Scala analysis: 680_T87
Tempered tetrachord in cents 110 + 140 + 250, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 110.000 cents 110.000000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 110.0000 cents 110.0000 2: 140.0000 cents 140.0000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 110.00000 cents 1: 1 140.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 360.00000 cents 2: 1 390.00000 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 : 110.0 250.0 500.0 110.0: 140.0 390.0 500.0 250.0: 250.0 360.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 110.0000 .. 250.0000 cents 140.00000 cents 110.00000 cents 2: 250.0000 .. 390.0000 cents 140.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 110.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 1.515152 Largest / Average step : 1.500000 Largest / Smallest step : 2.272727 Median interval of one step : 140.00000 cents, amount: 1 Least squares average step : 150.71429 cents, oct.: 452.14286 cents Scale is proper Scale has trivalence property Scale is a mode of a 50-tone equal temperament with octave 500.000 cents degrees: 11 25 50 Least number of segments generator : 27 of 270.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 27 of 270.000 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.144475 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.440000 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 : 30.00000 cents Most common intervals : 250.00000 cents & inv., amount: 2 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 : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 58.1823 c. M:-83.3333 c. 4: 1 1 2 P M ME S SD: 8.6603 c. M:-15.0000 c. 10: 2 3 5 P T3 SD: 5.7735 c. M: 10.0000 c. 14: 3 4 7 P T3 SD: 1.6496 c. M: 2.8571 c. 18: 4 5 9 P T3 SD: 0.6415 c. M:-1.1111 c. 32: 7 9 16 P T3 SD: 0.3608 c. M: 0.6250 c. 50: 11 14 25 P 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: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7 x 8:9 S SD: 33.7953 cents 8 x 9:11 SD: 34.4885 cents 9 x 10:12 S SD: 33.8123 cents 10:11:12:13 H SD: 32.3704 cents 11:12:13:15 SD: 22.4948 cents 12:13:14:16 S SD: 11.0797 cents 18:19:21:24 SD: 7.8691 cents 26:28:30:35 S SD: 7.8418 cents 27:29:31:36 SD: 5.8606 cents 30:32:35:40 SD: 5.6906 cents 32:34:37:43 SD: 4.2152 cents 33:35:38:44 SD: 3.3854 cents 45:48:52:60 SD: 0.8763 cents 122:130:141:163 SD: 0.5637 cents 167:178:193:223 SD: 0.3065 cents 212:226:245:283 SD: 0.2837 cents 245:261:283:327 SD: 0.2123 cents 290:309:335:387 SD: 0.1843 cents 367:391:424:490 SD: 0.1753 cents 412:439:476:550 SD: 0.0606 cents 457:487:528:610 SD: 0.0322 cents