Scala analysis: 613_T20
Aristoxenian style tetrachord 6 + 20 + 4, Savas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100.000 cents 100.000000 2: 433.333 cents 433.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 66.6667 cents 66.6667 1: 100.0000 cents 100.0000 2: 333.3333 cents 333.3333 3: 66.6667 cents 66.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.66667 cents 1: 1 100.00000 cents 1: 1 333.33333 cents 2: 1 166.66667 cents 2: 1 400.00000 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 : 100.0 433.3 500.0 100.0: 333.3 400.0 500.0 433.3: 66.7 166.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 333.3333 cents 266.66666 cents 66.66667 cents 2: 166.6667 .. 433.3333 cents 266.66666 cents -166.66666 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 : 333.33333 cents Average / Smallest step : 2.500000 Largest / Average step : 2.000000 Largest / Smallest step : 5.000000 Median interval of one step : 100.00000 cents, amount: 1 Least squares average step : 176.19048 cents, oct.: 528.57143 cents Scale is not proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 3 13 15 Least number of segments generator : 8 of 266.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 14 of 466.667 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 1 1 0 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.66667 cents Scale diversity : 0.890769 Lumma stability : 0.266667 Lumma impropriety factor : 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: 81.6497 c. M: 100.0000 c. 4: 1 2 1 P M ME I SD: 36.6414 c. M: 58.3333 c. 5: 1 3 1 N M DE I SD: 19.2450 c. M: 33.3333 c. 6: 1 4 1 N M DE I SD: 13.6083 c. M: 16.6667 c. 9: 2 6 1 N T3 SD: 9.0722 c. M:-11.1111 c. 14: 3 9 2 N T3 SD: 4.9563 c. M:-7.1429 c. 15: 3 10 2 N 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: 47.0196 cents 5 x 6:7 S SD: 71.8674 cents 6 x x 8 S SD: 1.9550 cents 7:8:9 x S SD: 65.5929 cents 8:9:10:11 H SD: 41.6889 cents 9:10 x 12 S SD: 41.2134 cents 10:11:13 x SD: 34.1378 cents 11:12:14:15 S SD: 21.5508 cents 12:13:15:16 SD: 20.2828 cents 13:14:17 x SD: 21.0217 cents 14:15:18:19 S SD: 11.5664 cents 15:16:19:20 SD: 8.9550 cents 16:17 x 21 SD: 14.8182 cents 17:18:22:23 SD: 8.9108 cents 18:19:23:24 SD: 3.7296 cents 35:37:45:47 SD: 3.7260 cents 48:51:62:64 SD: 3.7027 cents 50:53:64:67 SD: 2.9985 cents 53:56:68:71 SD: 2.6620 cents 63:67:81:84 SD: 2.3586 cents 66:70:85:88 SD: 1.7966 cents 81:86:104:108 SD: 1.4097 cents 84:89:108:112 SD: 0.8754 cents 102:108:131:136 SD: 0.7404 cents 134:142:172:179 SD: 0.5802 cents 200:212:257:267 SD: 0.3992 cents 218:231:280:291 SD: 0.0932 cents