Scala analysis: 630_T37
Aristoxenian style tetrachord 14/3 + 28/3 + 16, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 77.778 cents 77.777780 2: 233.333 cents 233.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 266.6667 cents 266.6667 1: 77.7778 cents 77.7778 2: 155.5556 cents 155.5556 3: 266.6667 cents 266.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 77.77778 cents 1: 1 155.55555 cents 1: 1 266.66667 cents 2: 1 233.33333 cents 2: 1 344.44445 cents 2: 1 422.22222 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 : 77.8 233.3 500.0 77.8 : 155.6 422.2 500.0 233.3: 266.7 344.4 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.7778 .. 266.6667 cents 188.88889 cents 77.77778 cents 2: 233.3333 .. 422.2222 cents 188.88889 cents -33.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 77.77778 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 266.66667 cents Average / Smallest step : 2.142857 Largest / Average step : 1.600000 Largest / Smallest step : 3.428571 Median interval of one step : 155.55555 cents, amount: 1 Least squares average step : 146.03175 cents, oct.: 438.09524 cents Scale is not proper Scale has trivalence property Scale is a mode of a 45-tone equal temperament with octave 500.000 cents degrees: 7 21 45 Least number of segments generator : 23 of 255.556 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 38 of 422.222 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.33334 cents Scale diversity : 1.070690 Lumma stability : 0.311111 Lumma impropriety factor : 0.066667 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 : 33.33334 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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: 59.1434 c. M: 77.7778 c. 4: 1 1 2 P M ME S SD: 28.9120 c. M:-47.2222 c. 5: 1 1 3 N M DE S SD: 23.1296 c. M: 33.3333 c. 6: 1 2 3 P T3 SD: 10.1430 c. M:-16.6667 c. 11: 2 3 6 N T3 SD: 8.3499 c. M:-13.1313 c. 13: 2 4 7 N T3 SD: 1.5605 c. M: 2.5641 c. 32: 5 10 17 N T3 SD: 0.6339 c. M:-1.0417 c. 45: 7 14 24 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: 58.2728 cents 6 x 7:8 S SD: 16.7973 cents 7 x 8:9 S SD: 32.4759 cents 8 x 9:11 SD: 29.5773 cents 9 x 10:12 S SD: 25.4836 cents 10 x 11:13 SD: 41.1255 cents 11:12:13:15 SD: 32.9916 cents 12:13:14:16 S SD: 23.1531 cents 13:14:15:17 SD: 21.1484 cents 14:15:16:19 SD: 16.8773 cents 15:16:17:20 SD: 12.6217 cents 18:19:21:24 SD: 12.3784 cents 19:20:22:25 SD: 11.3524 cents 20:21:23:27 SD: 7.4642 cents 21:22:24:28 S SD: 1.3374 cents 90:94:103:120 SD: 1.0597 cents 110:115:126:147 SD: 0.9257 cents 111:116:127:148 SD: 0.8243 cents 131:137:150:175 SD: 0.5939 cents 152:159:174:203 SD: 0.3788 cents 173:181:198:231 SD: 0.2681 cents 194:203:222:259 SD: 0.2610 cents 263:275:301:351 SD: 0.2303 cents 284:297:325:379 SD: 0.1786 cents 436:456:499:582 SD: 0.1159 cents 457:478:523:610 SD: 0.0720 cents