Scala analysis: 635_T42
Aristoxenian style tetrachord 3 + 12 + 15, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.000 cents 50.000000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 50.0000 cents 50.0000 2: 200.0000 cents 200.0000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50.00000 cents 1: 1 200.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 300.00000 cents 2: 1 450.00000 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 : 50.0 250.0 500.0 50.0 : 200.0 450.0 500.0 250.0: 250.0 300.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 250.0000 cents 200.00000 cents 50.00000 cents 2: 250.0000 .. 450.0000 cents 200.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 3.333333 Largest / Average step : 1.500000 Largest / Smallest step : 5.000000 Median interval of one step : 200.00000 cents, amount: 1 Least squares average step : 146.42857 cents, oct.: 439.28571 cents Scale is proper Scale has trivalence property Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 1 5 10 Least number of segments generator : 7 of 350.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 7 of 350.000 cents and inv. generated superset size: 6 = 3 more = 200.000% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 1 0 0 1 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.739849 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.200000 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 : 50.00000 cents Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 56.1084 c. M: 83.3333 c. 4: 0 2 2 P M DE S SD: 28.8675 c. M: 50.0000 c. 6: 1 2 3 P T3 SD: 19.2450 c. M:-33.3333 c. 8: 1 3 4 P T3 SD: 7.2169 c. M:-12.5000 c. 10: 1 4 5 P T3 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: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7 x 8:9 S SD: 33.7953 cents 8 x 9:11 SD: 34.4885 cents 9 x 10:12 S SD: 33.8123 cents 10 x 12:13 S SD: 40.0161 cents 11 x 13:15 SD: 26.9386 cents 14:15:16:19 SD: 25.8192 cents 15:16:17:20 SD: 23.3912 cents 17:18:20:23 SD: 20.8797 cents 18:19:21:24 SD: 15.5980 cents 19:20:22:25 SD: 15.4174 cents 20:21:23:27 SD: 13.4778 cents 21:22:24:28 S SD: 11.9757 cents 24:25:28:32 SD: 8.9181 cents 26:27:30:35 S SD: 7.1012 cents 27:28:31:36 SD: 5.6675 cents 32:33:37:43 SD: 4.0163 cents 33:34:38:44 SD: 2.1037 cents 65:67:75:87 SD: 1.9202 cents 71:73:82:95 SD: 1.5311 cents 96:99:111:128 SD: 1.3475 cents 102:105:118:136 SD: 0.9983 cents 134:138:155:179 SD: 0.8589 cents 135:139:156:180 SD: 0.6846 cents 167:172:193:223 SD: 0.4480 cents 200:206:231:267 SD: 0.4345 cents 206:212:238:275 SD: 0.1100 cents 579:596:669:773 SD: 0.1100 cents