Scala analysis: 681_T88
Tempered tetrachord in cents 87.5 + 237.5 + 175, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87.500 cents 87.500000 2: 325.000 cents 325.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 175.0000 cents 175.0000 1: 87.5000 cents 87.5000 2: 237.5000 cents 237.5000 3: 175.0000 cents 175.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 87.50000 cents 1: 1 175.00000 cents 1: 1 237.50000 cents 2: 1 262.50000 cents 2: 1 325.00000 cents 2: 1 412.50000 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 : 87.5 325.0 500.0 87.5 : 237.5 412.5 500.0 325.0: 175.0 262.5 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.5000 .. 237.5000 cents 150.00000 cents 87.50000 cents 2: 262.5000 .. 412.5000 cents 150.00000 cents 25.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 87.50000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 237.50000 cents Average / Smallest step : 1.904762 Largest / Average step : 1.425000 Largest / Smallest step : 2.714286 Median interval of one step : 175.00000 cents, amount: 1 Least squares average step : 159.82143 cents, oct.: 479.46429 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: 7 26 40 Least number of segments generator : 21 of 262.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 33 of 412.500 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 : SLM Interval vector is [ 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 25.00000 cents Scale diversity : 1.119381 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400000 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 : 25.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths 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: 45.9594 c. M:-79.1667 c. 4: 1 2 1 P M ME I SD: 36.0844 c. M:-50.0000 c. 5: 1 2 2 SP M ME S SD: 16.1374 c. M: 25.0000 c. 6: 1 3 2 P T3 SD: 5.3791 c. M:-8.3333 c. 11: 2 5 4 SP T3 SD: 4.4011 c. M: 6.8182 c. 17: 3 8 6 SP T3 SD: 0.9493 c. M: 1.4706 c. 23: 4 11 8 SP T3 SD: 0.7016 c. M:-1.0870 c. 40: 7 19 14 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: 61.3137 cents 5 x 6:7 S SD: 41.5206 cents 6 x 7:8 S SD: 29.0810 cents 7 x 8:9 S SD: 57.0469 cents 8:9:10:11 H SD: 47.0746 cents 9:10:11:12 H SD: 32.5109 cents 10:11:12:13 H SD: 30.1678 cents 11:12:13:15 SD: 27.1469 cents 12:13:14:16 S SD: 25.8010 cents 13:14:16:17 S SD: 21.3911 cents 14:15:17:19 SD: 14.7842 cents 15:16:18:20 S SD: 8.6831 cents 18:19:22:24 SD: 7.7688 cents 20:21:24:27 S SD: 7.2956 cents 24:25:29:32 SD: 5.7142 cents 33:35:40:44 SD: 5.5265 cents 35:37:42:47 SD: 5.4856 cents 38:40:46:51 SD: 3.6998 cents 39:41:47:52 SD: 0.9760 cents 116:122:140:155 SD: 0.6230 cents 155:163:187:207 SD: 0.3062 cents 194:204:234:259 SD: 0.2404 cents 406:427:490:542 SD: 0.2066 cents 445:468:537:594 SD: 0.1420 cents 484:509:584:646 SD: 0.1280 cents