Scala analysis: 623_T30
Aristoxenian style tetrachord 4.5 + 7.5 + 18, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 200.000 cents 200.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 300.0000 cents 300.0000 1: 75.0000 cents 75.0000 2: 125.0000 cents 125.0000 3: 300.0000 cents 300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 75.00000 cents 1: 1 125.00000 cents 1: 1 300.00000 cents 2: 1 200.00000 cents 2: 1 375.00000 cents 2: 1 425.00000 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 : 75.0 200.0 500.0 75.0 : 125.0 425.0 500.0 200.0: 300.0 375.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 300.0000 cents 225.00000 cents 75.00000 cents 2: 200.0000 .. 425.0000 cents 225.00000 cents -100.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 300.00000 cents Average / Smallest step : 2.222222 Largest / Average step : 1.800000 Largest / Smallest step : 4.000000 Median interval of one step : 125.00000 cents, amount: 1 Least squares average step : 141.07143 cents, oct.: 423.21429 cents Scale is not proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 3 8 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 425.000 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 0 1 0 1 0 0 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 75.00000 cents Scale diversity : 1.050690 Lumma stability : 0.300000 Lumma impropriety factor : 0.200000 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: 47.3853 c. M: 75.0000 c. 5: 1 1 3 N M DE S SD: 14.4338 c. M:-25.0000 c. 7: 1 2 4 N T3 SD: 8.5017 c. M:-14.2857 c. 8: 1 2 5 N T3 SD: 10.2062 c. M: 12.5000 c. 12: 2 3 7 N T3 SD: 6.8041 c. M:-8.3333 c. 13: 2 3 8 N T3 SD: 4.5778 c. M: 7.6923 c. 15: 2 4 9 N T3 SD: 4.8113 c. M: 8.3333 c. 20: 3 5 12 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: 71.0302 cents 6 x 7:8 S SD: 33.4497 cents 7 x 8:9 S SD: 36.0066 cents 8 x 9:11 SD: 25.7333 cents 9 x 10:12 S SD: 8.8523 cents 10 x 11:13 SD: 28.8143 cents 11 x 12:15 S SD: 30.8304 cents 12 x 13:16 SD: 30.7292 cents 13:14:15:17 SD: 26.6360 cents 14:15:16:19 SD: 20.4666 cents 15:16:17:20 SD: 13.4638 cents 17:18:19:23 SD: 11.4163 cents 18:19:20:24 S SD: 8.5604 cents 23:24:26:31 SD: 6.9348 cents 24:25:27:32 SD: 2.0504 cents 65:68:73:87 SD: 1.9032 cents 66:69:74:88 SD: 1.1240 cents 90:94:101:120 SD: 0.6699 cents 155:162:174:207 SD: 0.5670 cents 179:187:201:239 SD: 0.3593 cents 245:256:275:327 SD: 0.3506 cents 269:281:302:359 SD: 0.2449 cents 385:402:432:514 SD: 0.2296 cents 409:427:459:546 SD: 0.1900 cents 499:521:560:666 SD: 0.1687 cents 564:589:633:753 SD: 0.1343 cents 588:614:660:785 SD: 0.0897 cents