Scala analysis: 612_T19
Aristoxenian style tetrachord 6 + 3 + 21, Aristoxenos
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: 150.000 cents 150.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 350.0000 cents 350.0000 1: 100.0000 cents 100.0000 2: 50.0000 cents 50.0000 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 : 100.0 150.0 500.0 100.0: 50.0 400.0 500.0 150.0: 350.0 450.0 500.0 500.0
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 : 135.71429 cents, oct.: 407.14286 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: 2 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 : MSL 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 0 2 N G T3 SD: 39.6746 c. M:-66.6667 c. 4: 1 0 3 N G T3 SD: 20.4124 c. M: 25.0000 c. 6: 1 1 4 N M DE S SD: 13.6083 c. M: 16.6667 c. 9: 2 1 6 N T3 SD: 11.5648 c. M:-16.6667 c. 10: 2 1 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 14:15 x 19 SD: 17.3275 cents 15:16 x 20 S SD: 5.9465 cents 16:17 x 21 SD: 14.8182 cents 18:19:20:24 S SD: 11.0290 cents 20:21:22:27 SD: 9.7105 cents 21:22:23:28 SD: 6.9824 cents 26 x 28:35 S SD: 13.0812 cents 27:29 x 36 SD: 11.8963 cents 29:31:32:39 SD: 9.5604 cents 30:32:33:40 SD: 6.3820 cents 32:34:35:43 SD: 4.5170 cents 33:35:36:44 SD: 0.9257 cents 134:142:146:179 SD: 0.6727 cents 167:177:182:223 SD: 0.4783 cents 200:212:218:267 SD: 0.4031 cents 221:234:241:295 SD: 0.3485 cents 254:269:277:339 SD: 0.2387 cents 287:304:313:383 SD: 0.1998 cents 421:446:459:562 SD: 0.1416 cents 454:481:495:606 SD: 0.1069 cents