Scala analysis: 700_S9
Semi-tempered tetrachord (4/3)**(1/5) * (4/3)**(1/5) * (4/3)**(3/5)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.609 cents 99.609000 2: 199.218 cents 199.218000 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 298.8270 cents 298.8270 1: 99.6090 cents 99.6090 2: 99.6090 cents 99.6090 3: 298.8270 cents 298.8270
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 99.60900 cents 1: 1 298.82700 cents 2: 1 199.21800 cents 2: 2 398.43600 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 : 99.6 199.2 498.0 99.6 : 99.6 398.4 498.0 199.2: 298.8 398.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.6090 .. 298.8270 cents 199.21800 cents 99.60900 cents 2: 199.2180 .. 398.4360 cents 199.21800 cents -99.60900 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 99.60900 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 298.82700 cents Average / Smallest step : 1.666667 Largest / Average step : 1.800000 Largest / Smallest step : 3.000000 Median interval of one step : 99.60900 cents, amount: 2 Most common interval of one step : 99.60900 cents, amount: 2 Least squares average step : 142.29857 cents, oct.: 426.89571 cents Scale is not proper Scale has Myhill's property chromas: 199.21800 cents and 99.60900 cents, ratio: 2.000000 generators: 1 of 99.60900 cents and 398.43600 cents ET pair of linear temperament : 10&10 Scale is distributional even Scale is a mode of a 5-tone equal temperament with octave 4/3 degrees: 1 2 5 generators: 1 and 4 Number of contiguous 1-step segments: 1 Scale is a Winograd/Gamer deep scale Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 2 1 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 99.60900 cents Scale diversity : 1.071369 Lumma stability : 0.400000 Lumma impropriety factor : 0.200000 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 : 99.60900 cents Most common intervals : 99.60900 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
3: 0 1 2 N G T3 SD: 60.6201 c. M: 99.6090 c. 4: 1 1 2 P M ME S SD: 32.1487 c. M:-49.8045 c. 5: 1 1 3 N M DE 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 71.9185 cents 6 x 7:8 S SD: 33.8265 cents 7 x 8:9 S SD: 35.3032 cents 8 x 9:11 SD: 26.7396 cents 9 x 10:12 S SD: 8.4071 cents 10 x 11:13 SD: 27.8017 cents 11 x 12:15 S SD: 31.1198 cents 12:13 x 16 SD: 19.4818 cents 14:15:16:19 SD: 16.1710 cents 15:16:17:20 SD: 7.0876 cents 18:19:20:24 S SD: 5.9516 cents 32:34:36:43 SD: 5.0784 cents 33:35:37:44 SD: 0.8441 cents 156:165:175:208 SD: 0.8391 cents 171:181:192:228 SD: 0.5970 cents 189:200:212:252 SD: 0.5736 cents 204:216:229:272 SD: 0.3753 cents 237:251:266:316 SD: 0.2255 cents 270:286:303:360 SD: 0.1387 cents 303:321:340:404 SD: 0.1279 cents 525:556:589:700 SD: 0.0995 cents 558:591:626:744 SD: 0.0656 cents