Scala analysis: 625_T32
Aristoxenian style tetrachord 5 + 7 + 18, Chapter 4
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: 200.000 cents 200.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 300.0000 cents 300.0000 1: 83.3333 cents 83.3333 2: 116.6667 cents 116.6667 3: 300.0000 cents 300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.33333 cents 1: 1 116.66667 cents 1: 1 300.00000 cents 2: 1 200.00000 cents 2: 1 383.33333 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 : 83.3 200.0 500.0 83.3 : 116.7 416.7 500.0 200.0: 300.0 383.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 300.0000 cents 216.66667 cents 83.33333 cents 2: 200.0000 .. 416.6667 cents 216.66667 cents -100.00000 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 : 300.00000 cents Average / Smallest step : 2.000000 Largest / Average step : 1.800000 Largest / Smallest step : 3.600000 Median interval of one step : 116.66667 cents, amount: 1 Least squares average step : 141.66667 cents, oct.: 425.00000 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 12 30 Least number of segments generator : 17 of 283.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 23 of 383.333 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 0 1 0 0 0 0 1 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 83.33333 cents Scale diversity : 1.078374 Lumma stability : 0.333333 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 : 33.33334 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: 51.8188 c. M: 83.3333 c. 5: 1 1 3 N M DE S SD: 9.6225 c. M:-16.6667 c. 7: 1 2 4 N T3 SD: 10.7363 c. M:-14.2857 c. 12: 2 3 7 N T3 SD: 4.8113 c. M:-8.3333 c. 13: 2 3 8 N T3 SD: 5.7811 c. M: 7.6923 c. 17: 3 4 10 N T3 SD: 4.4208 c. M:-5.8824 c. 18: 3 4 11 N T3 SD: 3.2075 c. M: 5.5556 c. 23: 4 5 14 N T3 SD: 3.2676 c. M: 4.3478 c. 25: 4 6 15 N T3 SD: 1.9245 c. M: 3.3333 c. 30: 5 7 18 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 12:13 x 16 SD: 27.6370 cents 13:14:15:17 SD: 24.8695 cents 14:15:16:19 SD: 18.5552 cents 15:16:17:20 SD: 10.9985 cents 17:18:19:23 SD: 9.6792 cents 18:19:20:24 S SD: 6.8225 cents 24:25:27:32 SD: 4.4648 cents 39:41:44:52 SD: 3.2046 cents 41:43:46:55 SD: 2.8834 cents 42:44:47:56 SD: 2.0939 cents 57:60:64:76 SD: 1.9436 cents 80:84:90:107 SD: 1.7781 cents 81:85:91:108 SD: 0.8291 cents 122:128:137:163 SD: 0.5907 cents 164:172:184:219 SD: 0.4543 cents 203:213:228:271 SD: 0.3609 cents 221:232:248:295 SD: 0.2942 cents 245:257:275:327 SD: 0.1938 cents 424:445:476:566 SD: 0.1530 cents 466:489:523:622 SD: 0.0847 cents 588:617:660:785 SD: 0.0843 cents