Scala analysis: 671_T78
Tempered tetrachord in cents 100 + 275 + 125, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100.000 cents 100.000000 2: 375.000 cents 375.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 125.0000 cents 125.0000 1: 100.0000 cents 100.0000 2: 275.0000 cents 275.0000 3: 125.0000 cents 125.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.00000 cents 1: 1 125.00000 cents 1: 1 275.00000 cents 2: 1 225.00000 cents 2: 1 375.00000 cents 2: 1 400.00000 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 : 100.0 375.0 500.0 100.0: 275.0 400.0 500.0 375.0: 125.0 225.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 275.0000 cents 175.00000 cents 100.00000 cents 2: 225.0000 .. 400.0000 cents 175.00000 cents -50.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 275.00000 cents Average / Smallest step : 1.666667 Largest / Average step : 1.650000 Largest / Smallest step : 2.750000 Median interval of one step : 125.00000 cents, amount: 1 Least squares average step : 167.85714 cents, oct.: 503.57143 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: 4 15 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 11 of 275.000 cents and inv. generated superset size: 6 = 3 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Interval vector is [ 0 0 0 1 1 0 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 : 1.152404 Lumma stability : 0.400000 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 : 25.00000 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: 62.5463 c. M: 100.0000 c. 4: 1 2 1 P M ME I SD: 14.4338 c. M:-25.0000 c. 9: 2 5 2 N M DE I SD: 10.2690 c. M:-13.8889 c. 11: 2 6 3 N T3 SD: 8.4019 c. M: 11.3636 c. 15: 3 8 4 N T3 SD: 4.8113 c. M: 8.3333 c. 16: 3 9 4 N T3 SD: 3.6084 c. M: 6.2500 c. 20: 4 11 5 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: 11.3137 cents 5 x 6:7 S SD: 50.8225 cents 6 x 7:8 S SD: 54.0734 cents 7:8:9 x S SD: 72.1400 cents 8:9:10:11 H SD: 38.8141 cents 9:10:11:12 H SD: 28.9742 cents 11:12:14:15 S SD: 25.2463 cents 12:13:15:16 SD: 13.4151 cents 15:16:19:20 SD: 12.0836 cents 16:17:20:21 SD: 10.5741 cents 17:18:21:23 SD: 8.3602 cents 21:22:26:28 SD: 6.7513 cents 29:31:36:39 SD: 6.7161 cents 30:32:37:40 SD: 5.6139 cents 33:35:41:44 SD: 0.9387 cents 116:123:144:155 SD: 0.7930 cents 149:158:185:199 SD: 0.6120 cents 170:180:211:227 SD: 0.5102 cents 203:215:252:271 SD: 0.2987 cents 236:250:293:315 SD: 0.1773 cents 269:285:334:359 SD: 0.1552 cents 505:535:627:674 SD: 0.1537 cents