Scala analysis: 638_T45
Aristoxenian style tetrachord 6 + 9 + 15, 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: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 100.0000 cents 100.0000 2: 150.0000 cents 150.0000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.00000 cents 1: 1 150.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 350.00000 cents 2: 1 400.00000 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 : 100.0 250.0 500.0 100.0: 150.0 400.0 500.0 250.0: 250.0 350.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 250.0000 cents 150.00000 cents 100.00000 cents 2: 250.0000 .. 400.0000 cents 150.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.666667 Largest / Average step : 1.500000 Largest / Smallest step : 2.500000 Median interval of one step : 150.00000 cents, amount: 1 Least squares average step : 150.00000 cents, oct.: 450.00000 cents Scale is proper Scale has trivalence property Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 2 5 10 Least number of segments generator : 7 of 350.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 7 of 350.000 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 1 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.136403 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.400000 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 75.1542 c. M: 100.0000 c. 4: 1 1 2 P M ME S SD: 14.4338 c. M:-25.0000 c. 6: 1 2 3 P T3 SD: 9.6225 c. M: 16.6667 c. 10: 2 3 5 P 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: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7 x 8:9 S SD: 33.7953 cents 8 x 9:11 SD: 34.4885 cents 9 x 10:12 S SD: 33.8123 cents 11:12:13:15 SD: 24.6461 cents 12:13:14:16 S SD: 14.0487 cents 14:15:16:19 SD: 13.1461 cents 15:16:17:20 SD: 11.7909 cents 18:19:21:24 SD: 6.0495 cents 32:34:37:43 SD: 4.2034 cents 33:35:38:44 SD: 2.1209 cents 51:54:59:68 SD: 1.0556 cents 84:89:97:112 SD: 0.7162 cents 135:143:156:180 SD: 0.6688 cents 167:177:193:223 SD: 0.3529 cents 200:212:231:267 SD: 0.3483 cents 218:231:252:291 SD: 0.3188 cents 251:266:290:335 SD: 0.1801 cents 573:607:662:765 SD: 0.1249 cents