Scala analysis: 606_T13
Aristoxenian style tetrachord 3 + 5 + 22, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.000 cents 50.000000 2: 133.333 cents 133.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 366.6667 cents 366.6667 1: 50.0000 cents 50.0000 2: 83.3333 cents 83.3333 3: 366.6667 cents 366.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50.00000 cents 1: 1 83.33333 cents 1: 1 366.66667 cents 2: 1 133.33333 cents 2: 1 416.66667 cents 2: 1 450.00000 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 : 50.0 133.3 500.0 50.0 : 83.3 450.0 500.0 133.3: 366.7 416.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 366.6667 cents 316.66667 cents 50.00000 cents 2: 133.3333 .. 450.0000 cents 316.66667 cents -233.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 366.66667 cents Average / Smallest step : 3.333333 Largest / Average step : 2.200000 Largest / Smallest step : 7.333333 Median interval of one step : 83.33333 cents, amount: 1 Least squares average step : 129.76190 cents, oct.: 389.28571 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: 3 8 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: 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 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.648803 Lumma stability : 0.200000 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: 34.6944 c. M: 50.0000 c. 4: 0 1 3 N G T3 SD: 29.2657 c. M: 50.0000 c. 5: 0 1 4 N G T3 SD: 34.6944 c. M: 50.0000 c. 7: 1 1 5 N M DE S SD: 13.5387 c. M:-21.4286 c. 8: 1 1 6 N M DE S SD: 8.6736 c. M:-12.5000 c. 10: 1 2 7 N T3 SD: 9.6225 c. M:-16.6667 c. 11: 1 2 8 N T3 SD: 3.1540 c. M: 4.5455 c. 19: 2 3 14 N T3 SD: 1.8260 c. M:-2.6316 c. 30: 3 5 22 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 20:21:22:27 SD: 16.9092 cents 21:22:23:28 SD: 12.9959 cents 22:23:24:29 SD: 12.9045 cents 23:24:25:31 SD: 10.3449 cents 24:25:26:32 SD: 7.1385 cents 27:28:29:36 SD: 5.4199 cents 35:36:38:47 SD: 4.6033 cents 36:37:39:48 SD: 2.0509 cents 63:65:68:84 SD: 1.5605 cents 98:101:106:131 SD: 1.3835 cents 99:102:107:132 SD: 0.9481 cents 101:104:109:135 SD: 0.9265 cents 137:141:148:183 SD: 0.4233 cents 200:206:216:267 SD: 0.3984 cents 236:243:255:315 SD: 0.3155 cents 239:246:258:319 SD: 0.3042 cents 275:283:297:367 SD: 0.1768 cents 412:424:445:550 SD: 0.1117 cents 475:489:513:634 SD: 0.1106 cents