Scala analysis: 618_T25
Aristoxenian style tetrachord 5 + 19 + 6, Xenakis
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: 400.000 cents 400.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 100.0000 cents 100.0000 1: 83.3333 cents 83.3333 2: 316.6667 cents 316.6667 3: 100.0000 cents 100.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.33333 cents 1: 1 100.00000 cents 1: 1 316.66667 cents 2: 1 183.33333 cents 2: 1 400.00000 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 : 83.3 400.0 500.0 83.3 : 316.7 416.7 500.0 400.0: 100.0 183.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 316.6667 cents 233.33334 cents 83.33333 cents 2: 183.3333 .. 416.6667 cents 233.33334 cents -133.33334 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 : 316.66667 cents Average / Smallest step : 2.000000 Largest / Average step : 1.900000 Largest / Smallest step : 3.800000 Median interval of one step : 100.00000 cents, amount: 1 Least squares average step : 170.23809 cents, oct.: 510.71428 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 24 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: 7 = 4 more = 233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Interval vector is [ 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 83.33333 cents Scale diversity : 1.008382 Lumma stability : 0.333333 Lumma impropriety factor : 0.266667 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 : 16.66667 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 2 1 N G T3 SD: 61.6141 c. M: 83.3333 c. 4: 1 2 1 P M ME I SD: 28.0542 c. M:-41.6667 c. 5: 1 3 1 N M DE I SD: 9.6225 c. M:-16.6667 c. 6: 1 4 1 N M DE I SD: 9.6225 c. M:-16.6667 c. 11: 2 7 2 N M DE I SD: 6.8322 c. M:-9.0909 c. 18: 3 11 4 N T3 SD: 6.4150 c. M: 11.1111 c. 19: 3 12 4 N T3 SD: 3.9555 c. M: 5.2632 c. 24: 4 15 5 N T3 SD: 2.4056 c. M: 4.1667 c. 25: 4 16 5 N T3 SD: 1.9245 c. M: 3.3333 c. 30: 5 19 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 5 x S SD: 13.6863 cents 5 x 6:7 S SD: 59.0014 cents 6 x x 8 S SD: 1.9550 cents 7:8:9 x S SD: 75.9733 cents 8:9:10:11 H SD: 43.9186 cents 9:10:11:12 H SD: 37.3938 cents 10:11 x 13 SD: 46.8148 cents 11:12:14:15 S SD: 26.2502 cents 12:13:15:16 SD: 18.9810 cents 15:16:19:20 SD: 9.9762 cents 18:19:23:24 SD: 8.8375 cents 19:20:24:25 S SD: 8.6211 cents 20:21:25:27 SD: 7.9642 cents 23:24:29:31 SD: 6.4619 cents 24:25:30:32 S SD: 6.2489 cents 35:37:44:47 SD: 5.6543 cents 38:40:48:51 S SD: 3.9148 cents 39:41:49:52 SD: 2.0466 cents 42:44:53:56 SD: 1.4552 cents 81:85:102:108 SD: 0.7198 cents 143:150:180:191 SD: 0.6773 cents 161:169:203:215 SD: 0.5394 cents 185:194:233:247 SD: 0.4409 cents 200:210:252:267 SD: 0.3859 cents 242:254:305:323 SD: 0.2470 cents 346:363:436:462 SD: 0.2252 cents 385:404:485:514 SD: 0.1295 cents 427:448:538:570 SD: 0.0779 cents