Scala analysis: 670_T77
Tempered tetrachord in cents 75 + 275 + 150, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 350.000 cents 350.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 150.0000 cents 150.0000 1: 75.0000 cents 75.0000 2: 275.0000 cents 275.0000 3: 150.0000 cents 150.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 75.00000 cents 1: 1 150.00000 cents 1: 1 275.00000 cents 2: 1 225.00000 cents 2: 1 350.00000 cents 2: 1 425.00000 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 : 75.0 350.0 500.0 75.0 : 275.0 425.0 500.0 350.0: 150.0 225.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 275.0000 cents 200.00000 cents 75.00000 cents 2: 225.0000 .. 425.0000 cents 200.00000 cents -50.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 275.00000 cents Average / Smallest step : 2.222222 Largest / Average step : 1.650000 Largest / Smallest step : 3.666667 Median interval of one step : 150.00000 cents, amount: 1 Least squares average step : 162.50000 cents, oct.: 487.50000 cents Scale is not proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 3 14 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 425.000 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 1 0 0 1 0 0 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 1.065241 Lumma stability : 0.300000 Lumma impropriety factor : 0.100000 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 : 50.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 2 1 N G T3 SD: 44.3576 c. M: 75.0000 c. 4: 1 2 1 P M ME I SD: 32.2749 c. M:-50.0000 c. 6: 1 3 2 P T3 SD: 10.7583 c. M: 16.6667 c. 7: 1 4 2 N T3 SD: 4.6107 c. M:-7.1429 c. 13: 2 7 4 N T3 SD: 2.4827 c. M: 3.8462 c. 20: 3 11 6 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 5 x S SD: 36.3137 cents 5 x 6:7 S SD: 44.6900 cents 6 x 7:8 S SD: 41.5760 cents 7 x x 9 SD: 64.9159 cents 8:9:10:11 H SD: 47.8075 cents 9:10:11:12 H SD: 35.8176 cents 10:11:12:13 H SD: 35.5553 cents 11:12:13:15 SD: 34.6118 cents 12:13:15:16 SD: 24.4131 cents 13:14:16:17 S SD: 21.5917 cents 14:15:17:19 SD: 18.2285 cents 15:16:18:20 S SD: 16.7781 cents 17:18:21:23 SD: 12.3290 cents 18:19:22:24 SD: 6.2947 cents 27:28:33:36 SD: 4.1564 cents 44:46:54:59 SD: 3.0945 cents 45:47:55:60 SD: 1.0863 cents 89:93:109:119 SD: 1.0820 cents 111:116:136:148 SD: 0.9545 cents 116:121:142:155 SD: 0.8771 cents 134:140:164:179 SD: 0.5132 cents 179:187:219:239 SD: 0.3932 cents 227:237:278:303 SD: 0.3154 cents 272:284:333:363 SD: 0.1792 cents 406:424:497:542 SD: 0.0785 cents 451:471:552:602 SD: 0.0654 cents