Scala analysis: 723_S32
Semi-tempered tetrachord (4/3)**(2/5) * (4/3)**(3/10) * (4/3)**(3/10)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 199.218 cents 199.218000 2: 348.631 cents 348.631500 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 149.4135 cents 149.4135 1: 199.2180 cents 199.2180 2: 149.4135 cents 149.4135 3: 149.4135 cents 149.4135
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 149.41350 cents 1: 1 199.21800 cents 2: 1 298.82700 cents 2: 2 348.63150 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 199.2 348.6 498.0 199.2: 149.4 298.8 498.0 348.6: 149.4 348.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 149.4135 .. 199.2180 cents 49.80450 cents 149.41350 cents 2: 298.8270 .. 348.6315 cents 49.80450 cents 99.60900 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 149.41350 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 199.21800 cents Average / Smallest step : 1.111111 Largest / Average step : 1.200000 Largest / Smallest step : 1.333333 Median interval of one step : 149.41350 cents, amount: 2 Most common interval of one step : 149.41350 cents, amount: 2 Least squares average step : 170.75829 cents, oct.: 512.27486 cents Scale is strictly proper Scale has Myhill's property chromas: 49.80450 cents and 99.60900 cents, ratio: 2.000000 generators: 149.41350 cents and 2 of 348.63150 cents Scale is maximally even in 10-tone equal temperament ET pair of linear temperament : 20&383678066 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 10-tone equal temperament with octave 4/3 degrees: 4 7 10 generators: 3 and 7 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABB Step pattern size order : LSS Interval vector is [ 0 0 2 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 99.60900 cents Scale diversity : 1.333006 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.800000 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 49.80450 cents Most common intervals : 149.41350 cents & inv., amount: 2 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 decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 0-1 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
3: 1 1 1 SP B ME I SD: 21.4324 c. M: 33.2030 c. 7: 3 2 2 SP M ME S SD: 9.1853 c. M:-14.2299 c. 10: 4 3 3 SP M ME S SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 37.6822 cents 5 x 6:7 S SD: 45.3405 cents 6:7 x 8 S SD: 33.8265 cents 7:8 x 9 S SD: 35.3032 cents 8:9:10:11 H SD: 21.8072 cents 9:10:11:12 H SD: 5.6196 cents 32:36:39:43 SD: 5.1783 cents 39:44:48:52 SD: 4.8306 cents 40:45:49:53 SD: 4.0436 cents 41:46:50:55 SD: 3.8934 cents 48:54:59:64 SD: 3.2612 cents 49:55:60:65 SD: 3.0357 cents 57:64:70:76 SD: 2.3872 cents 66:74:81:88 SD: 2.0086 cents 72:81:88:96 SD: 1.6163 cents 81:91:99:108 SD: 0.8730 cents 90:101:110:120 SD: 0.4304 cents 189:212:231:252 SD: 0.4295 cents 237:266:290:316 SD: 0.3308 cents 246:276:301:328 SD: 0.2316 cents 327:367:400:436 SD: 0.2034 cents 336:377:411:448 SD: 0.0699 cents 426:478:521:568 SD: 0.0687 cents