Scala analysis: 643_T50
Aristoxenian style tetrachord 4 + 14 + 12, Aristoxenos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666670 2: 300.000 cents 300.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 200.0000 cents 200.0000 1: 66.6667 cents 66.6667 2: 233.3333 cents 233.3333 3: 200.0000 cents 200.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.66667 cents 1: 1 200.00000 cents 1: 1 233.33333 cents 2: 1 266.66667 cents 2: 1 300.00000 cents 2: 1 433.33333 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 : 66.7 300.0 500.0 66.7 : 233.3 433.3 500.0 300.0: 200.0 266.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 233.3333 cents 166.66666 cents 66.66667 cents 2: 266.6667 .. 433.3333 cents 166.66666 cents 33.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66.66667 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 233.33333 cents Average / Smallest step : 2.500000 Largest / Average step : 1.400000 Largest / Smallest step : 3.500000 Median interval of one step : 200.00000 cents, amount: 1 Least squares average step : 154.76190 cents, oct.: 464.28571 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 2 9 15 Least number of segments generator : 8 of 266.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 8 of 266.667 cents and inv. generated superset size: 5 = 2 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Interval vector is [ 0 1 0 0 0 1 1 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33334 cents Scale diversity : 0.890769 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.333333 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 : 33.33333 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% -- Rational properties --
FIT/MODE
3: 0 2 1 N G T3 SD: 43.0332 c. M: 66.6667 c. 4: 0 2 2 P M DE S SD: 48.1125 c. M: 66.6667 c. 5: 1 2 2 SP M ME S SD: 19.2450 c. M:-33.3333 c. 6: 1 3 2 P T3 SD: 21.5166 c. M:-33.3333 c. 7: 1 3 3 SP M DE S SD: 8.6940 c. M: 14.2857 c. 8: 1 4 3 P T3 SD: 7.6073 c. M:-12.5000 c. 13: 2 6 5 SP T3 SD: 7.4019 c. M:-10.2564 c. 15: 2 7 6 SP 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 5 x S SD: 86.3137 cents 5 x 6:7 S SD: 41.9908 cents 6 x 7:8 S SD: 16.5934 cents 7 x 8:9 S SD: 47.3051 cents 8 x 10:11 S SD: 50.2085 cents 9:10:11:12 H SD: 41.6952 cents 10:11:12:13 H SD: 36.5320 cents 11:12:13:15 SD: 30.7911 cents 12:13:14:16 S SD: 26.3983 cents 14:15:17:19 SD: 23.3657 cents 15:16:18:20 S SD: 15.9140 cents 17:18:20:23 SD: 14.6583 cents 18:19:21:24 SD: 14.2475 cents 20:21:24:27 S SD: 10.2402 cents 21:22:25:28 SD: 4.7095 cents 27:28:32:36 S SD: 2.4026 cents 48:50:57:64 SD: 1.7014 cents 74:77:88:99 SD: 1.4771 cents 75:78:89:100 SD: 1.4549 cents 101:105:120:135 SD: 0.9573 cents 126:131:150:168 SD: 0.9267 cents 149:155:177:199 SD: 0.8968 cents 152:158:181:203 SD: 0.8313 cents 153:159:182:204 SD: 0.6721 cents 179:186:213:239 SD: 0.3984 cents 206:214:245:275 SD: 0.2467 cents 227:236:270:303 SD: 0.2412 cents 254:264:302:339 SD: 0.1529 cents 433:450:515:578 SD: 0.0834 cents