Scala analysis: 668_T75
Tempered tetrachord in cents 87.5 + 287.5 + 125, 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: 375.000 cents 375.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 125.0000 cents 125.0000 1: 87.5000 cents 87.5000 2: 287.5000 cents 287.5000 3: 125.0000 cents 125.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 87.50000 cents 1: 1 125.00000 cents 1: 1 287.50000 cents 2: 1 212.50000 cents 2: 1 375.00000 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 : 87.5 375.0 500.0 87.5 : 287.5 412.5 500.0 375.0: 125.0 212.5 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.5000 .. 287.5000 cents 200.00000 cents 87.50000 cents 2: 212.5000 .. 412.5000 cents 200.00000 cents -75.00000 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 : 287.50000 cents Average / Smallest step : 1.904762 Largest / Average step : 1.725000 Largest / Smallest step : 3.285714 Median interval of one step : 125.00000 cents, amount: 1 Least squares average step : 166.96429 cents, oct.: 500.89286 cents Scale is not proper Scale has trivalence property Scale is a mode of a 40-tone equal temperament with octave 500.000 cents degrees: 7 30 40 Least number of segments generator : 21 of 262.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 23 of 287.500 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 : SLM Interval vector is [ 0 0 0 0 0 0 1 0 0 1 0 0 0 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 : 1.119381 Lumma stability : 0.350000 Lumma impropriety factor : 0.150000 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 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: 55.9534 c. M: 87.5000 c. 4: 1 2 1 P M ME I SD: 21.6506 c. M:-37.5000 c. 5: 1 3 1 N M DE I SD: 16.1374 c. M:-25.0000 c. 7: 1 4 2 N T3 SD: 13.8705 c. M: 17.8571 c. 11: 2 6 3 N T3 SD: 6.8497 c. M: 11.3636 c. 12: 2 7 3 N T3 SD: 2.4056 c. M: 4.1667 c. 28: 5 16 7 N T3 SD: 1.0310 c. M:-1.7857 c. 40: 7 23 10 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: 77.8658 cents 8:9:10:11 H SD: 42.5739 cents 9:10:11:12 H SD: 32.9509 cents 11:12:14:15 S SD: 28.2028 cents 12:13:15:16 SD: 17.4491 cents 15:16:19:20 SD: 13.9986 cents 16:17:20:21 SD: 11.9557 cents 17:18:21:23 SD: 9.1842 cents 20:21:25:27 SD: 7.5972 cents 21:22:26:28 SD: 2.9796 cents 54:57:67:72 SD: 2.1984 cents 57:60:71:76 SD: 1.9105 cents 74:78:92:99 SD: 1.8871 cents 75:79:93:100 SD: 1.3566 cents 78:82:97:104 SD: 1.0796 cents 95:100:118:127 SD: 0.9744 cents 116:122:144:155 SD: 0.6344 cents 173:182:215:231 SD: 0.4736 cents 194:204:241:259 SD: 0.2662 cents 269:283:334:359 SD: 0.1910 cents 385:405:478:514 SD: 0.1796 cents 442:465:549:590 SD: 0.1492 cents 463:487:575:618 SD: 0.0351 cents