Scala analysis: 599_T6
Aristoxenian style tetrachord 2 + 5 + 23, 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: 116.667 cents 116.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 383.3333 cents 383.3333 1: 33.3333 cents 33.3333 2: 83.3333 cents 83.3333 3: 383.3333 cents 383.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 83.33334 cents 1: 1 383.33333 cents 2: 1 116.66667 cents 2: 1 416.66666 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 : 33.3 116.7 500.0 33.3 : 83.3 466.7 500.0 116.7: 383.3 416.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 383.3333 cents 350.00000 cents 33.33333 cents 2: 116.6667 .. 466.6667 cents 350.00000 cents -266.66666 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 : 383.33333 cents Average / Smallest step : 5.000001 Largest / Average step : 2.300000 Largest / Smallest step : 11.500001 Median interval of one step : 83.33334 cents, amount: 1 Least squares average step : 126.19048 cents, oct.: 378.57143 cents Scale is not proper Scale has trivalence property Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 2 7 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 23 of 383.333 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 : SML Interval vector is [ 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 0.488451 Lumma stability : 0.133333 Lumma impropriety factor : 0.533333 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 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 34.6944 c. M:-50.0000 c. 4: 0 1 3 N G T3 SD: 19.8373 c. M: 33.3333 c. 5: 0 1 4 N G T3 SD: 21.5166 c. M: 33.3333 c. 8: 1 1 6 N M DE S SD: 17.5132 c. M:-29.1667 c. 9: 1 1 7 N M DE S SD: 13.2249 c. M:-22.2222 c. 11: 1 2 8 N T3 SD: 13.3528 c. M:-19.6970 c. 12: 1 2 9 N T3 SD: 6.8041 c. M:-8.3333 c. 13: 1 2 10 N T3 SD: 3.0519 c. M:-5.1282 c. 17: 1 3 13 N T3 SD: 2.3338 c. M: 3.9216 c. 29: 2 5 22 N T3 SD: 2.4156 c. M:-4.0230 c. 30: 2 5 23 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 x 5 S SD: 113.6863 cents 5 x x 7 SD: 82.5122 cents 6 x 7:8 S SD: 75.1085 cents 7 x 8:9 S SD: 65.8142 cents 8 x 9:11 SD: 50.6086 cents 9 x 10:12 S SD: 32.8831 cents 10 x 11:13 SD: 33.2899 cents 11 x 12:15 S SD: 25.0965 cents 12 x 13:16 SD: 10.9965 cents 13 x 14:17 SD: 18.7128 cents 14 x 15:19 SD: 14.4106 cents 15 x 16:20 S SD: 2.6542 cents 16 x 17:21 SD: 15.7394 cents 17 x 18:23 SD: 14.6415 cents 18 x 19:24 SD: 11.5732 cents 19 x 20:25 S SD: 18.6802 cents 20 x 21:27 SD: 18.8352 cents 21 x 22:28 SD: 18.0912 cents 22 x 24:29 SD: 20.1659 cents 23:24:25:31 SD: 17.2414 cents 24:25:26:32 SD: 14.4449 cents 25:26:27:33 SD: 14.3142 cents 26:27:28:35 S SD: 12.3516 cents 27:28:29:36 SD: 10.1722 cents 29:30:31:39 SD: 9.4930 cents 30:31:32:40 S SD: 8.0091 cents 33:34:35:44 SD: 7.8850 cents 38:39:41:51 SD: 7.0333 cents 39:40:42:52 SD: 5.2633 cents 41:42:44:55 S SD: 4.4093 cents 42:43:45:56 SD: 2.7150 cents 45:46:48:60 S SD: 2.3672 cents 56:57:60:75 S SD: 2.3115 cents 57:58:61:76 SD: 1.2815 cents 99:101:106:132 SD: 0.9478 cents 101:103:108:135 SD: 0.8308 cents 155:158:166:207 SD: 0.7337 cents 158:161:169:211 SD: 0.3692 cents 200:204:214:267 SD: 0.3594 cents 257:262:275:343 SD: 0.1985 cents 358:365:383:478 SD: 0.1787 cents 415:423:444:554 SD: 0.1364 cents 460:469:492:614 SD: 0.1088 cents