Scala analysis: xen18-erlich-superpyth-17
5L 12s MOS for Superpyth, L=114.84, 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: 166.790 cents 166.790000 3: 218.740 cents 218.740000 4: 270.690 cents 270.690000 5: 322.640 cents 322.640000 6: 437.480 cents 437.480000 7: 489.430 cents 489.430000 8: 541.380 cents 541.380000 9: 656.220 cents 656.220000 10: 708.170 cents 708.170000 11: 760.120 cents 760.120000 12: 874.960 cents 874.960000 13: 926.910 cents 926.910000 14: 978.860 cents 978.860000 15: 1030.810 cents 1030.810000 16: 1145.650 cents 1145.650000 17: 1197.600 cents 1197.600000
SHOW/INTERVAL
0: 51.9500 cents 51.9500 1: 51.9500 cents 51.9500 2: 114.8400 cents 114.8400 3: 51.9500 cents 51.9500 4: 51.9500 cents 51.9500 5: 51.9500 cents 51.9500 6: 114.8400 cents 114.8400 7: 51.9500 cents 51.9500 8: 51.9500 cents 51.9500 9: 114.8400 cents 114.8400 10: 51.9500 cents 51.9500 11: 51.9500 cents 51.9500 12: 114.8400 cents 114.8400 13: 51.9500 cents 51.9500 14: 51.9500 cents 51.9500 15: 51.9500 cents 51.9500 16: 114.8400 cents 114.8400 17: 51.9500 cents 51.9500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 51.95000 cents 1: 5 114.84000 cents 2: 7 103.90000 cents 2: 10 166.79000 cents 3: 2 155.85000 cents 3: 15 218.74000 cents 4: 14 270.69000 cents 4: 3 333.58000 cents 5: 9 322.64000 cents 5: 8 385.53000 cents 6: 4 374.59000 cents 6: 13 437.48000 cents 7: 16 489.43000 cents 7: 1 552.32000 cents 8: 11 541.38000 cents 8: 6 604.27000 cents 9: 6 593.33000 cents 9: 11 656.22000 cents 10: 1 645.28000 cents 10: 16 708.17000 cents 11: 13 760.12000 cents 11: 4 823.01000 cents 12: 8 812.07000 cents 12: 9 874.96000 cents 13: 3 864.02000 cents 13: 14 926.91000 cents 14: 15 978.86000 cents 14: 2 1041.75000 cents 15: 10 1030.81000 cents 15: 7 1093.70000 cents 16: 5 1082.76000 cents 16: 12 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 0.0 : 51.9 166.8 218.7 270.7 322.6 437.5 489.4 541.4 656.2 708.2 760.1 875.0 926.9 978.9 1030.8 1145.7 1197.6 51.9 : 114.8 166.8 218.7 270.7 385.5 437.5 489.4 604.3 656.2 708.2 823.0 875.0 926.9 978.9 1093.7 1145.6 1197.6 166.8 : 52.0 103.9 155.9 270.7 322.6 374.6 489.4 541.4 593.3 708.2 760.1 812.1 864.0 978.9 1030.8 1082.8 1197.6 218.7 : 51.9 103.9 218.7 270.7 322.6 437.5 489.4 541.4 656.2 708.2 760.1 812.1 926.9 978.9 1030.8 1145.6 1197.6 270.7 : 51.9 166.8 218.7 270.7 385.5 437.5 489.4 604.3 656.2 708.2 760.1 875.0 926.9 978.9 1093.7 1145.6 1197.6 322.6 : 114.8 166.8 218.7 333.6 385.5 437.5 552.3 604.3 656.2 708.2 823.0 875.0 926.9 1041.7 1093.7 1145.6 1197.6 437.5 : 51.9 103.9 218.7 270.7 322.6 437.5 489.4 541.4 593.3 708.2 760.1 812.1 926.9 978.9 1030.8 1082.8 1197.6 489.4 : 51.9 166.8 218.7 270.7 385.5 437.5 489.4 541.4 656.2 708.2 760.1 875.0 926.9 978.9 1030.8 1145.6 1197.6 541.4 : 114.8 166.8 218.7 333.6 385.5 437.5 489.4 604.3 656.2 708.2 823.0 875.0 926.9 978.9 1093.7 1145.6 1197.6 656.2 : 51.9 103.9 218.7 270.7 322.6 374.6 489.4 541.4 593.3 708.2 760.1 812.1 864.0 978.9 1030.8 1082.8 1197.6 708.2 : 51.9 166.8 218.7 270.7 322.6 437.5 489.4 541.4 656.2 708.2 760.1 812.1 926.9 978.9 1030.8 1145.6 1197.6 760.1 : 114.8 166.8 218.7 270.7 385.5 437.5 489.4 604.3 656.2 708.2 760.1 875.0 926.9 978.9 1093.7 1145.6 1197.6 875.0 : 51.9 103.9 155.8 270.7 322.6 374.6 489.4 541.4 593.3 645.3 760.1 812.1 864.0 978.9 1030.8 1082.8 1197.6 926.9 : 51.9 103.9 218.7 270.7 322.6 437.5 489.4 541.4 593.3 708.2 760.1 812.1 926.9 978.9 1030.8 1145.6 1197.6 978.9 : 51.9 166.8 218.7 270.7 385.5 437.5 489.4 541.4 656.2 708.2 760.1 875.0 926.9 978.9 1093.7 1145.7 1197.6 1030.8: 114.8 166.8 218.7 333.6 385.5 437.5 489.4 604.3 656.2 708.2 823.0 875.0 926.9 1041.8 1093.7 1145.6 1197.6 1145.7: 51.9 103.9 218.7 270.7 322.6 374.6 489.4 541.4 593.3 708.2 760.1 812.1 926.9 978.9 1030.8 1082.8 1197.6 1197.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.9500 .. 114.8400 cents 62.89000 cents 51.95000 cents 2: 103.9000 .. 166.7900 cents 62.89000 cents -10.94000 cents 3: 155.8500 .. 218.7400 cents 62.89000 cents -10.94000 cents 4: 270.6900 .. 333.5800 cents 62.89000 cents 51.95000 cents 5: 322.6400 .. 385.5300 cents 62.89000 cents -10.94000 cents 6: 374.5900 .. 437.4800 cents 62.89000 cents -10.94000 cents 7: 489.4300 .. 552.3200 cents 62.89000 cents 51.95000 cents 8: 541.3800 .. 604.2700 cents 62.89000 cents -10.94000 cents 9: 593.3300 .. 656.2200 cents 62.89000 cents -10.94000 cents 10: 645.2800 .. 708.1700 cents 62.89000 cents -10.94000 cents 11: 760.1200 .. 823.0100 cents 62.89000 cents 51.95000 cents 12: 812.0700 .. 874.9600 cents 62.89000 cents -10.94000 cents 13: 864.0200 .. 926.9100 cents 62.89000 cents -10.94000 cents 14: 978.8600 .. 1041.7500 cents 62.89000 cents 51.95000 cents 15: 1030.8100 .. 1093.7000 cents 62.89000 cents -10.94000 cents 16: 1082.7600 .. 1145.6500 cents 62.89000 cents -10.94000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 51.95000 cents, class 1 Average step (divided formal octave): 70.4471 cents Largest one step interval : 114.84000 cents Average / Smallest step : 1.356055 Largest / Average step : 1.630160 Largest / Smallest step : 2.210587 Median interval of one step : 51.95000 cents, amount: 12 Most common interval of one step : 51.95000 cents, amount: 12 Least squares average step : 70.51752 cents, oct.: 1198.79790 cents Scale is not proper Scale has Myhill's property chromas: 62.89000 cents and 10.94000 cents, ratio: 5.748629 generators: 7 of 489.43000 cents and 10 of 708.17000 cents ET pair of linear temperament : 22&93 Scale is distributional even Scale is a mode of a 438-tone equal temperament with octave 1197.600 cents degrees: 19 61 80 99 118 160 179 198 240 259 278 320 339 358 377 419 438 generators: 179 and 259 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABAABAAABA Step pattern size order : SLSSSLSSLSSLSSSLS Scale is a Constant Structure, by a margin of 10.94000 cents Scale diversity : 1.155239 Lumma stability : 0.260271 Lumma impropriety factor : 0.100484 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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: 16 Scale is a chain of 8 triads 0.0 489.430 978.860 cents Most common triad is 0.0 489.430 708.170 cents, amount: 15 Number of recognisable fifths : 16, average 708.1700 cents Number of recognisable fourths : 16, average 489.4300 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.1233 c. M: 29.5953 c. 20: 1 2 1 1 0 2 1 1 2 1 1 2 0 1 1 2 1 N D3 I SD: 17.0598 c. M: 28.7100 c. 22: 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1 P M ME I SD: 2.4361 c. M: 3.9782 c. 71: 3 7 3 3 3 7 3 3 7 3 3 7 3 3 3 7 3 N M DE I SD: 1.3200 c. M: 2.1555 c. 93: 4 9 4 4 4 9 4 4 9 4 4 9 4 4 4 9 4 N M DE I SD: 0.4314 c. M: 0.7045 c. 115: 5 11 5 5 5 11 5 5 11 5 5 11 5 5 5 11 5 N M DE I SD: 0.1171 c. M: 0.1913 c. 323: 14 31 14 14 14 31 14 14 31 14 14 31 14 14 14 31 14 N M DE I SD: 0.0408 c. M: 0.0666 c. 438: 19 42 19 19 19 42 19 19 42 19 19 42 19 19 19 42 19 N M DE I SD: 0.0007 c. M: 0.0011 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: 13.1412 cents 5 .. 10 match: 5 H SD: 13.8428 cents 6 .. 12 match: 6 H SD: 3.9642 cents 7 .. 14 match: 7 H SD: 8.8958 cents 8 .. 16 match: 7 S SD: 9.3321 cents 9 .. 18 match: 9 H SD: 6.7762 cents 10 .. 20 match: 10 H SD: 7.9797 cents 11 .. 22 match: 11 H SD: 4.7260 cents 12 .. 24 match: 11 S SD: 6.8696 cents 13 .. 26 match: 12 S SD: 6.5329 cents 14 .. 28 match: 13 SD: 5.8410 cents 15 .. 30 match: 12 SD: 5.2691 cents 16 .. 32 match: 13 SD: 5.7742 cents 17 .. 34 match: 13 SD: 5.0868 cents 18 .. 36 match: 16 SD: 4.4259 cents 19 .. 38 match: 15 SD: 5.3127 cents 20 .. 40 match: 15 SD: 3.7344 cents 21 .. 42 match: 16 SD: 3.6735 cents 23 .. 46 match: 16 SD: 4.2130 cents 24 .. 48 match: 17 SD: 3.0184 cents 25 .. 50 match: 16 SD: 3.4660 cents 26 .. 52 match: 16 SD: 3.9891 cents 27 .. 54 match: 17 SD: 3.4004 cents 28 .. 56 match: 17 SD: 2.4803 cents 30 .. 60 match: 17 SD: 2.0577 cents 38 .. 76 match: 17 SD: 1.8956 cents 46 .. 92 match: 17 SD: 1.8925 cents 49 .. 98 match: 17 SD: 1.6221 cents 52 .. 104 match: 17 SD: 1.4667 cents 58 .. 116 match: 17 SD: 1.1003 cents 59 .. 118 match: 17 SD: 1.0308 cents 76 .. 152 match: 17 SD: 0.9882 cents 87 .. 174 match: 17 SD: 0.8580 cents 89 .. 178 match: 17 SD: 0.8400 cents 96 .. 192 match: 17 SD: 0.7994 cents 97 .. 194 match: 17 SD: 0.7710 cents 98 .. 196 match: 17 SD: 0.7652 cents 107 .. 214 match: 17 SD: 0.6926 cents 111 .. 222 match: 17 SD: 0.6697 cents 117 .. 234 match: 17 SD: 0.6532 cents 125 .. 250 match: 17 SD: 0.6119 cents 126 .. 252 match: 17 SD: 0.5966 cents 128 .. 256 match: 17 SD: 0.5427 cents 141 .. 282 match: 17 SD: 0.5151 cents 147 .. 294 match: 17 SD: 0.5092 cents 156 .. 312 match: 17 SD: 0.4889 cents 160 .. 320 match: 17 SD: 0.4646 cents 171 .. 342 match: 17 SD: 0.4147 cents 195 .. 389 match: 17 SD: 0.3993 cents 196 .. 391 match: 17 SD: 0.3548 cents 199 .. 397 match: 17 SD: 0.3440 cents 226 .. 451 match: 17 SD: 0.3212 cents 229 .. 457 match: 17 SD: 0.2906 cents 230 .. 459 match: 17 SD: 0.2551 cents 254 .. 507 match: 17 SD: 0.2399 cents 267 .. 533 match: 17 SD: 0.2287 cents 289 .. 577 match: 17 SD: 0.2197 cents 297 .. 593 match: 17 SD: 0.2070 cents 327 .. 653 match: 17 SD: 0.1842 cents 356 .. 711 match: 17 SD: 0.1722 cents 386 .. 771 match: 17 SD: 0.1528 cents 425 .. 849 match: 17 SD: 0.1250 cents 566 .. 1130 match: 17 SD: 0.1147 cents