Scala analysis: 721_S30
Semi-tempered tetrachord (4/3)**(1/5) * (4/3)**(2/5) * (4/3)**(2/5)
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: 298.827 cents 298.827000 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 199.2180 cents 199.2180 1: 99.6090 cents 99.6090 2: 199.2180 cents 199.2180 3: 199.2180 cents 199.2180
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 99.60900 cents 1: 2 199.21800 cents 2: 2 298.82700 cents 2: 1 398.43600 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 : 99.6 298.8 498.0 99.6 : 199.2 398.4 498.0 298.8: 199.2 298.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.6090 .. 199.2180 cents 99.60900 cents 99.60900 cents 2: 298.8270 .. 398.4360 cents 99.60900 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 : 199.21800 cents Average / Smallest step : 1.666667 Largest / Average step : 1.200000 Largest / Smallest step : 2.000000 Median interval of one step : 199.21800 cents, amount: 2 Most common interval of one step : 199.21800 cents, amount: 2 Least squares average step : 156.52843 cents, oct.: 469.58529 cents Scale is strictly proper Scale has Myhill's property chromas: 99.60900 cents and 1/1, 0.0000 cents generators: 199.21800 cents and 2 of 298.82700 cents Scale is maximally even in 5-tone equal temperament ET pair of linear temperament : 10&10 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 5-tone equal temperament with octave 4/3 degrees: 1 3 5 generators: 2 and 3 Number of contiguous 1-step segments: 1 Scale is a Winograd/Gamer deep scale Step pattern alph. order: ABB Step pattern size order : SLL Interval vector is [ 1 2 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 99.60900 cents Scale diversity : 1.071369 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.600000 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 : 199.21800 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Steps are increasing 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: 42.8649 c. M:-66.4060 c. 4: 1 1 2 P M ME S SD: 32.1487 c. M: 49.8045 c. 5: 1 2 2 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: 87.4867 cents 5 x 6:7 S SD: 43.0622 cents 6 x 7:8 S SD: 15.9780 cents 7 x 8:9 S SD: 46.2087 cents 8 x 10:11 S SD: 51.2151 cents 9:10:11:12 H SD: 31.9984 cents 10:11:12:13 H SD: 26.8337 cents 11:12:13:15 SD: 21.6282 cents 12:13:14:16 S SD: 16.7974 cents 15:16:18:20 S SD: 6.9095 cents 21:22:25:28 SD: 6.4365 cents 31:33:37:41 SD: 6.0271 cents 32:34:38:43 SD: 4.8514 cents 33:35:39:44 SD: 3.2929 cents 48:51:57:64 SD: 1.8352 cents 69:73:82:92 SD: 0.6830 cents 117:124:139:156 SD: 0.3748 cents 186:197:221:248 SD: 0.1205 cents 456:483:542:608 SD: 0.0949 cents 573:607:681:764 SD: 0.0728 cents