Scala analysis: 609_T16
Aristoxenian style tetrachord 3 + 6 + 21, 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: 150.000 cents 150.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 350.0000 cents 350.0000 1: 50.0000 cents 50.0000 2: 100.0000 cents 100.0000 3: 350.0000 cents 350.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50.00000 cents 1: 1 100.00000 cents 1: 1 350.00000 cents 2: 1 150.00000 cents 2: 1 400.00000 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 : 50.0 150.0 500.0 50.0 : 100.0 450.0 500.0 150.0: 350.0 400.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 350.0000 cents 300.00000 cents 50.00000 cents 2: 150.0000 .. 450.0000 cents 300.00000 cents -200.00000 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 : 350.00000 cents Average / Smallest step : 3.333333 Largest / Average step : 2.100000 Largest / Smallest step : 7.000000 Median interval of one step : 100.00000 cents, amount: 1 Least squares average step : 132.14286 cents, oct.: 396.42857 cents Scale is not proper Scale has trivalence property Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 1 3 10 Least number of segments generator : 7 of 350.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 9 of 450.000 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 1 1 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.739849 Lumma stability : 0.200000 Lumma impropriety factor : 0.400000 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 : 50.00000 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: 30.4290 c. M: 50.0000 c. 4: 0 1 3 N G T3 SD: 32.2749 c. M: 50.0000 c. 6: 1 1 4 N M DE S SD: 21.5166 c. M:-33.3333 c. 7: 1 1 5 N M DE S SD: 13.0410 c. M:-21.4286 c. 9: 1 2 6 N T3 SD: 10.1430 c. M:-16.6667 c. 10: 1 2 7 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 6:7 S SD: 92.5274 cents 6 x 7:8 S SD: 58.4436 cents 7 x 8:9 S SD: 51.9695 cents 8 x 9:11 SD: 37.2150 cents 9 x 10:12 S SD: 16.2313 cents 10 x 11:13 SD: 24.0909 cents 11 x 12:15 S SD: 18.4781 cents 12 x 13:16 SD: 5.7967 cents 13 x 14:17 SD: 20.8348 cents 14 x 15:19 SD: 20.9565 cents 15 x 16:20 S SD: 19.1593 cents 16 x 17:21 SD: 26.8457 cents 17:18:19:23 SD: 22.9770 cents 18:19:20:24 S SD: 18.1201 cents 19:20:21:25 SD: 17.2117 cents 20:21:22:27 SD: 14.1239 cents 21:22:23:28 SD: 10.5012 cents 23:24:25:31 SD: 9.8522 cents 24:25:26:32 SD: 7.9005 cents 30:31:33:40 SD: 5.5251 cents 32:33:35:43 SD: 4.3434 cents 33:34:36:44 SD: 0.8856 cents 134:138:146:179 SD: 0.7281 cents 167:172:182:223 SD: 0.5522 cents 200:206:218:267 SD: 0.4795 cents 209:215:228:279 SD: 0.3969 cents 242:249:264:323 SD: 0.3046 cents 275:283:300:367 SD: 0.2745 cents 343:353:374:458 SD: 0.2173 cents 376:387:410:502 SD: 0.1259 cents 409:421:446:546 SD: 0.0618 cents 442:455:482:590 SD: 0.0616 cents