Scala analysis: 614_T21
Aristoxenian style tetrachord 10/3 + 20/3 + 20, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55.556 cents 55.555560 2: 166.667 cents 166.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 333.3333 cents 333.3333 1: 55.5556 cents 55.5556 2: 111.1111 cents 111.1111 3: 333.3333 cents 333.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55.55556 cents 1: 1 111.11111 cents 1: 1 333.33333 cents 2: 1 166.66667 cents 2: 1 388.88889 cents 2: 1 444.44444 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 : 55.6 166.7 500.0 55.6 : 111.1 444.4 500.0 166.7: 333.3 388.9 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.5556 .. 333.3333 cents 277.77777 cents 55.55556 cents 2: 166.6667 .. 444.4444 cents 277.77777 cents -166.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55.55556 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 333.33333 cents Average / Smallest step : 3.000000 Largest / Average step : 2.000000 Largest / Smallest step : 5.999999 Median interval of one step : 111.11111 cents, amount: 1 Least squares average step : 134.92064 cents, oct.: 404.76191 cents Scale is not proper Scale has trivalence property Scale is a mode of a 9-tone equal temperament with octave 500.000 cents degrees: 1 3 9 Least number of segments generator : 7 of 388.889 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 8 of 444.444 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 1 1 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 55.55556 cents Scale diversity : 0.843575 Lumma stability : 0.222222 Lumma impropriety factor : 0.333333 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 : 55.55555 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: 32.0750 c. M: 55.5556 c. 6: 1 1 4 N M DE S SD: 16.0375 c. M:-27.7778 c. 7: 1 1 5 N M DE S SD: 16.5212 c. M: 23.8095 c. 8: 1 2 5 N T3 SD: 12.6788 c. M:-20.8333 c. 9: 1 2 6 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: 85.1494 cents 6 x 7:8 S SD: 50.1117 cents 7 x 8:9 S SD: 45.7583 cents 8 x 9:11 SD: 31.7041 cents 9 x 10:12 S SD: 7.9290 cents 10 x 11:13 SD: 22.9081 cents 11 x 12:15 S SD: 20.1389 cents 12 x 13:16 SD: 14.0810 cents 13 x 14:17 SD: 26.1607 cents 14 x 15:19 SD: 27.6272 cents 15 x 17:20 SD: 25.0291 cents 16:17:18:21 S SD: 22.8063 cents 17:18:19:23 SD: 18.5520 cents 18:19:20:24 S SD: 13.7400 cents 20:21:22:27 SD: 11.6471 cents 21:22:23:28 SD: 8.8947 cents 27:28:30:36 S SD: 5.8340 cents 29:30:32:39 SD: 4.6007 cents 30:31:33:40 SD: 0.9459 cents 119:123:131:159 SD: 0.7998 cents 149:154:164:199 SD: 0.6481 cents 158:163:174:211 SD: 0.6092 cents 179:185:197:239 SD: 0.5913 cents 188:194:207:251 SD: 0.4056 cents 218:225:240:291 SD: 0.2893 cents 248:256:273:331 SD: 0.2469 cents 337:348:371:450 SD: 0.2225 cents 367:379:404:490 SD: 0.1899 cents 523:540:576:698 SD: 0.1880 cents 553:571:609:738 SD: 0.1735 cents 585:604:644:781 SD: 0.1561 cents