1159 cents