Scala analysis: 660_T67
Aristoxenian style tetrachord 12 + 5 + 11, Tiby
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 211.714 cents 211.714290 2: 299.929 cents 299.928570 3: 494.000 cents 494.000000
SHOW/INTERVAL
0: 194.0714 cents 194.0714 1: 211.7143 cents 211.7143 2: 88.2143 cents 88.2143 3: 194.0714 cents 194.0714
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88.21428 cents 1: 1 194.07143 cents 1: 1 211.71429 cents 2: 1 282.28571 cents 2: 1 299.92857 cents 2: 1 405.78572 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 : 211.7 299.9 494.0 211.7: 88.2 282.3 494.0 299.9: 194.1 405.8 494.0 494.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.2143 .. 211.7143 cents 123.50001 cents 88.21428 cents 2: 282.2857 .. 405.7857 cents 123.50001 cents 70.57142 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 88.21428 cents, class 1 Average step (divided formal octave): 164.6667 cents Largest one step interval : 211.71429 cents Average / Smallest step : 1.866667 Largest / Average step : 1.285714 Largest / Smallest step : 2.400000 Median interval of one step : 194.07143 cents, amount: 1 Least squares average step : 163.82653 cents, oct.: 491.47959 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 28-tone equal temperament with octave 494.000 cents degrees: 12 17 28 Least number of segments generator : 15 of 264.643 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 299.929 cents and inv. generated superset size: 5 = 2 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Interval vector is [ 0 0 0 0 1 0 0 0 0 0 1 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.57142 cents Scale diversity : 1.052682 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.500000 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 : 17.64286 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 32.0319 c. M: 47.0476 c. 5: 2 1 2 SP M ME I SD: 8.3997 c. M: 14.1143 c. 12: 5 2 5 SP M DE I SD: 7.5923 c. M: 11.7619 c. Raga Sarvasri, Warao tritonic: South America 16: 7 3 6 SP T3 SD: 5.6942 c. M:-8.8214 c. 18: 8 3 7 SP T3 SD: 4.6665 c. M:-7.8413 c. 21: 9 4 8 SP T3 SD: 3.3954 c. M:-5.8810 c. 23: 10 4 9 SP T3 SD: 1.8260 c. M:-3.0683 c. 28: 12 5 11 SP T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 706.0000 cents 2 x x 3 S SD: 207.9550 cents 3 x x 4 S SD: 4.0450 cents 4 x 5 x S SD: 86.3851 cents 5 x 6:7 S SD: 44.9480 cents 6 x 7:8 S SD: 16.6521 cents 7:8 x 9 S SD: 31.0232 cents 9:10:11:12 H SD: 18.6481 cents 12 x 14:16 S SD: 16.6521 cents 13:15 x 17 SD: 23.3048 cents 14:16:17:19 SD: 17.9270 cents 15:17:18:20 SD: 5.6566 cents 31:35:37:41 SD: 3.9827 cents 37:42:44:49 SD: 3.6333 cents 46:52:55:61 SD: 3.6246 cents 48:54:57:64 SD: 3.0387 cents 54:61:64:72 SD: 2.3667 cents 63:71:75:84 SD: 2.1766 cents 69:78:82:92 SD: 1.4084 cents 85:96:101:113 SD: 0.6646 cents 100:113:119:133 SD: 0.4217 cents 185:209:220:246 SD: 0.2799 cents 254:287:302:338 SD: 0.2433 cents 339:383:403:451 SD: 0.2420 cents 354:400:421:471 SD: 0.1525 cents 439:496:522:584 SD: 0.1355 cents 539:609:641:717 SD: 0.1159 cents