Scala analysis: xen18-erlich-superpyth-22
5L 17s MOS for Superpyth, L=62.89, s=51.95
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51.950 cents 51.950000 2: 103.900 cents 103.900000 3: 166.790 cents 166.790000 4: 218.740 cents 218.740000 5: 270.690 cents 270.690000 6: 322.640 cents 322.640000 7: 385.530 cents 385.530000 8: 437.480 cents 437.480000 9: 489.430 cents 489.430000 10: 541.380 cents 541.380000 11: 593.330 cents 593.330000 12: 656.220 cents 656.220000 13: 708.170 cents 708.170000 14: 760.120 cents 760.120000 15: 812.070 cents 812.070000 16: 874.960 cents 874.960000 17: 926.910 cents 926.910000 18: 978.860 cents 978.860000 19: 1030.810 cents 1030.810000 20: 1093.700 cents 1093.700000 21: 1145.650 cents 1145.650000 22: 1197.600 cents 1197.600000
SHOW/INTERVAL
0: 51.9500 cents 51.9500 1: 51.9500 cents 51.9500 2: 51.9500 cents 51.9500 3: 62.8900 cents 62.8900 4: 51.9500 cents 51.9500 5: 51.9500 cents 51.9500 6: 51.9500 cents 51.9500 7: 62.8900 cents 62.8900 8: 51.9500 cents 51.9500 9: 51.9500 cents 51.9500 10: 51.9500 cents 51.9500 11: 51.9500 cents 51.9500 12: 62.8900 cents 62.8900 13: 51.9500 cents 51.9500 14: 51.9500 cents 51.9500 15: 51.9500 cents 51.9500 16: 62.8900 cents 62.8900 17: 51.9500 cents 51.9500 18: 51.9500 cents 51.9500 19: 51.9500 cents 51.9500 20: 62.8900 cents 62.8900 21: 51.9500 cents 51.9500 22: 51.9500 cents 51.9500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 17 51.95000 cents 1: 5 62.89000 cents 2: 12 103.90000 cents 2: 10 114.84000 cents 3: 7 155.85000 cents 3: 15 166.79000 cents 4: 2 207.80000 cents 4: 20 218.74000 cents 5: 19 270.69000 cents 5: 3 281.63000 cents 6: 14 322.64000 cents 6: 8 333.58000 cents 7: 9 374.59000 cents 7: 13 385.53000 cents 8: 4 426.54000 cents 8: 18 437.48000 cents 9: 21 489.43000 cents 9: 1 500.37000 cents 10: 16 541.38000 cents 10: 6 552.32000 cents 11: 11 593.33000 cents 11: 11 604.27000 cents 12: 6 645.28000 cents 12: 16 656.22000 cents 13: 1 697.23000 cents 13: 21 708.17000 cents 14: 18 760.12000 cents 14: 4 771.06000 cents 15: 13 812.07000 cents 15: 9 823.01000 cents 16: 8 864.02000 cents 16: 14 874.96000 cents 17: 3 915.97000 cents 17: 19 926.91000 cents 18: 20 978.86000 cents 18: 2 989.80000 cents 19: 15 1030.81000 cents 19: 7 1041.75000 cents 20: 10 1082.76000 cents 20: 12 1093.70000 cents 21: 5 1134.71000 cents 21: 17 1145.65000 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 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.0 : 51.9 103.9 166.8 218.7 270.7 322.6 385.5 437.5 489.4 541.4 593.3 656.2 708.2 760.1 812.1 875.0 926.9 978.9 1030.8 1093.7 1145.7 1197.6 51.9 : 51.9 114.8 166.8 218.7 270.7 333.6 385.5 437.5 489.4 541.4 604.3 656.2 708.2 760.1 823.0 875.0 926.9 978.9 1041.8 1093.7 1145.6 1197.6 103.9 : 62.9 114.8 166.8 218.7 281.6 333.6 385.5 437.5 489.4 552.3 604.3 656.2 708.2 771.1 823.0 875.0 926.9 989.8 1041.8 1093.7 1145.7 1197.6 166.8 : 52.0 103.9 155.9 218.7 270.7 322.6 374.6 426.5 489.4 541.4 593.3 645.3 708.2 760.1 812.1 864.0 926.9 978.9 1030.8 1082.8 1134.7 1197.6 218.7 : 51.9 103.9 166.8 218.7 270.7 322.6 374.6 437.5 489.4 541.4 593.3 656.2 708.2 760.1 812.1 875.0 926.9 978.9 1030.8 1082.8 1145.6 1197.6 270.7 : 51.9 114.8 166.8 218.7 270.7 322.6 385.5 437.5 489.4 541.4 604.3 656.2 708.2 760.1 823.0 875.0 926.9 978.9 1030.8 1093.7 1145.6 1197.6 322.6 : 62.9 114.8 166.8 218.7 270.7 333.6 385.5 437.5 489.4 552.3 604.3 656.2 708.2 771.1 823.0 875.0 926.9 978.9 1041.7 1093.7 1145.6 1197.6 385.5 : 51.9 103.9 155.9 207.8 270.7 322.6 374.6 426.5 489.4 541.4 593.3 645.3 708.2 760.1 812.1 864.0 916.0 978.9 1030.8 1082.8 1134.7 1197.6 437.5 : 51.9 103.9 155.8 218.7 270.7 322.6 374.6 437.5 489.4 541.4 593.3 656.2 708.2 760.1 812.1 864.0 926.9 978.9 1030.8 1082.8 1145.6 1197.6 489.4 : 51.9 103.9 166.8 218.7 270.7 322.6 385.5 437.5 489.4 541.4 604.3 656.2 708.2 760.1 812.1 875.0 926.9 978.9 1030.8 1093.7 1145.6 1197.6 541.4 : 51.9 114.8 166.8 218.7 270.7 333.6 385.5 437.5 489.4 552.3 604.3 656.2 708.2 760.1 823.0 875.0 926.9 978.9 1041.8 1093.7 1145.6 1197.6 593.3 : 62.9 114.8 166.8 218.7 281.6 333.6 385.5 437.5 500.4 552.3 604.3 656.2 708.2 771.1 823.0 875.0 926.9 989.8 1041.8 1093.7 1145.6 1197.6 656.2 : 51.9 103.9 155.9 218.7 270.7 322.6 374.6 437.5 489.4 541.4 593.3 645.3 708.2 760.1 812.1 864.0 926.9 978.9 1030.8 1082.8 1134.7 1197.6 708.2 : 51.9 103.9 166.8 218.7 270.7 322.6 385.5 437.5 489.4 541.4 593.3 656.2 708.2 760.1 812.1 875.0 926.9 978.9 1030.8 1082.8 1145.6 1197.6 760.1 : 51.9 114.8 166.8 218.7 270.7 333.6 385.5 437.5 489.4 541.4 604.3 656.2 708.2 760.1 823.0 875.0 926.9 978.9 1030.8 1093.7 1145.6 1197.6 812.1 : 62.9 114.8 166.8 218.7 281.6 333.6 385.5 437.5 489.4 552.3 604.3 656.2 708.2 771.1 823.0 875.0 926.9 978.9 1041.8 1093.7 1145.6 1197.6 875.0 : 51.9 103.9 155.8 218.7 270.7 322.6 374.6 426.5 489.4 541.4 593.3 645.3 708.2 760.1 812.1 864.0 916.0 978.9 1030.8 1082.8 1134.7 1197.6 926.9 : 51.9 103.9 166.8 218.7 270.7 322.6 374.6 437.5 489.4 541.4 593.3 656.2 708.2 760.1 812.1 864.0 926.9 978.9 1030.8 1082.8 1145.6 1197.6 978.9 : 51.9 114.8 166.8 218.7 270.7 322.6 385.5 437.5 489.4 541.4 604.3 656.2 708.2 760.1 812.1 875.0 926.9 978.9 1030.8 1093.7 1145.7 1197.6 1030.8: 62.9 114.8 166.8 218.7 270.7 333.6 385.5 437.5 489.4 552.3 604.3 656.2 708.2 760.1 823.0 875.0 926.9 978.9 1041.8 1093.7 1145.6 1197.6 1093.7: 52.0 103.9 155.9 207.8 270.7 322.6 374.6 426.5 489.4 541.4 593.3 645.3 697.2 760.1 812.1 864.0 916.0 978.9 1030.8 1082.8 1134.7 1197.6 1145.7: 51.9 103.9 155.8 218.7 270.7 322.6 374.6 437.5 489.4 541.4 593.3 645.3 708.2 760.1 812.1 864.0 926.9 978.9 1030.8 1082.8 1145.6 1197.6 1197.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.9500 .. 62.8900 cents 10.94000 cents 51.95000 cents 2: 103.9000 .. 114.8400 cents 10.94000 cents 41.01000 cents 3: 155.8500 .. 166.7900 cents 10.94000 cents 41.01000 cents 4: 207.8000 .. 218.7400 cents 10.94000 cents 41.01000 cents 5: 270.6900 .. 281.6300 cents 10.94000 cents 51.95000 cents 6: 322.6400 .. 333.5800 cents 10.94000 cents 41.01000 cents 7: 374.5900 .. 385.5300 cents 10.94000 cents 41.01000 cents 8: 426.5400 .. 437.4800 cents 10.94000 cents 41.01000 cents 9: 489.4300 .. 500.3700 cents 10.94000 cents 51.95000 cents 10: 541.3800 .. 552.3200 cents 10.94000 cents 41.01000 cents 11: 593.3300 .. 604.2700 cents 10.94000 cents 41.01000 cents 12: 645.2800 .. 656.2200 cents 10.94000 cents 41.01000 cents 13: 697.2300 .. 708.1700 cents 10.94000 cents 41.01000 cents 14: 760.1200 .. 771.0600 cents 10.94000 cents 51.95000 cents 15: 812.0700 .. 823.0100 cents 10.94000 cents 41.01000 cents 16: 864.0200 .. 874.9600 cents 10.94000 cents 41.01000 cents 17: 915.9700 .. 926.9100 cents 10.94000 cents 41.01000 cents 18: 978.8600 .. 989.8000 cents 10.94000 cents 51.95000 cents 19: 1030.8100 .. 1041.7500 cents 10.94000 cents 41.01000 cents 20: 1082.7600 .. 1093.7000 cents 10.94000 cents 41.01000 cents 21: 1134.7100 .. 1145.6500 cents 10.94000 cents 41.01000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 51.95000 cents, class 1 Average step (divided formal octave): 54.4364 cents Largest one step interval : 62.89000 cents Average / Smallest step : 1.047861 Largest / Average step : 1.155294 Largest / Smallest step : 1.210587 Median interval of one step : 51.95000 cents, amount: 17 Most common interval of one step : 51.95000 cents, amount: 17 Least squares average step : 54.44357 cents, oct.: 1197.75855 cents Scale is strictly proper Scale has Myhill's property chromas: 10.94000 cents and 41.01000 cents, ratio: 3.748629 generators: 9 of 489.43000 cents and 13 of 708.17000 cents ET pair of linear temperament : 22&93 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 438-tone equal temperament with octave 1197.600 cents degrees: 19 38 61 80 99 118 141 160 179 198 217 240 259 278 297 320 339 358 377 400 419 438 generators: 179 and 259 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAAABAAABAAABAA Step pattern size order : SSLSSSLSSSSLSSSLSSSLSS Scale is a Constant Structure, by a margin of 41.01000 cents Scale diversity : 1.117259 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.808166 Rothenberg efficiency : 0.696970 redundancy: 0.303030 Efficiency x scale size : 15.333333 Number of different interval sizes : 42 = 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 : 10.94000 cents Most common intervals : 489.43000 cents & inv., amount: 21 Scale is a chain of 11 triads 0.0 103.900 708.170 cents Most common triad is 0.0 489.430 708.170 cents, amount: 20 Number of recognisable fifths : 22, average 707.6727 cents Number of recognisable fourths : 22, average 489.9273 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 21 = 95.4545% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 15-16 -- Rational properties --
FIT/MODE
22: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 3.1646 c. M:-5.4700 c. 71: 3 3 4 3 3 3 4 3 3 3 3 4 3 3 3 4 3 3 3 4 3 3 SP M ME SD: 1.7147 c. M: 2.9638 c. 93: 4 4 5 4 4 4 5 4 4 4 4 5 4 4 4 5 4 4 4 5 4 4 SP M ME SD: 0.5604 c. M: 0.9687 c. 115: 5 5 6 5 5 5 6 5 5 5 5 6 5 5 5 6 5 5 5 6 5 5 SP M ME SD: 0.1522 c. M:-0.2630 c. 323: 14 14 17 14 14 14 17 14 14 14 14 17 14 14 14 17 14 14 14 17 14 14 SP M DE SD: 0.0530 c. M: 0.0916 c. 438: 19 19 23 19 19 19 23 19 19 19 19 23 19 19 19 23 19 19 19 23 19 19 SP M DE SD: 0.0009 c. M:-0.0015 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 2.4000 cents 2 .. 4 match: 2 H SD: 3.3311 cents 3 .. 6 match: 3 H SD: 4.3245 cents 4 .. 8 match: 4 H SD: 3.0175 cents 5 .. 10 match: 5 H SD: 3.7362 cents 6 .. 12 match: 6 H SD: 3.9642 cents 7 .. 14 match: 7 H SD: 6.0150 cents 8 .. 16 match: 8 H SD: 4.5134 cents 9 .. 18 match: 9 H SD: 4.6926 cents 10 .. 20 match: 10 H SD: 3.2333 cents 11 .. 22 match: 11 H SD: 4.7067 cents 12 .. 24 match: 12 H SD: 3.9114 cents 13 .. 26 match: 13 H SD: 5.3914 cents 14 .. 28 match: 14 H SD: 4.1237 cents 15 .. 30 match: 15 H SD: 3.2828 cents 16 .. 32 match: 16 H SD: 3.7843 cents 17 .. 34 match: 17 H SD: 3.0656 cents 18 .. 36 match: 18 H SD: 3.2787 cents 19 .. 38 match: 18 S SD: 4.0551 cents 20 .. 40 match: 19 S SD: 2.8267 cents 21 .. 42 match: 20 S SD: 3.5289 cents 22 .. 44 match: 20 SD: 3.3384 cents 23 .. 46 match: 20 SD: 3.7046 cents 24 .. 48 match: 21 SD: 2.6209 cents 25 .. 50 match: 21 SD: 3.0965 cents 26 .. 52 match: 21 SD: 3.6874 cents 27 .. 54 match: 22 SD: 2.8806 cents 28 .. 56 match: 22 SD: 2.3243 cents 30 .. 60 match: 22 SD: 2.0738 cents 35 .. 70 match: 22 SD: 1.9443 cents 37 .. 74 match: 22 SD: 1.8800 cents 43 .. 86 match: 22 SD: 1.7661 cents 44 .. 88 match: 22 SD: 1.7210 cents 47 .. 94 match: 22 SD: 1.6340 cents 48 .. 96 match: 22 SD: 1.6214 cents 49 .. 98 match: 22 SD: 1.3358 cents 52 .. 104 match: 22 SD: 1.2227 cents 58 .. 116 match: 22 SD: 1.1830 cents 59 .. 118 match: 22 SD: 0.9997 cents 65 .. 130 match: 22 SD: 0.9554 cents 67 .. 134 match: 22 SD: 0.9370 cents 76 .. 152 match: 22 SD: 0.8787 cents 83 .. 166 match: 22 SD: 0.8699 cents 87 .. 174 match: 22 SD: 0.8381 cents 91 .. 182 match: 22 SD: 0.8343 cents 93 .. 186 match: 22 SD: 0.7566 cents 95 .. 190 match: 22 SD: 0.7244 cents 96 .. 192 match: 22 SD: 0.7042 cents 97 .. 194 match: 22 SD: 0.6702 cents 107 .. 214 match: 22 SD: 0.6468 cents 111 .. 222 match: 22 SD: 0.6220 cents 112 .. 224 match: 22 SD: 0.5990 cents 117 .. 234 match: 22 SD: 0.5427 cents 125 .. 250 match: 22 SD: 0.5155 cents 128 .. 256 match: 22 SD: 0.4779 cents 147 .. 294 match: 22 SD: 0.4451 cents 160 .. 320 match: 22 SD: 0.3975 cents 161 .. 322 match: 22 SD: 0.3935 cents 178 .. 356 match: 22 SD: 0.3860 cents 194 .. 387 match: 22 SD: 0.3680 cents 195 .. 389 match: 22 SD: 0.3519 cents 196 .. 391 match: 22 SD: 0.3019 cents 225 .. 449 match: 22 SD: 0.2840 cents 229 .. 457 match: 22 SD: 0.2571 cents 230 .. 459 match: 22 SD: 0.2550 cents 254 .. 507 match: 22 SD: 0.2291 cents 288 .. 575 match: 22 SD: 0.2196 cents 289 .. 577 match: 22 SD: 0.1861 cents 337 .. 673 match: 22 SD: 0.1789 cents 354 .. 707 match: 22 SD: 0.1759 cents 356 .. 711 match: 22 SD: 0.1640 cents 386 .. 771 match: 22 SD: 0.1327 cents 425 .. 849 match: 22 SD: 0.1276 cents 453 .. 905 match: 22 SD: 0.1168 cents 484 .. 967 match: 22 SD: 0.1153 cents 521 .. 1041 match: 22 SD: 0.1091 cents 566 .. 1130 match: 22 SD: 0.1047 cents 585 .. 1168 match: 22 SD: 0.1026 cents