Scala analysis: 634_T41
Aristoxenian style tetrachord 2 + 13 + 15, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.333 cents 33.333330 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 33.3333 cents 33.3333 2: 216.6667 cents 216.6667 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 216.66667 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 283.33333 cents 2: 1 466.66667 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 : 33.3 250.0 500.0 33.3 : 216.7 466.7 500.0 250.0: 250.0 283.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 250.0000 cents 216.66667 cents 33.33333 cents 2: 250.0000 .. 466.6667 cents 216.66667 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 5.000001 Largest / Average step : 1.500000 Largest / Smallest step : 7.500001 Median interval of one step : 216.66667 cents, amount: 1 Least squares average step : 145.23809 cents, oct.: 435.71428 cents Scale is proper Scale has trivalence property Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 2 15 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 283.333 cents and inv. generated superset size: 16 = 13 more = 533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.545555 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.133333 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 : 33.33333 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: 51.8188 c. M: 83.3333 c. 4: 0 2 2 P M DE S SD: 19.2450 c. M: 33.3333 c. 8: 1 3 4 P T3 SD: 16.8394 c. M:-29.1667 c. 10: 1 4 5 P T3 SD: 9.6225 c. M:-16.6667 c. 12: 1 5 6 P T3 SD: 4.8113 c. M:-8.3333 c. 14: 1 6 7 P T3 SD: 1.3746 c. M:-2.3810 c. 16: 1 7 8 P T3 SD: 1.2028 c. M: 2.0833 c. 30: 2 13 15 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 17:18:20:23 SD: 25.4586 cents 18:19:21:24 SD: 20.8723 cents 19:20:22:25 SD: 20.3043 cents 20:21:23:27 SD: 18.4438 cents 21:22:24:28 S SD: 16.9523 cents 24:25:28:32 SD: 13.6734 cents 25:26:29:33 SD: 13.4072 cents 26:27:30:35 S SD: 11.7514 cents 27:28:31:36 SD: 10.5351 cents 30:31:35:40 SD: 9.6470 cents 31:32:36:41 SD: 9.4387 cents 32:33:37:43 SD: 7.6888 cents 33:34:38:44 SD: 6.4437 cents 38:39:44:51 SD: 5.1445 cents 39:40:45:52 SD: 3.6382 cents 45:46:52:60 SD: 1.7051 cents 51:52:59:68 SD: 1.0009 cents 149:152:172:199 SD: 0.7061 cents 155:158:179:207 SD: 0.3818 cents 200:204:231:267 SD: 0.3688 cents 206:210:238:275 SD: 0.0504 cents