Scala analysis: 636_T43
Aristoxenian style tetrachord 4 + 11 + 15, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666670 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 66.6667 cents 66.6667 2: 183.3333 cents 183.3333 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.66667 cents 1: 1 183.33333 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 316.66667 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 : 66.7 250.0 500.0 66.7 : 183.3 433.3 500.0 250.0: 250.0 316.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 250.0000 cents 183.33333 cents 66.66667 cents 2: 250.0000 .. 433.3333 cents 183.33333 cents 1/1, 0.0000 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 : 250.00000 cents Average / Smallest step : 2.500000 Largest / Average step : 1.500000 Largest / Smallest step : 3.750000 Median interval of one step : 183.33333 cents, amount: 1 Least squares average step : 147.61905 cents, oct.: 442.85714 cents Scale is proper Scale has trivalence property Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 4 15 30 Least number of segments generator : 19 of 316.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 283.333 cents and inv. generated superset size: 16 = 13 more = 533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.918085 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.266667 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 : 66.66667 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: 61.6141 c. M: 83.3333 c. 4: 1 1 2 P M ME S SD: 33.6788 c. M:-58.3333 c. 5: 1 2 2 SP M ME S SD: 34.6944 c. M:-50.0000 c. 6: 1 2 3 P T3 SD: 9.6225 c. M:-16.6667 c. 8: 1 3 4 P T3 SD: 2.4056 c. M: 4.1667 c. 22: 3 8 11 P T3 SD: 0.8748 c. M:-1.5151 c. 30: 4 11 15 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 10 x 12:13 S SD: 40.0161 cents 11:12:13:15 SD: 33.2562 cents 12:13:14:16 S SD: 24.6282 cents 13:14:15:17 SD: 23.7322 cents 14:15:16:19 SD: 20.9833 cents 15:16:17:20 SD: 18.6917 cents 17:18:20:23 SD: 16.8972 cents 18:19:21:24 SD: 10.6145 cents 20:21:23:27 SD: 9.2120 cents 21:22:24:28 S SD: 7.8218 cents 24:25:28:32 SD: 5.8166 cents 26:27:30:35 S SD: 4.9484 cents 27:28:31:36 SD: 3.8706 cents 45:47:52:60 SD: 2.9468 cents 51:53:59:68 SD: 0.9967 cents 128:133:148:171 SD: 0.6616 cents 155:161:179:207 SD: 0.4864 cents 200:208:231:267 SD: 0.4527 cents 206:214:238:275 SD: 0.2406 cents 406:422:469:542 SD: 0.1358 cents 457:475:528:610 SD: 0.0742 cents