Scala analysis: xen18-erlich-vishnu-18
16L 2s MOS for Vishnu, L=71.15, s=30.77
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: 284.600 cents 284.600000 5: 315.370 cents 315.370000 6: 386.520 cents 386.520000 7: 457.670 cents 457.670000 8: 528.820 cents 528.820000 9: 599.970 cents 599.970000 10: 671.120 cents 671.120000 11: 742.270 cents 742.270000 12: 813.420 cents 813.420000 13: 884.570 cents 884.570000 14: 915.340 cents 915.340000 15: 986.490 cents 986.490000 16: 1057.640 cents 1057.640000 17: 1128.790 cents 1128.790000 18: 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: 71.1500 cents 71.1500 5: 30.7700 cents 30.7700 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: 71.1500 cents 71.1500 13: 71.1500 cents 71.1500 14: 30.7700 cents 30.7700 15: 71.1500 cents 71.1500 16: 71.1500 cents 71.1500 17: 71.1500 cents 71.1500 18: 71.1500 cents 71.1500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 30.77000 cents 1: 16 71.15000 cents 2: 4 101.92000 cents 2: 14 142.30000 cents 3: 6 173.07000 cents 3: 12 213.45000 cents 4: 8 244.22000 cents 4: 10 284.60000 cents 5: 10 315.37000 cents 5: 8 355.75000 cents 6: 12 386.52000 cents 6: 6 426.90000 cents 7: 14 457.67000 cents 7: 4 498.05000 cents 8: 16 528.82000 cents 8: 2 569.20000 cents 9: 18 599.97000 cents 10: 2 630.74000 cents 10: 16 671.12000 cents 11: 4 701.89000 cents 11: 14 742.27000 cents 12: 6 773.04000 cents 12: 12 813.42000 cents 13: 8 844.19000 cents 13: 10 884.57000 cents 14: 10 915.34000 cents 14: 8 955.72000 cents 15: 12 986.49000 cents 15: 6 1026.87000 cents 16: 14 1057.64000 cents 16: 4 1098.02000 cents 17: 16 1128.79000 cents 17: 2 1169.17000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.94118 = 33/17
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.0 : 71.2 142.3 213.5 284.6 315.4 386.5 457.7 528.8 600.0 671.1 742.3 813.4 884.6 915.3 986.5 1057.6 1128.8 1199.9 71.2 : 71.2 142.3 213.5 244.2 315.4 386.5 457.7 528.8 600.0 671.1 742.3 813.4 844.2 915.3 986.5 1057.6 1128.8 1199.9 142.3 : 71.2 142.3 173.1 244.2 315.4 386.5 457.7 528.8 600.0 671.1 742.3 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 213.5 : 71.2 101.9 173.1 244.2 315.4 386.5 457.7 528.8 600.0 671.1 701.9 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 284.6 : 30.8 101.9 173.1 244.2 315.4 386.5 457.7 528.8 600.0 630.7 701.9 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 315.4 : 71.2 142.3 213.5 284.6 355.8 426.9 498.1 569.2 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1098.0 1169.2 1199.9 386.5 : 71.2 142.3 213.5 284.6 355.8 426.9 498.1 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1098.0 1128.8 1199.9 457.7 : 71.2 142.3 213.5 284.6 355.7 426.9 457.7 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1057.6 1128.8 1199.9 528.8 : 71.2 142.3 213.5 284.6 355.8 386.5 457.7 528.8 600.0 671.1 742.3 813.4 884.6 955.7 986.5 1057.6 1128.8 1199.9 600.0 : 71.2 142.3 213.5 284.6 315.4 386.5 457.7 528.8 600.0 671.1 742.3 813.4 884.6 915.3 986.5 1057.6 1128.8 1199.9 671.1 : 71.2 142.3 213.5 244.2 315.4 386.5 457.7 528.8 600.0 671.1 742.3 813.4 844.2 915.3 986.5 1057.6 1128.8 1199.9 742.3 : 71.2 142.3 173.1 244.2 315.4 386.5 457.7 528.8 600.0 671.1 742.3 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 813.4 : 71.2 101.9 173.1 244.2 315.4 386.5 457.7 528.8 600.0 671.1 701.9 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 884.6 : 30.8 101.9 173.1 244.2 315.4 386.5 457.7 528.8 600.0 630.7 701.9 773.0 844.2 915.3 986.5 1057.6 1128.8 1199.9 915.3 : 71.2 142.3 213.5 284.6 355.8 426.9 498.1 569.2 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1098.0 1169.2 1199.9 986.5 : 71.2 142.3 213.5 284.6 355.7 426.9 498.0 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1098.0 1128.8 1199.9 1057.6: 71.2 142.3 213.5 284.6 355.7 426.9 457.7 528.8 600.0 671.1 742.3 813.4 884.6 955.7 1026.9 1057.6 1128.8 1199.9 1128.8: 71.2 142.3 213.5 284.6 355.8 386.5 457.7 528.8 600.0 671.1 742.3 813.4 884.6 955.7 986.5 1057.6 1128.8 1199.9 1199.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.7700 .. 71.1500 cents 40.38000 cents 30.77000 cents 2: 101.9200 .. 142.3000 cents 40.38000 cents 30.77000 cents 3: 173.0700 .. 213.4500 cents 40.38000 cents 30.77000 cents 4: 244.2200 .. 284.6000 cents 40.38000 cents 30.77000 cents 5: 315.3700 .. 355.7500 cents 40.38000 cents 30.77000 cents 6: 386.5200 .. 426.9000 cents 40.38000 cents 30.77000 cents 7: 457.6700 .. 498.0500 cents 40.38000 cents 30.77000 cents 8: 528.8200 .. 569.2000 cents 40.38000 cents 30.77000 cents 9: 599.9700 .. 599.9700 cents 1/1, 0.0000 cents 30.77000 cents 10: 630.7400 .. 671.1200 cents 40.38000 cents 30.77000 cents 11: 701.8900 .. 742.2700 cents 40.38000 cents 30.77000 cents 12: 773.0400 .. 813.4200 cents 40.38000 cents 30.77000 cents 13: 844.1900 .. 884.5700 cents 40.38000 cents 30.77000 cents 14: 915.3400 .. 955.7200 cents 40.38000 cents 30.77000 cents 15: 986.4900 .. 1026.8700 cents 40.38000 cents 30.77000 cents 16: 1057.6400 .. 1098.0200 cents 40.38000 cents 30.77000 cents 17: 1128.7900 .. 1169.1700 cents 40.38000 cents 30.77000 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 30.77000 cents, class 1 Average step (divided formal octave): 66.6633 cents Largest one step interval : 71.15000 cents Average / Smallest step : 2.166504 Largest / Average step : 1.067303 Largest / Smallest step : 2.312317 Median interval of one step : 71.15000 cents, amount: 16 Most common interval of one step : 71.15000 cents, amount: 16 Least squares average step : 66.53569 cents, oct.: 1197.64242 cents Scale is strictly proper Scale has 2 repeating blocks of 9 notes Blocks have Myhill's property chromas: 40.38000 cents and 9.61000 cents, ratio: 4.201873 generators: 1 of 71.15000 cents and 8 of 528.82000 cents ET pair of linear temperament : 34&118 Scale is distributional even Scale is a mode of a 624-tone equal temperament with octave 1199.940 cents degrees: 37 74 111 148 164 201 238 275 312 349 386 423 460 476 513 550 587 624 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: 321 = 303 more = 1783.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAAAAABAAAA Step pattern size order : LLLLSLLLLLLLLSLLLL Scale is a Constant Structure, by a margin of 30.77000 cents Scale diversity : 1.213734 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.461573 Number of different interval sizes : 33 = 1.94118 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.94118 = 33/17 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 30.77000 cents Most common intervals : 599.97000 cents & inv., amount: 18 Number of recognisable fifths : 4, average 701.8900 cents Number of recognisable fourths : 4, average 498.0500 cents Scale contains two identical disjunct "tetrachords" of 9 notes Formal octave complements present : 18 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 9 Limited inverse transpositions : 9 Inversional symmetry on degrees : 0 9 Inversional symmetry on intervals : 4-5 13-14 -- Rational properties --
FIT/MODE
18: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.5845 c. M: 17.9467 c. 28: 2 1 2 2 0 2 2 1 2 2 1 2 2 0 2 2 1 2 P B D3 I SD: 11.9073 c. M: 15.3850 c. 32: 2 2 2 2 0 2 2 2 2 2 2 2 2 0 2 2 2 2 P B DE I SD: 9.9310 c. M: 15.3850 c. 34: 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 SP B ME I SD: 1.4596 c. M: 2.2612 c. 84: 5 5 5 5 2 5 5 5 5 5 5 5 5 2 5 5 5 5 SP B DE I SD: 0.7100 c. M:-1.1000 c. 118: 7 7 7 7 3 7 7 7 7 7 7 7 7 3 7 7 7 7 SP B DE I SD: 0.0849 c. M: 0.1315 c. 388: 23 23 23 23 10 23 23 23 23 23 23 23 23 10 23 23 23 23 SP B DE I SD: 0.0504 c. M: 0.0781 c. 506: 30 30 30 30 13 30 30 30 30 30 30 30 30 13 30 30 30 30 SP B DE I SD: 0.0189 c. M: 0.0292 c. 624: 37 37 37 37 16 37 37 37 37 37 37 37 37 16 37 37 37 37 SP B DE I 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: 10.2586 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: 7.9596 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: 8.2422 cents 10 .. 20 match: 10 H SD: 5.5417 cents 11 .. 22 match: 11 H SD: 5.9780 cents 12 .. 24 match: 12 H SD: 4.5193 cents 13 .. 26 match: 13 H SD: 4.7957 cents 14 .. 28 match: 14 H SD: 5.2997 cents 15 .. 30 match: 14 SD: 4.7559 cents 16 .. 32 match: 15 SD: 5.5539 cents 17 .. 34 match: 16 SD: 3.5592 cents 18 .. 36 match: 16 SD: 5.8579 cents 19 .. 38 match: 16 S SD: 4.4531 cents 20 .. 40 match: 17 SD: 3.6981 cents 21 .. 42 match: 17 SD: 3.7889 cents 22 .. 44 match: 16 SD: 3.5067 cents 23 .. 46 match: 18 SD: 2.9161 cents 24 .. 48 match: 18 SD: 2.7857 cents 25 .. 50 match: 17 SD: 3.1174 cents 26 .. 52 match: 17 SD: 3.0699 cents 27 .. 54 match: 17 SD: 2.9478 cents 30 .. 60 match: 18 SD: 2.6827 cents 31 .. 62 match: 17 SD: 2.7674 cents 32 .. 64 match: 17 SD: 2.5832 cents 33 .. 66 match: 18 SD: 2.4396 cents 36 .. 72 match: 18 SD: 2.1345 cents 37 .. 74 match: 17 SD: 2.3479 cents 39 .. 78 match: 18 SD: 1.7932 cents 42 .. 84 match: 17 SD: 2.4353 cents 43 .. 86 match: 18 SD: 1.8989 cents 44 .. 88 match: 18 SD: 1.6739 cents 45 .. 90 match: 18 SD: 1.3996 cents 56 .. 112 match: 18 SD: 1.3052 cents 60 .. 120 match: 18 SD: 1.2411 cents 67 .. 134 match: 18 SD: 1.1412 cents 68 .. 136 match: 18 SD: 1.1386 cents 69 .. 138 match: 18 SD: 0.9869 cents 84 .. 168 match: 18 SD: 0.9353 cents 89 .. 178 match: 18 SD: 0.8333 cents 90 .. 180 match: 18 SD: 0.7782 cents 95 .. 190 match: 18 SD: 0.6582 cents 112 .. 224 match: 18 SD: 0.6400 cents 116 .. 232 match: 18 SD: 0.5536 cents 129 .. 258 match: 18 SD: 0.5221 cents 135 .. 270 match: 18 SD: 0.5139 cents 139 .. 278 match: 18 SD: 0.5072 cents 140 .. 280 match: 18 SD: 0.4669 cents 145 .. 290 match: 18 SD: 0.4504 cents 152 .. 304 match: 18 SD: 0.4290 cents 165 .. 330 match: 18 SD: 0.4134 cents 184 .. 368 match: 18 SD: 0.3887 cents 185 .. 370 match: 18 SD: 0.3298 cents 215 .. 430 match: 18 SD: 0.3113 cents 220 .. 440 match: 18 SD: 0.3073 cents 234 .. 468 match: 18 SD: 0.3050 cents 235 .. 470 match: 18 SD: 0.2349 cents 280 .. 560 match: 18 SD: 0.2002 cents 336 .. 672 match: 18 SD: 0.1456 cents 420 .. 840 match: 18 SD: 0.1314 cents 525 .. 1050 match: 18 SD: 0.1261 cents 526 .. 1052 match: 18 SD: 0.1250 cents 549 .. 1098 match: 18 SD: 0.1178 cents 570 .. 1140 match: 18 SD: 0.1160 cents 572 .. 1144 match: 18 SD: 0.1060 cents 594 .. 1188 match: 18 SD: 0.0980 cents