Scala analysis: 619_T26
Aristoxenian style tetrachord 5 + 6 + 19, Macran
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.333 cents 83.333330 2: 183.333 cents 183.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 316.6667 cents 316.6667 1: 83.3333 cents 83.3333 2: 100.0000 cents 100.0000 3: 316.6667 cents 316.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.33333 cents 1: 1 100.00000 cents 1: 1 316.66667 cents 2: 1 183.33333 cents 2: 1 400.00000 cents 2: 1 416.66667 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 : 83.3 183.3 500.0 83.3 : 100.0 416.7 500.0 183.3: 316.7 400.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 316.6667 cents 233.33334 cents 83.33333 cents 2: 183.3333 .. 416.6667 cents 233.33334 cents -133.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 83.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 316.66667 cents Average / Smallest step : 2.000000 Largest / Average step : 1.900000 Largest / Smallest step : 3.800000 Median interval of one step : 100.00000 cents, amount: 1 Least squares average step : 139.28571 cents, oct.: 417.85714 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: 5 11 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 19 of 316.667 cents and inv. generated superset size: 7 = 4 more = 233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 83.33333 cents Scale diversity : 1.008382 Lumma stability : 0.333333 Lumma impropriety factor : 0.266667 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 : 16.66667 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% Limited inverse transpositions with margin 216.6667 cents: 2 -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 49.0653 c. M: 83.3333 c. 4: 0 1 3 N G T3 SD: 58.7288 c. M: 83.3333 c. 5: 1 1 3 N M DE S SD: 13.6083 c. M:-16.6667 c. 6: 1 1 4 N M DE S SD: 9.6225 c. M: 16.6667 c. 11: 2 2 7 N M DE S SD: 4.4605 c. M:-7.5758 c. 17: 3 3 11 N M DE S SD: 4.8692 c. M: 6.8627 c. 19: 3 4 12 N T3 SD: 2.5824 c. M: 4.3860 c. 24: 4 5 15 N T3 SD: 2.4056 c. M:-4.1667 c. 25: 4 5 16 N T3 SD: 2.7217 c. M: 3.3333 c. 30: 5 6 19 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: 77.9642 cents 6 x 7:8 S SD: 41.7802 cents 7 x 8:9 S SD: 40.3200 cents 8 x 9:11 SD: 27.6448 cents 9 x 10:12 S SD: 1.0824 cents 10 x 11:13 SD: 24.6593 cents 11 x 12:15 S SD: 24.6698 cents 12 x 13:16 SD: 22.4017 cents 13:14 x 17 SD: 28.6672 cents 14:15:16:19 SD: 22.1500 cents 15:16:17:20 SD: 14.6162 cents 16:17:18:21 S SD: 13.9231 cents 17:18:19:23 SD: 9.8482 cents 18:19:20:24 S SD: 3.4985 cents 45:47:50:60 SD: 2.7788 cents 60:63:67:80 SD: 2.6765 cents 62:65:69:83 SD: 1.8533 cents 63:66:70:84 SD: 1.1788 cents 81:85:90:108 SD: 0.7226 cents 143:150:159:191 SD: 0.4186 cents 161:169:179:215 SD: 0.3236 cents 224:235:249:299 SD: 0.1247 cents 385:404:428:514 SD: 0.1000 cents 466:489:518:622 SD: 0.0744 cents