Scala analysis: 603_T10
Aristoxenian style tetrachord 2 + 6 + 22, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.333 cents 33.333330 2: 133.333 cents 133.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 366.6667 cents 366.6667 1: 33.3333 cents 33.3333 2: 100.0000 cents 100.0000 3: 366.6667 cents 366.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 100.00000 cents 1: 1 366.66667 cents 2: 1 133.33333 cents 2: 1 400.00000 cents 2: 1 466.66667 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 : 33.3 133.3 500.0 33.3 : 100.0 466.7 500.0 133.3: 366.7 400.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 366.6667 cents 333.33334 cents 33.33333 cents 2: 133.3333 .. 466.6667 cents 333.33334 cents -233.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 366.66667 cents Average / Smallest step : 5.000001 Largest / Average step : 2.200000 Largest / Smallest step : 11.000001 Median interval of one step : 100.00000 cents, amount: 1 Least squares average step : 128.57143 cents, oct.: 385.71428 cents Scale is not proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 500.000 cents degrees: 1 4 15 Least number of segments generator : 11 of 366.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 11 of 366.667 cents and inv. generated superset size: 5 = 2 more = 166.667% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 1 0 1 1 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 0.571710 Lumma stability : 0.133333 Lumma impropriety factor : 0.466667 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 : 33.33333 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: 27.2166 c. M:-33.3333 c. 4: 0 1 3 N G T3 SD: 19.8373 c. M: 33.3333 c. 9: 0 2 7 N G T3 SD: 23.1296 c. M: 33.3333 c. 10: 1 2 7 N T3 SD: 13.6083 c. M:-16.6667 c. 11: 1 2 8 N T3 SD: 7.2136 c. M:-12.1212 c. 12: 1 2 9 N T3 SD: 6.8041 c. M:-8.3333 c. 14: 1 3 10 N T3 SD: 5.6678 c. M:-9.5238 c. 15: 1 3 11 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: 100.0556 cents 6 x 7:8 S SD: 66.7759 cents 7 x 8:9 S SD: 58.7088 cents 8 x 9:11 SD: 43.6308 cents 9 x 10:12 S SD: 24.5547 cents 10 x 11:13 SD: 27.8362 cents 11 x 12:15 S SD: 20.4008 cents 12 x 13:16 SD: 2.7961 cents 13 x 14:17 SD: 17.9634 cents 14 x 15:19 SD: 15.9366 cents 15 x 16:20 S SD: 10.8452 cents 16 x 17:21 SD: 20.3658 cents 17 x 18:23 SD: 20.7706 cents 18 x 19:24 SD: 19.8892 cents 19 x 21:25 SD: 23.5269 cents 20 x 22:27 SD: 18.6098 cents 21:22:23:28 SD: 17.6878 cents 22:23:24:29 SD: 17.2403 cents 23:24:25:31 SD: 15.0195 cents 24:25:26:32 SD: 12.5852 cents 26:27:28:35 S SD: 11.8468 cents 27:28:29:36 SD: 10.4040 cents 33:34:36:44 SD: 8.4323 cents 35:36:38:47 SD: 6.8920 cents 36:37:39:48 SD: 5.0564 cents 38:39:41:51 SD: 5.0210 cents 39:40:42:52 SD: 3.9353 cents 47:48:51:63 SD: 3.7579 cents 48:49:52:64 SD: 2.0237 cents 51:52:55:68 SD: 1.0917 cents 99:101:107:132 SD: 0.8775 cents 149:152:161:199 SD: 0.5646 cents 200:204:216:267 SD: 0.3256 cents 263:268:284:351 SD: 0.2873 cents 311:317:336:415 SD: 0.2696 cents 361:368:390:482 SD: 0.2089 cents 412:420:445:550 SD: 0.0538 cents