Scala analysis: xen18-erlich-srutal-22
12L 10s MOS for Srutal, L=76.06, s=28.64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.060 cents 76.060000 2: 104.700 cents 104.700000 3: 180.760 cents 180.760000 4: 209.400 cents 209.400000 5: 285.460 cents 285.460000 6: 314.100 cents 314.100000 7: 390.160 cents 390.160000 8: 418.800 cents 418.800000 9: 494.860 cents 494.860000 10: 523.500 cents 523.500000 11: 599.560 cents 599.560000 12: 675.620 cents 675.620000 13: 704.260 cents 704.260000 14: 780.320 cents 780.320000 15: 808.960 cents 808.960000 16: 885.020 cents 885.020000 17: 913.660 cents 913.660000 18: 989.720 cents 989.720000 19: 1018.360 cents 1018.360000 20: 1094.420 cents 1094.420000 21: 1123.060 cents 1123.060000 22: 1199.120 cents 1199.120000
SHOW/INTERVAL
0: 76.0600 cents 76.0600 1: 76.0600 cents 76.0600 2: 28.6400 cents 28.6400 3: 76.0600 cents 76.0600 4: 28.6400 cents 28.6400 5: 76.0600 cents 76.0600 6: 28.6400 cents 28.6400 7: 76.0600 cents 76.0600 8: 28.6400 cents 28.6400 9: 76.0600 cents 76.0600 10: 28.6400 cents 28.6400 11: 76.0600 cents 76.0600 12: 76.0600 cents 76.0600 13: 28.6400 cents 28.6400 14: 76.0600 cents 76.0600 15: 28.6400 cents 28.6400 16: 76.0600 cents 76.0600 17: 28.6400 cents 28.6400 18: 76.0600 cents 76.0600 19: 28.6400 cents 28.6400 20: 76.0600 cents 76.0600 21: 28.6400 cents 28.6400 22: 76.0600 cents 76.0600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 28.64000 cents 1: 12 76.06000 cents 2: 20 104.70000 cents 2: 2 152.12000 cents 3: 8 133.34000 cents 3: 14 180.76000 cents 4: 18 209.40000 cents 4: 4 256.82000 cents 5: 6 238.04000 cents 5: 16 285.46000 cents 6: 16 314.10000 cents 6: 6 361.52000 cents 7: 4 342.74000 cents 7: 18 390.16000 cents 8: 14 418.80000 cents 8: 8 466.22000 cents 9: 2 447.44000 cents 9: 20 494.86000 cents 10: 12 523.50000 cents 10: 10 570.92000 cents 11: 22 599.56000 cents 12: 10 628.20000 cents 12: 12 675.62000 cents 13: 20 704.26000 cents 13: 2 751.68000 cents 14: 8 732.90000 cents 14: 14 780.32000 cents 15: 18 808.96000 cents 15: 4 856.38000 cents 16: 6 837.60000 cents 16: 16 885.02000 cents 17: 16 913.66000 cents 17: 6 961.08000 cents 18: 4 942.30000 cents 18: 18 989.72000 cents 19: 14 1018.36000 cents 19: 8 1065.78000 cents 20: 2 1047.00000 cents 20: 20 1094.42000 cents 21: 12 1123.06000 cents 21: 10 1170.48000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.95238 = 41/21
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 : 76.1 104.7 180.8 209.4 285.5 314.1 390.2 418.8 494.9 523.5 599.6 675.6 704.3 780.3 809.0 885.0 913.7 989.7 1018.4 1094.4 1123.1 1199.1 76.1 : 28.6 104.7 133.3 209.4 238.0 314.1 342.7 418.8 447.4 523.5 599.6 628.2 704.3 732.9 809.0 837.6 913.7 942.3 1018.4 1047.0 1123.1 1199.1 104.7 : 76.1 104.7 180.8 209.4 285.5 314.1 390.2 418.8 494.9 570.9 599.6 675.6 704.3 780.3 809.0 885.0 913.7 989.7 1018.4 1094.4 1170.5 1199.1 180.8 : 28.6 104.7 133.3 209.4 238.0 314.1 342.7 418.8 494.9 523.5 599.6 628.2 704.3 732.9 809.0 837.6 913.7 942.3 1018.4 1094.4 1123.1 1199.1 209.4 : 76.1 104.7 180.8 209.4 285.5 314.1 390.2 466.2 494.9 570.9 599.6 675.6 704.3 780.3 809.0 885.0 913.7 989.7 1065.8 1094.4 1170.5 1199.1 285.5 : 28.6 104.7 133.3 209.4 238.0 314.1 390.2 418.8 494.9 523.5 599.6 628.2 704.3 732.9 809.0 837.6 913.7 989.7 1018.4 1094.4 1123.1 1199.1 314.1 : 76.1 104.7 180.8 209.4 285.5 361.5 390.2 466.2 494.9 570.9 599.6 675.6 704.3 780.3 809.0 885.0 961.1 989.7 1065.8 1094.4 1170.5 1199.1 390.2 : 28.6 104.7 133.3 209.4 285.5 314.1 390.2 418.8 494.9 523.5 599.6 628.2 704.3 732.9 809.0 885.0 913.7 989.7 1018.4 1094.4 1123.1 1199.1 418.8 : 76.1 104.7 180.8 256.8 285.5 361.5 390.2 466.2 494.9 570.9 599.6 675.6 704.3 780.3 856.4 885.0 961.1 989.7 1065.8 1094.4 1170.5 1199.1 494.9 : 28.6 104.7 180.8 209.4 285.5 314.1 390.2 418.8 494.9 523.5 599.6 628.2 704.3 780.3 809.0 885.0 913.7 989.7 1018.4 1094.4 1123.1 1199.1 523.5 : 76.1 152.1 180.8 256.8 285.5 361.5 390.2 466.2 494.9 570.9 599.6 675.6 751.7 780.3 856.4 885.0 961.1 989.7 1065.8 1094.4 1170.5 1199.1 599.6 : 76.1 104.7 180.8 209.4 285.5 314.1 390.2 418.8 494.9 523.5 599.6 675.6 704.3 780.3 809.0 885.0 913.7 989.7 1018.4 1094.4 1123.1 1199.1 675.6 : 28.6 104.7 133.3 209.4 238.0 314.1 342.7 418.8 447.4 523.5 599.6 628.2 704.3 732.9 809.0 837.6 913.7 942.3 1018.4 1047.0 1123.1 1199.1 704.3 : 76.1 104.7 180.8 209.4 285.5 314.1 390.2 418.8 494.9 570.9 599.6 675.6 704.3 780.3 809.0 885.0 913.7 989.7 1018.4 1094.4 1170.5 1199.1 780.3 : 28.6 104.7 133.3 209.4 238.0 314.1 342.7 418.8 494.9 523.5 599.6 628.2 704.3 732.9 809.0 837.6 913.7 942.3 1018.4 1094.4 1123.1 1199.1 809.0 : 76.1 104.7 180.8 209.4 285.5 314.1 390.2 466.2 494.9 570.9 599.6 675.6 704.3 780.3 809.0 885.0 913.7 989.7 1065.8 1094.4 1170.5 1199.1 885.0 : 28.6 104.7 133.3 209.4 238.0 314.1 390.2 418.8 494.9 523.5 599.6 628.2 704.3 732.9 809.0 837.6 913.7 989.7 1018.4 1094.4 1123.1 1199.1 913.7 : 76.1 104.7 180.8 209.4 285.5 361.5 390.2 466.2 494.9 570.9 599.6 675.6 704.3 780.3 809.0 885.0 961.1 989.7 1065.8 1094.4 1170.5 1199.1 989.7 : 28.6 104.7 133.3 209.4 285.5 314.1 390.2 418.8 494.9 523.5 599.6 628.2 704.3 732.9 809.0 885.0 913.7 989.7 1018.4 1094.4 1123.1 1199.1 1018.4: 76.1 104.7 180.8 256.8 285.5 361.5 390.2 466.2 494.9 570.9 599.6 675.6 704.3 780.3 856.4 885.0 961.1 989.7 1065.8 1094.4 1170.5 1199.1 1094.4: 28.6 104.7 180.8 209.4 285.5 314.1 390.2 418.8 494.9 523.5 599.6 628.2 704.3 780.3 809.0 885.0 913.7 989.7 1018.4 1094.4 1123.1 1199.1 1123.1: 76.1 152.1 180.8 256.8 285.5 361.5 390.2 466.2 494.9 570.9 599.6 675.6 751.7 780.3 856.4 885.0 961.1 989.7 1065.8 1094.4 1170.5 1199.1 1199.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 28.6400 .. 76.0600 cents 47.42000 cents 28.64000 cents 2: 104.7000 .. 152.1200 cents 47.42000 cents 28.64000 cents 3: 133.3400 .. 180.7600 cents 47.42000 cents -18.78000 cents 4: 209.4000 .. 256.8200 cents 47.42000 cents 28.64000 cents 5: 238.0400 .. 285.4600 cents 47.42000 cents -18.78000 cents 6: 314.1000 .. 361.5200 cents 47.42000 cents 28.64000 cents 7: 342.7400 .. 390.1600 cents 47.42000 cents -18.78000 cents 8: 418.8000 .. 466.2200 cents 47.42000 cents 28.64000 cents 9: 447.4400 .. 494.8600 cents 47.42000 cents -18.78000 cents 10: 523.5000 .. 570.9200 cents 47.42000 cents 28.64000 cents 11: 599.5600 .. 599.5600 cents 1/1, 0.0000 cents 28.64000 cents 12: 628.2000 .. 675.6200 cents 47.42000 cents 28.64000 cents 13: 704.2600 .. 751.6800 cents 47.42000 cents 28.64000 cents 14: 732.9000 .. 780.3200 cents 47.42000 cents -18.78000 cents 15: 808.9600 .. 856.3800 cents 47.42000 cents 28.64000 cents 16: 837.6000 .. 885.0200 cents 47.42000 cents -18.78000 cents 17: 913.6600 .. 961.0800 cents 47.42000 cents 28.64000 cents 18: 942.3000 .. 989.7200 cents 47.42000 cents -18.78000 cents 19: 1018.3600 .. 1065.7800 cents 47.42000 cents 28.64000 cents 20: 1047.0000 .. 1094.4200 cents 47.42000 cents -18.78000 cents 21: 1123.0600 .. 1170.4800 cents 47.42000 cents 28.64000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 28.64000 cents, class 1 Average step (divided formal octave): 54.5055 cents Largest one step interval : 76.06000 cents Average / Smallest step : 1.903123 Largest / Average step : 1.395457 Largest / Smallest step : 2.655726 Median interval of one step : 76.06000 cents, amount: 12 Most common interval of one step : 76.06000 cents, amount: 12 Least squares average step : 54.38050 cents, oct.: 1196.37101 cents Scale is not proper Scale has 2 repeating blocks of 11 notes Blocks have Myhill's property chromas: 47.42000 cents and 18.78000 cents, ratio: 2.525027 generators: 2 of 104.70000 cents and 9 of 494.86000 cents ET pair of linear temperament : 34&46 Scale is distributional even Scale is a mode of a 1214-tone equal temperament with octave 1199.120 cents degrees: 77 106 183 212 289 318 395 424 501 530 607 684 713 790 819 896 925 1002 1031 1108 1137 1214 Least number of segments generator : 609 of 601.535 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 713 of 704.261 cents and inv. generated superset size: 618 = 596 more = 2809.091% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABAABABABABABA Step pattern size order : LSLSLSLSLSLLSLSLSLSLSL Scale is a Constant Structure, by a margin of 18.78000 cents Scale diversity : 1.189591 Lumma stability : 0.334379 Lumma impropriety factor : 0.125292 Number of different interval sizes : 41 = 1.95238 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.95238 = 41/21 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 18.78000 cents Most common intervals : 599.56000 cents & inv., amount: 22 Number of recognisable fifths : 20, average 704.2600 cents Number of recognisable fourths : 20, average 494.8600 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 22 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 11 Limited inverse transpositions : 11 Inversional symmetry on degrees : 0 11 Inversional symmetry on intervals : 5-6 16-17 -- 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: 13.6323 c. M: 21.5545 c. 26: 2 0 2 1 1 1 1 1 2 0 2 2 0 2 1 1 1 1 1 2 0 2 N B D3 I SD: 13.1889 c. M: 21.2000 c. 27: 2 0 2 1 1 1 2 0 2 1 1 2 1 2 0 2 1 1 1 2 0 2 N D3 SD: 12.7469 c. M: 22.2059 c. 28: 2 0 2 1 2 0 2 1 2 0 2 2 0 2 1 2 0 2 1 2 0 2 N B D3 I SD: 11.8452 c. M: 19.0486 c. 30: 2 1 2 0 2 1 2 0 2 1 2 2 1 2 0 2 1 2 0 2 1 2 N B I SD: 11.5543 c. M: 19.0933 c. 32: 2 1 2 1 2 0 2 1 2 1 2 2 1 2 1 2 0 2 1 2 1 2 N B D3 I SD: 9.9790 c. M: 15.4350 c. 34: 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 P B ME I SD: 3.4934 c. M: 5.5235 c. 46: 3 1 3 1 3 1 3 1 3 1 3 3 1 3 1 3 1 3 1 3 1 3 N B DE I SD: 1.3557 c. M: 2.1435 c. 80: 5 2 5 2 5 2 5 2 5 2 5 5 2 5 2 5 2 5 2 5 2 5 N B DE I SD: 0.7052 c. M: 1.1150 c. 126: 8 3 8 3 8 3 8 3 8 3 8 8 3 8 3 8 3 8 3 8 3 8 N B DE I SD: 0.0472 c. M: 0.0746 c. 710: 45 17 45 17 45 17 45 17 45 17 45 45 17 45 17 45 17 45 17 45 17 45 N B DE I SD: 0.0376 c. M: 0.0594 c. 836: 53 20 53 20 53 20 53 20 53 20 53 53 20 53 20 53 20 53 20 53 20 53 N B DE I SD: 0.0248 c. M: 0.0392 c. 962: 61 23 61 23 61 23 61 23 61 23 61 61 23 61 23 61 23 61 23 61 23 61 N B DE I SD: 0.0154 c. M: 0.0243 c. 1088: 69 26 69 26 69 26 69 26 69 26 69 69 26 69 26 69 26 69 26 69 26 69 N B DE I SD: 0.0081 c. M: 0.0129 c. 1214: 77 29 77 29 77 29 77 29 77 29 77 77 29 77 29 77 29 77 29 77 29 77 N B DE I SD: 0.0024 c. M: 0.0038 c. 1340: 85 32 85 32 85 32 85 32 85 32 85 85 32 85 32 85 32 85 32 85 32 85 N B DE I SD: 0.0023 c. M: 0.0036 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.8800 cents 2 .. 4 match: 2 H SD: 1.2336 cents 3 .. 6 match: 3 H SD: 1.1233 cents 4 .. 8 match: 4 H SD: 5.3470 cents 5 .. 10 match: 5 H SD: 3.5592 cents 6 .. 12 match: 6 H SD: 6.0631 cents 7 .. 14 match: 7 H SD: 6.3267 cents 8 .. 16 match: 8 H SD: 5.9893 cents 9 .. 18 match: 9 H SD: 5.8988 cents 10 .. 20 match: 10 H SD: 4.4608 cents 11 .. 22 match: 11 H SD: 6.3910 cents 12 .. 24 match: 12 H SD: 4.6579 cents 13 .. 26 match: 13 H SD: 7.0218 cents 14 .. 28 match: 14 H SD: 4.3705 cents 15 .. 30 match: 14 SD: 3.5586 cents 16 .. 32 match: 16 H SD: 4.2270 cents 17 .. 34 match: 17 H SD: 3.8909 cents 18 .. 36 match: 15 SD: 4.1820 cents 19 .. 38 match: 15 S SD: 4.1306 cents 20 .. 40 match: 16 SD: 3.4946 cents 21 .. 42 match: 18 S SD: 3.5378 cents 22 .. 44 match: 16 SD: 3.0263 cents 23 .. 46 match: 17 SD: 3.1253 cents 24 .. 48 match: 18 SD: 3.2191 cents 25 .. 50 match: 20 SD: 3.0552 cents 26 .. 52 match: 17 SD: 2.5216 cents 27 .. 54 match: 19 SD: 2.5535 cents 28 .. 56 match: 20 SD: 2.8507 cents 29 .. 58 match: 19 SD: 2.5623 cents 30 .. 60 match: 21 SD: 2.3019 cents 31 .. 62 match: 19 SD: 2.4633 cents 32 .. 64 match: 19 SD: 2.1748 cents 33 .. 66 match: 21 SD: 2.3824 cents 34 .. 68 match: 19 SD: 1.7492 cents 35 .. 70 match: 20 SD: 2.2539 cents 36 .. 72 match: 20 SD: 1.7841 cents 37 .. 74 match: 20 SD: 2.0389 cents 38 .. 76 match: 19 SD: 2.2883 cents 39 .. 78 match: 21 SD: 1.6085 cents 40 .. 80 match: 21 SD: 1.5039 cents 41 .. 82 match: 20 SD: 2.2212 cents 42 .. 84 match: 19 SD: 1.7841 cents 44 .. 88 match: 22 SD: 1.4398 cents 45 .. 90 match: 22 SD: 1.4128 cents 46 .. 92 match: 22 SD: 1.3169 cents 50 .. 100 match: 21 SD: 1.5435 cents 51 .. 102 match: 22 SD: 1.3638 cents 54 .. 108 match: 22 SD: 1.3493 cents 56 .. 112 match: 21 SD: 1.2656 cents 60 .. 120 match: 22 SD: 1.1192 cents 62 .. 124 match: 22 SD: 1.0877 cents 63 .. 126 match: 22 SD: 1.0860 cents 65 .. 130 match: 22 SD: 1.0341 cents 66 .. 132 match: 22 SD: 1.0272 cents 70 .. 140 match: 22 SD: 0.9545 cents 79 .. 158 match: 22 SD: 0.8331 cents 84 .. 168 match: 22 SD: 0.6850 cents 91 .. 182 match: 22 SD: 0.6569 cents 102 .. 204 match: 22 SD: 0.6479 cents 109 .. 218 match: 22 SD: 0.6166 cents 111 .. 222 match: 22 SD: 0.4653 cents 155 .. 310 match: 22 SD: 0.4356 cents 157 .. 314 match: 22 SD: 0.4105 cents 161 .. 322 match: 22 SD: 0.3594 cents 193 .. 386 match: 22 SD: 0.3213 cents 201 .. 402 match: 22 SD: 0.3147 cents 218 .. 436 match: 22 SD: 0.3115 cents 226 .. 452 match: 22 SD: 0.2919 cents 227 .. 454 match: 22 SD: 0.2570 cents 241 .. 482 match: 22 SD: 0.2546 cents 272 .. 544 match: 22 SD: 0.2308 cents 285 .. 570 match: 22 SD: 0.2233 cents 289 .. 578 match: 22 SD: 0.2120 cents 311 .. 622 match: 22 SD: 0.2069 cents 312 .. 624 match: 22 SD: 0.2061 cents 335 .. 670 match: 22 SD: 0.1976 cents 336 .. 672 match: 22 SD: 0.1681 cents 357 .. 714 match: 22 SD: 0.1668 cents 381 .. 762 match: 22 SD: 0.1562 cents 402 .. 804 match: 22 SD: 0.1502 cents 442 .. 884 match: 22 SD: 0.1461 cents 462 .. 924 match: 22 SD: 0.1461 cents 467 .. 934 match: 22 SD: 0.1439 cents 482 .. 964 match: 22 SD: 0.1427 cents 490 .. 980 match: 22 SD: 0.1279 cents 498 .. 995 match: 22 SD: 0.1250 cents 529 .. 1057 match: 22 SD: 0.1204 cents 558 .. 1115 match: 22 SD: 0.1196 cents 562 .. 1123 match: 22 SD: 0.1177 cents 574 .. 1147 match: 22 SD: 0.0951 cents