Scala analysis: 687_T94
Tempered tetrachord in cents 212.5 + 162.5 + 125, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 212.500 cents 212.500000 2: 375.000 cents 375.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 125.0000 cents 125.0000 1: 212.5000 cents 212.5000 2: 162.5000 cents 162.5000 3: 125.0000 cents 125.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 125.00000 cents 1: 1 162.50000 cents 1: 1 212.50000 cents 2: 1 287.50000 cents 2: 1 337.50000 cents 2: 1 375.00000 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 : 212.5 375.0 500.0 212.5: 162.5 287.5 500.0 375.0: 125.0 337.5 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 125.0000 .. 212.5000 cents 87.50000 cents 125.00000 cents 2: 287.5000 .. 375.0000 cents 87.50000 cents 75.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 125.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 212.50000 cents Average / Smallest step : 1.333333 Largest / Average step : 1.275000 Largest / Smallest step : 1.700000 Median interval of one step : 162.50000 cents, amount: 1 Least squares average step : 175.89286 cents, oct.: 527.67857 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 40-tone equal temperament with octave 500.000 cents degrees: 17 30 40 Least number of segments generator : 21 of 262.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 21 of 262.500 cents and inv. generated superset size: 11 = 8 more = 366.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Interval vector is [ 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 75.00000 cents Scale diversity : 1.348261 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.650000 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 : 37.50000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly decreasing 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: 35.7622 c. M: 45.8333 c. 4: 2 1 1 P M ME S SD: 21.6506 c. M:-37.5000 c. 5: 2 2 1 SP M ME S SD: 16.1374 c. M:-25.0000 c. 7: 3 2 2 SP M ME S SD: 10.3612 c. M: 17.8571 c. 9: 4 3 2 SP T3 SD: 9.7881 c. M:-13.8889 c. 12: 5 4 3 SP T3 SD: 2.4056 c. M: 4.1667 c. 28: 12 9 7 SP T3 SD: 1.0310 c. M:-1.7857 c. 40: 17 13 10 SP 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: 11.3137 cents 5 x 6:7 S SD: 50.8225 cents 6:7 x 8 S SD: 27.2030 cents 7:8:9 x S SD: 31.4596 cents 8:9:10:11 H SD: 17.7492 cents 9:10:11:12 H SD: 13.6257 cents 15:17:19:20 SD: 11.5182 cents 16:18:20:21 S SD: 10.8297 cents 17:19:21:23 SD: 10.6752 cents 21:24:26:28 S SD: 6.4991 cents 24:27:30:32 S SD: 4.7797 cents 30:34:37:40 SD: 4.2629 cents 38:43:47:51 SD: 3.9393 cents 45:51:56:60 SD: 1.9530 cents 54:61:67:72 SD: 0.9684 cents 99:112:123:132 SD: 0.7924 cents 137:155:170:183 SD: 0.7291 cents 153:173:190:204 SD: 0.6548 cents 161:182:200:215 SD: 0.3115 cents 215:243:267:287 SD: 0.1864 cents 451:510:560:602 SD: 0.1404 cents 475:537:590:634 SD: 0.1283 cents