Scala analysis: 621_T28
Aristoxenian style tetrachord 3 + 9 + 18, 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: 200.000 cents 200.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 300.0000 cents 300.0000 1: 50.0000 cents 50.0000 2: 150.0000 cents 150.0000 3: 300.0000 cents 300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50.00000 cents 1: 1 150.00000 cents 1: 1 300.00000 cents 2: 1 200.00000 cents 2: 1 350.00000 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 : 50.0 200.0 500.0 50.0 : 150.0 450.0 500.0 200.0: 300.0 350.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 300.0000 cents 250.00000 cents 50.00000 cents 2: 200.0000 .. 450.0000 cents 250.00000 cents -100.00000 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 : 300.00000 cents Average / Smallest step : 3.333333 Largest / Average step : 1.800000 Largest / Smallest step : 6.000000 Median interval of one step : 150.00000 cents, amount: 1 Least squares average step : 139.28571 cents, oct.: 417.85714 cents Scale is not proper Scale has trivalence property Scale is a mode of a 10-tone equal temperament with octave 500.000 cents degrees: 1 4 10 Least number of segments generator : 9 of 450.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 7 of 350.000 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 0 1 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.872124 Lumma stability : 0.200000 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: 34.6944 c. M: 50.0000 c. 5: 0 2 3 N G T3 SD: 28.8675 c. M: 50.0000 c. 6: 1 1 4 N M DE S SD: 27.2166 c. M: 33.3333 c. 7: 1 2 4 N T3 SD: 14.8690 c. M:-21.4286 c. 8: 1 2 5 N T3 SD: 10.2062 c. M: 12.5000 c. 10: 1 3 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: 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 x 15:17 SD: 29.7682 cents 14:15:16:19 SD: 27.1151 cents 15:16:17:20 SD: 21.3256 cents 16:17:18:21 S SD: 20.7877 cents 17:18:19:23 SD: 18.2444 cents 18:19:20:24 S SD: 15.6868 cents 21:22:24:28 S SD: 14.5608 cents 22:23:25:29 SD: 13.5540 cents 23:24:26:31 SD: 10.4979 cents 24:25:27:32 SD: 7.0432 cents 30:31:34:40 SD: 6.0375 cents 32:33:36:43 SD: 4.1986 cents 33:34:37:44 SD: 1.0736 cents 105:108:118:140 SD: 1.0354 cents 131:135:147:175 SD: 0.8401 cents 138:142:155:184 SD: 0.7717 cents 140:144:157:187 SD: 0.7703 cents 164:169:184:219 SD: 0.7497 cents 170:175:191:227 SD: 0.5858 cents 203:209:228:271 SD: 0.3870 cents 236:243:265:315 SD: 0.2976 cents 269:277:302:359 SD: 0.2927 cents 343:353:385:458 SD: 0.2064 cents 376:387:422:502 SD: 0.1337 cents 409:421:459:546 SD: 0.1235 cents