Scala analysis: xen18-erlich-vishnu-16
2L 14s MOS for Vishnu, L=101.92, s=71.15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 71.150 cents 71.150000 2: 142.300 cents 142.300000 3: 213.450 cents 213.450000 4: 315.370 cents 315.370000 5: 386.520 cents 386.520000 6: 457.670 cents 457.670000 7: 528.820 cents 528.820000 8: 599.970 cents 599.970000 9: 671.120 cents 671.120000 10: 742.270 cents 742.270000 11: 813.420 cents 813.420000 12: 915.340 cents 915.340000 13: 986.490 cents 986.490000 14: 1057.640 cents 1057.640000 15: 1128.790 cents 1128.790000 16: 1199.940 cents 1199.940000
SHOW/INTERVAL
0: 71.1500 cents 71.1500 1: 71.1500 cents 71.1500 2: 71.1500 cents 71.1500 3: 71.1500 cents 71.1500 4: 101.9200 cents 101.9200 5: 71.1500 cents 71.1500 6: 71.1500 cents 71.1500 7: 71.1500 cents 71.1500 8: 71.1500 cents 71.1500 9: 71.1500 cents 71.1500 10: 71.1500 cents 71.1500 11: 71.1500 cents 71.1500 12: 101.9200 cents 101.9200 13: 71.1500 cents 71.1500 14: 71.1500 cents 71.1500 15: 71.1500 cents 71.1500 16: 71.1500 cents 71.1500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 71.15000 cents 1: 2 101.92000 cents 2: 12 142.30000 cents 2: 4 173.07000 cents 3: 10 213.45000 cents 3: 6 244.22000 cents 4: 8 284.60000 cents 4: 8 315.37000 cents 5: 6 355.75000 cents 5: 10 386.52000 cents 6: 4 426.90000 cents 6: 12 457.67000 cents 7: 2 498.05000 cents 7: 14 528.82000 cents 8: 16 599.97000 cents 9: 14 671.12000 cents 9: 2 701.89000 cents 10: 12 742.27000 cents 10: 4 773.04000 cents 11: 10 813.42000 cents 11: 6 844.19000 cents 12: 8 884.57000 cents 12: 8 915.34000 cents 13: 6 955.72000 cents 13: 10 986.49000 cents 14: 4 1026.87000 cents 14: 12 1057.64000 cents 15: 2 1098.02000 cents 15: 14 1128.79000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.93333 = 29/15
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 71.2 142.3 213.5 315.4 386.5 457.7 528.8 600.0 671.1 742.3 813.4 915.3 986.5 1057.6 1128.8 1199.9 71.2 : 71.2 142.3 244.2 315.4 386.5 457.7 528.8 600.0 671.1 742.3 844.2 915.3 986.5 1057.6 1128.8 1199.9 142.3 : 71.2 173.1 244.2 315.4 386.5 457.7 528.8 600.0 671.1 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 213.5 : 101.9 173.1 244.2 315.4 386.5 457.7 528.8 600.0 701.9 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 315.4 : 71.2 142.3 213.5 284.6 355.8 426.9 498.1 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1098.0 1199.9 386.5 : 71.2 142.3 213.5 284.6 355.8 426.9 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1128.8 1199.9 457.7 : 71.2 142.3 213.5 284.6 355.7 457.7 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1057.6 1128.8 1199.9 528.8 : 71.2 142.3 213.5 284.6 386.5 457.7 528.8 600.0 671.1 742.3 813.4 884.6 986.5 1057.6 1128.8 1199.9 600.0 : 71.2 142.3 213.5 315.4 386.5 457.7 528.8 600.0 671.1 742.3 813.4 915.3 986.5 1057.6 1128.8 1199.9 671.1 : 71.2 142.3 244.2 315.4 386.5 457.7 528.8 600.0 671.1 742.3 844.2 915.3 986.5 1057.6 1128.8 1199.9 742.3 : 71.2 173.1 244.2 315.4 386.5 457.7 528.8 600.0 671.1 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 813.4 : 101.9 173.1 244.2 315.4 386.5 457.7 528.8 600.0 701.9 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 915.3 : 71.2 142.3 213.5 284.6 355.8 426.9 498.1 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1098.0 1199.9 986.5 : 71.2 142.3 213.5 284.6 355.7 426.9 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1128.8 1199.9 1057.6: 71.2 142.3 213.5 284.6 355.7 457.7 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1057.6 1128.8 1199.9 1128.8: 71.2 142.3 213.5 284.6 386.5 457.7 528.8 600.0 671.1 742.3 813.4 884.6 986.5 1057.6 1128.8 1199.9 1199.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.1500 .. 101.9200 cents 30.77000 cents 71.15000 cents 2: 142.3000 .. 173.0700 cents 30.77000 cents 40.38000 cents 3: 213.4500 .. 244.2200 cents 30.77000 cents 40.38000 cents 4: 284.6000 .. 315.3700 cents 30.77000 cents 40.38000 cents 5: 355.7500 .. 386.5200 cents 30.77000 cents 40.38000 cents 6: 426.9000 .. 457.6700 cents 30.77000 cents 40.38000 cents 7: 498.0500 .. 528.8200 cents 30.77000 cents 40.38000 cents 8: 599.9700 .. 599.9700 cents 1/1, 0.0000 cents 71.15000 cents 9: 671.1200 .. 701.8900 cents 30.77000 cents 71.15000 cents 10: 742.2700 .. 773.0400 cents 30.77000 cents 40.38000 cents 11: 813.4200 .. 844.1900 cents 30.77000 cents 40.38000 cents 12: 884.5700 .. 915.3400 cents 30.77000 cents 40.38000 cents 13: 955.7200 .. 986.4900 cents 30.77000 cents 40.38000 cents 14: 1026.8700 .. 1057.6400 cents 30.77000 cents 40.38000 cents 15: 1098.0200 .. 1128.7900 cents 30.77000 cents 40.38000 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 71.15000 cents, class 1 Average step (divided formal octave): 74.9963 cents Largest one step interval : 101.92000 cents Average / Smallest step : 1.054058 Largest / Average step : 1.359001 Largest / Smallest step : 1.432467 Median interval of one step : 71.15000 cents, amount: 14 Most common interval of one step : 71.15000 cents, amount: 14 Least squares average step : 75.26364 cents, oct.: 1204.21818 cents Scale is strictly proper Scale has 2 repeating blocks of 8 notes Blocks have Myhill's property chromas: 30.77000 cents and 40.38000 cents, ratio: 1.312317 generators: 1 of 71.15000 cents and 7 of 528.82000 cents ET pair of linear temperament : 34&118 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 624-tone equal temperament with octave 1199.940 cents degrees: 37 74 111 164 201 238 275 312 349 386 423 476 513 550 587 624 Least number of segments generator : 313 of 601.893 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 349 of 671.120 cents and inv. generated superset size: 320 = 304 more = 2000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAAAABAAAA Step pattern size order : SSSLSSSSSSSLSSSS Scale is a Constant Structure, by a margin of 40.38000 cents Scale diversity : 1.190523 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.640999 Number of different interval sizes : 29 = 1.93333 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.93333 = 29/15 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 30.77000 cents Most common intervals : 599.97000 cents & inv., amount: 16 Number of recognisable fifths : 2, average 701.8900 cents Number of recognisable fourths : 2, average 498.0500 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 14 = 87.5000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 8 Limited inverse transpositions : 7 15 Inversional symmetry on intervals : 3-4 7-8 11-12 15-16 -- Rational properties --
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.0203 c. M: 15.3850 c. 34: 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 SP B ME SD: 1.3257 c. M:-2.2612 c. 84: 5 5 5 7 5 5 5 5 5 5 5 7 5 5 5 5 SP B DE SD: 0.6449 c. M: 1.1000 c. 118: 7 7 7 10 7 7 7 7 7 7 7 10 7 7 7 7 SP B DE SD: 0.0771 c. M: 0.1315 c. 388: 23 23 23 33 23 23 23 23 23 23 23 33 23 23 23 23 SP B DE SD: 0.0458 c. M:-0.0781 c. 506: 30 30 30 43 30 30 30 30 30 30 30 43 30 30 30 30 SP B DE SD: 0.0171 c. M:-0.0292 c. 624: 37 37 37 53 37 37 37 37 37 37 37 53 37 37 37 37 SP B DE SD: 0.0007 c. M: 0.0012 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0600 cents 2 .. 4 match: 2 H SD: 15.4175 cents 3 .. 6 match: 3 H SD: 14.5562 cents 4 .. 8 match: 4 H SD: 8.8842 cents 5 .. 10 match: 5 H SD: 7.1345 cents 6 .. 12 match: 6 H SD: 12.1088 cents 7 .. 14 match: 7 H SD: 7.2869 cents 8 .. 16 match: 8 H SD: 7.4299 cents 9 .. 18 match: 9 H SD: 8.9321 cents 10 .. 20 match: 10 H SD: 5.5417 cents 11 .. 22 match: 11 H SD: 6.7415 cents 12 .. 24 match: 12 H SD: 6.4219 cents 13 .. 26 match: 13 H SD: 4.7957 cents 14 .. 28 match: 13 S SD: 5.3702 cents 15 .. 30 match: 14 SD: 5.2455 cents 16 .. 32 match: 15 SD: 5.6144 cents 17 .. 34 match: 15 SD: 4.1956 cents 18 .. 36 match: 14 SD: 6.5739 cents 19 .. 38 match: 15 SD: 4.2834 cents 20 .. 40 match: 16 SD: 3.7719 cents 23 .. 46 match: 16 SD: 3.1069 cents 24 .. 48 match: 16 SD: 2.9315 cents 25 .. 50 match: 16 SD: 2.9013 cents 30 .. 60 match: 16 SD: 2.8072 cents 32 .. 64 match: 16 SD: 2.7657 cents 33 .. 66 match: 16 SD: 2.7294 cents 36 .. 72 match: 16 SD: 2.1304 cents 39 .. 78 match: 16 SD: 2.0159 cents 43 .. 86 match: 16 SD: 1.9671 cents 44 .. 88 match: 16 SD: 1.7908 cents 45 .. 90 match: 16 SD: 1.5724 cents 53 .. 106 match: 16 SD: 1.5276 cents 56 .. 112 match: 16 SD: 1.4127 cents 60 .. 120 match: 16 SD: 1.3294 cents 67 .. 134 match: 16 SD: 1.2455 cents 68 .. 136 match: 16 SD: 1.2205 cents 69 .. 138 match: 16 SD: 1.0202 cents 70 .. 140 match: 16 SD: 0.9540 cents 89 .. 178 match: 16 SD: 0.8960 cents 90 .. 180 match: 16 SD: 0.8715 cents 92 .. 184 match: 16 SD: 0.7880 cents 95 .. 190 match: 16 SD: 0.6996 cents 112 .. 224 match: 16 SD: 0.6971 cents 115 .. 230 match: 16 SD: 0.6124 cents 116 .. 232 match: 16 SD: 0.5488 cents 120 .. 240 match: 16 SD: 0.5403 cents 140 .. 280 match: 16 SD: 0.4976 cents 145 .. 290 match: 16 SD: 0.4846 cents 152 .. 304 match: 16 SD: 0.4467 cents 165 .. 330 match: 16 SD: 0.3797 cents 185 .. 370 match: 16 SD: 0.3463 cents 211 .. 422 match: 16 SD: 0.3374 cents 215 .. 430 match: 16 SD: 0.2797 cents 235 .. 470 match: 16 SD: 0.2522 cents 260 .. 520 match: 16 SD: 0.2165 cents 280 .. 560 match: 16 SD: 0.2157 cents 327 .. 654 match: 16 SD: 0.2114 cents 336 .. 672 match: 16 SD: 0.1630 cents 420 .. 840 match: 16 SD: 0.1469 cents 456 .. 912 match: 16 SD: 0.1118 cents 572 .. 1144 match: 16 SD: 0.1027 cents 596 .. 1192 match: 16 SD: 0.0984 cents