Scala analysis: xen18-schulter-didymic-1-4-17
1/4-Didymic temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.049 cents 76.048999 2: 117.108 cents 117.107858 3: 193.157 cents 193.156857 4: 269.206 cents 269.205856 5: 310.265 cents 310.264715 6: 386.314 cents 386.313714 7: 503.422 cents 503.421572 8: 579.471 cents 579.470571 9: 620.529 cents 620.529429 10: 696.578 cents 696.578428 11: 772.627 cents 772.627428 12: 813.686 cents 813.686286 13: 889.735 cents 889.735285 14: 965.784 cents 965.784285 15: 1006.843 cents 1006.843143 16: 1082.892 cents 1082.892142 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 117.1079 cents 117.1079 1: 76.0490 cents 76.0490 2: 41.0589 cents 41.0589 3: 76.0490 cents 76.0490 4: 76.0490 cents 76.0490 5: 41.0589 cents 41.0589 6: 76.0490 cents 76.0490 7: 117.1079 cents 117.1079 8: 76.0490 cents 76.0490 9: 41.0589 cents 41.0589 10: 76.0490 cents 76.0490 11: 76.0490 cents 76.0490 12: 41.0589 cents 41.0589 13: 76.0490 cents 76.0490 14: 76.0490 cents 76.0490 15: 41.0589 cents 41.0589 16: 76.0490 cents 76.0490 17: 117.1079 cents 117.1079
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 41.05886 cents 1: 10 76.04900 cents 1: 2 117.10786 cents 2: 10 117.10786 cents 2: 3 152.09800 cents 2: 4 193.15686 cents 3: 11 193.15686 cents 3: 4 234.21572 cents 3: 2 269.20586 cents 4: 3 234.21572 cents 4: 6 269.20586 cents 4: 8 310.26472 cents 5: 6 310.26472 cents 5: 1 345.25486 cents 5: 2 351.32357 cents 5: 8 386.31371 cents 6: 5 386.31371 cents 6: 8 427.37257 cents 6: 4 462.36271 cents 7: 1 427.37257 cents 7: 2 462.36271 cents 7: 14 503.42157 cents 8: 2 503.42157 cents 8: 4 544.48043 cents 8: 10 579.47057 cents 8: 1 620.52943 cents 9: 1 579.47057 cents 9: 10 620.52943 cents 9: 4 655.51957 cents 9: 2 696.57843 cents 10: 14 696.57843 cents 10: 2 737.63729 cents 10: 1 772.62743 cents 11: 4 737.63729 cents 11: 8 772.62743 cents 11: 5 813.68629 cents 12: 8 813.68629 cents 12: 2 848.67643 cents 12: 1 854.74514 cents 12: 6 889.73528 cents 13: 8 889.73528 cents 13: 6 930.79414 cents 13: 3 965.78428 cents 14: 2 930.79414 cents 14: 4 965.78429 cents 14: 11 1006.84314 cents 15: 4 1006.84314 cents 15: 3 1047.90200 cents 15: 10 1082.89214 cents 16: 2 1082.89214 cents 16: 10 1123.95100 cents 16: 5 1158.94114 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.25000 = 13/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 76.0 117.1 193.2 269.2 310.3 386.3 503.4 579.5 620.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1200.0 76.0 : 41.1 117.1 193.2 234.2 310.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1124.0 1200.0 117.1 : 76.0 152.1 193.2 269.2 386.3 462.4 503.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1082.9 1158.9 1200.0 193.2 : 76.0 117.1 193.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 772.6 813.7 889.7 1006.8 1082.9 1124.0 1200.0 269.2 : 41.1 117.1 234.2 310.3 351.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 930.8 1006.8 1047.9 1124.0 1200.0 310.3 : 76.0 193.2 269.2 310.3 386.3 462.4 503.4 579.5 655.5 696.6 772.6 889.7 965.8 1006.8 1082.9 1158.9 1200.0 386.3 : 117.1 193.2 234.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 503.4 : 76.0 117.1 193.2 269.2 310.3 386.3 462.4 503.4 579.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1200.0 579.5 : 41.1 117.1 193.2 234.2 310.3 386.3 427.4 503.4 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1124.0 1200.0 620.5 : 76.0 152.1 193.2 269.2 345.3 386.3 462.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1082.9 1158.9 1200.0 696.6 : 76.0 117.1 193.2 269.2 310.3 386.3 503.4 579.5 620.5 696.6 772.6 813.7 889.7 1006.8 1082.9 1124.0 1200.0 772.6 : 41.1 117.1 193.2 234.2 310.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 930.8 1006.8 1047.9 1124.0 1200.0 813.7 : 76.0 152.1 193.2 269.2 386.3 462.4 503.4 579.5 655.5 696.6 772.6 889.7 965.8 1006.8 1082.9 1158.9 1200.0 889.7 : 76.0 117.1 193.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 965.8 : 41.1 117.1 234.2 310.3 351.3 427.4 503.4 544.5 620.5 737.6 813.7 854.7 930.8 1006.8 1047.9 1124.0 1200.0 1006.8: 76.0 193.2 269.2 310.3 386.3 462.4 503.4 579.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1158.9 1200.0 1082.9: 117.1 193.2 234.2 310.3 386.3 427.4 503.4 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 117.1079 cents 76.04900 cents 41.05886 cents 2: 117.1079 .. 193.1569 cents 76.04900 cents 1/1, 0.0000 cents 3: 193.1569 .. 269.2059 cents 76.04900 cents 1/1, 0.0000 cents 4: 234.2157 .. 310.2647 cents 76.04900 cents -34.99014 cents 5: 310.2647 .. 386.3137 cents 76.04900 cents 1/1, 0.0000 cents 6: 386.3137 .. 462.3627 cents 76.04900 cents 1/1, 0.0000 cents 7: 427.3726 .. 503.4216 cents 76.04900 cents -34.99014 cents 8: 503.4216 .. 620.5294 cents 117.10786 cents -0.00000 cents 9: 579.4706 .. 696.5784 cents 117.10786 cents -41.05886 cents 10: 696.5784 .. 772.6274 cents 76.04900 cents -0.00000 cents 11: 737.6373 .. 813.6863 cents 76.04900 cents -34.99014 cents 12: 813.6863 .. 889.7353 cents 76.04900 cents 1/1, 0.0000 cents 13: 889.7353 .. 965.7843 cents 76.04900 cents 1/1, 0.0000 cents 14: 930.7941 .. 1006.8431 cents 76.04900 cents -34.99014 cents 15: 1006.8431 .. 1082.8921 cents 76.04900 cents 1/1, 0.0000 cents 16: 1082.8921 .. 1158.9411 cents 76.04900 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 41.05886 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 117.10786 cents Average / Smallest step : 1.719196 Largest / Average step : 1.659028 Largest / Smallest step : 2.852195 Median interval of one step : 76.04900 cents, amount: 10 Most common interval of one step : 76.04900 cents, amount: 10 Least squares average step : 68.75385 cents, oct.: 1168.81549 cents Scale is not proper Scale is a mode of a 789-tone equal temperament with octave 1200.000 cents degrees: 50 77 127 177 204 254 331 381 408 458 508 535 585 635 662 712 789 Least number of segments generator : 395 of 600.760 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 458 of 696.578 cents and inv. generated superset size: 17 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABACABAABAABAC Step pattern size order : MSMMSMLMSMMSMMSML Scale is not a Constant Structure Scale diversity : 1.216470 Lumma stability : 0.068431 Lumma impropriety factor : 0.150850 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 : 3 Highest interval variety : 4 Mean interval variety : 3.25000 = 13/4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.06872 cents Most common intervals : 503.42157 cents & inv., amount: 16 Scale has Generated (pseudo-Myhill) property, generator: 696.578 cents and inv. Scale is a chain of 8 triads 0.0 503.422 1006.843 cents Most common triad is 0.0 503.422 696.578 cents, amount: 15 Number of recognisable fifths : 16, average 696.5784 cents Scale contains two identical disjunct "tetrachords" of 8 notes Formal octave complements present : 13 = 76.4706% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 11-12 -- Rational properties --
FIT/MODE
17: 1 0 1 1 1 1 2 1 0 1 1 1 1 1 1 1 2 N T3 SD: 40.7060 c. M: 66.7451 c. 18: 1 1 1 1 1 1 2 1 0 1 2 0 1 1 1 1 2 N SD: 19.6862 c. M: 32.4510 c. 19: 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 N D3 S SD: 9.7448 c. M: 18.4159 c. 27: 2 1 1 2 1 2 2 2 1 2 1 1 2 2 1 1 3 N SD: 11.9074 c. M: 17.0719 c. 30: 2 1 2 2 1 2 3 1 2 1 2 1 2 2 1 2 3 N SD: 11.6505 c. M:-19.4706 c. 31: 2 1 2 2 1 2 3 2 1 2 2 1 2 2 1 2 3 N S SD: 1.0359 c. M:-1.9577 c. 112: 7 4 7 7 4 7 11 7 4 7 7 4 7 7 4 7 11 N G S SD: 0.7930 c. M: 1.4986 c. 143: 9 5 9 9 5 9 14 9 5 9 9 5 9 9 5 9 14 N G S SD: 0.3965 c. M: 0.7493 c. 174: 11 6 11 11 6 11 17 11 6 11 11 6 11 11 6 11 17 N G S SD: 0.1413 c. M: 0.2670 c. 205: 13 7 13 13 7 13 20 13 7 13 13 7 13 13 7 13 20 N G S SD: 0.0367 c. M:-0.0694 c. 584: 37 20 37 37 20 37 57 37 20 37 37 20 37 37 20 37 57 N G S SD: 0.0163 c. M: 0.0309 c. 789: 50 27 50 50 27 50 77 50 27 50 50 27 50 50 27 50 77 N G S SD: 0.0025 c. M: 0.0048 c. 1783: 113 61 113 113 61 113 174 113 61 113 113 61 113 113 61 113 174 N G S SD: 0.0020 c. M:-0.0037 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.6883 cents 3 .. 6 match: 3 H SD: 2.5345 cents 4 .. 8 match: 4 H SD: 1.5443 cents 5 .. 10 match: 5 H SD: 2.4802 cents 6 .. 12 match: 6 H SD: 5.8128 cents 7 .. 14 match: 7 H SD: 10.2240 cents 8 .. 16 match: 8 H SD: 5.1474 cents 9 .. 18 match: 9 H SD: 5.3478 cents 10 .. 20 match: 10 H SD: 7.0947 cents 11 .. 22 match: 11 H SD: 8.4639 cents 12 .. 24 match: 11 S SD: 4.3809 cents 13 .. 26 match: 12 S SD: 6.8102 cents 14 .. 28 match: 13 S SD: 6.6128 cents 15 .. 30 match: 14 S SD: 4.3429 cents 16 .. 32 match: 15 S SD: 4.1678 cents 17 .. 34 match: 12 SD: 5.0849 cents 18 .. 36 match: 16 S SD: 4.4080 cents 19 .. 38 match: 14 SD: 4.6711 cents 20 .. 40 match: 16 SD: 3.7530 cents 21 .. 42 match: 15 SD: 4.1561 cents 22 .. 44 match: 15 SD: 4.8880 cents 23 .. 46 match: 17 SD: 3.5258 cents 24 .. 48 match: 15 SD: 2.7327 cents 25 .. 50 match: 17 SD: 2.7158 cents 27 .. 54 match: 16 SD: 2.8067 cents 28 .. 56 match: 16 SD: 2.5130 cents 33 .. 66 match: 16 SD: 2.8665 cents 34 .. 68 match: 16 SD: 3.0638 cents 35 .. 70 match: 16 SD: 2.2873 cents 40 .. 80 match: 17 SD: 1.9404 cents 41 .. 82 match: 17 SD: 1.7927 cents 42 .. 84 match: 17 SD: 1.7424 cents 47 .. 94 match: 17 SD: 1.7185 cents 48 .. 96 match: 17 SD: 1.5309 cents 53 .. 106 match: 17 SD: 1.5146 cents 59 .. 118 match: 17 SD: 1.4777 cents 60 .. 120 match: 17 SD: 1.0300 cents 67 .. 134 match: 17 SD: 1.0248 cents 71 .. 142 match: 17 SD: 0.9399 cents 83 .. 166 match: 17 SD: 0.7899 cents 91 .. 182 match: 17 SD: 0.7874 cents 95 .. 190 match: 17 SD: 0.7670 cents 103 .. 206 match: 17 SD: 0.7451 cents 107 .. 214 match: 17 SD: 0.7408 cents 112 .. 224 match: 17 SD: 0.6495 cents 113 .. 226 match: 17 SD: 0.5627 cents 128 .. 256 match: 17 SD: 0.5280 cents 137 .. 274 match: 17 SD: 0.4991 cents 143 .. 286 match: 17 SD: 0.4976 cents 153 .. 306 match: 17 SD: 0.4109 cents 183 .. 366 match: 17 SD: 0.3928 cents 201 .. 402 match: 17 SD: 0.3903 cents 202 .. 404 match: 17 SD: 0.3745 cents 204 .. 408 match: 17 SD: 0.2990 cents 228 .. 456 match: 17 SD: 0.2843 cents 244 .. 488 match: 17 SD: 0.2378 cents 285 .. 570 match: 17 SD: 0.2357 cents 297 .. 594 match: 17 SD: 0.2228 cents 315 .. 630 match: 17 SD: 0.2004 cents 332 .. 664 match: 17 SD: 0.1729 cents 357 .. 714 match: 17 SD: 0.1711 cents 397 .. 794 match: 17 SD: 0.1632 cents 427 .. 854 match: 17 SD: 0.1597 cents 448 .. 896 match: 17 SD: 0.1496 cents 468 .. 936 match: 17 SD: 0.1387 cents 515 .. 1030 match: 17 SD: 0.1233 cents 560 .. 1120 match: 17 SD: 0.1157 cents