Scala analysis: xen18-schulter-pure-11-14-17
Temperament with pure 11:14 major thirds, fifth of 704.377 cents
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.115 cents 78.115000 2: 130.639 cents 130.639000 3: 208.754 cents 208.754000 4: 286.869 cents 286.869000 5: 339.393 cents 339.393000 6: 417.508 cents 417.508000 7: 495.623 cents 495.623000 8: 573.738 cents 573.738000 9: 626.262 cents 626.262000 10: 704.377 cents 704.377000 11: 782.492 cents 782.492000 12: 835.016 cents 835.016000 13: 913.131 cents 913.131000 14: 991.246 cents 991.246000 15: 1043.770 cents 1043.770000 16: 1121.885 cents 1121.885000 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.1150 cents 78.1150 1: 78.1150 cents 78.1150 2: 52.5240 cents 52.5240 3: 78.1150 cents 78.1150 4: 78.1150 cents 78.1150 5: 52.5240 cents 52.5240 6: 78.1150 cents 78.1150 7: 78.1150 cents 78.1150 8: 78.1150 cents 78.1150 9: 52.5240 cents 52.5240 10: 78.1150 cents 78.1150 11: 78.1150 cents 78.1150 12: 52.5240 cents 52.5240 13: 78.1150 cents 78.1150 14: 78.1150 cents 78.1150 15: 52.5240 cents 52.5240 16: 78.1150 cents 78.1150 17: 78.1150 cents 78.1150
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 52.52400 cents 1: 12 78.11500 cents 2: 10 130.63900 cents 2: 7 156.23000 cents 3: 15 208.75400 cents 3: 2 234.34500 cents 4: 3 261.27800 cents 4: 14 286.86900 cents 5: 8 339.39300 cents 5: 9 364.98400 cents 6: 13 417.50800 cents 6: 4 443.09900 cents 7: 1 470.03200 cents 7: 16 495.62300 cents 8: 6 548.14700 cents 8: 11 573.73800 cents 9: 11 626.26200 cents 9: 6 651.85300 cents 10: 16 704.37700 cents 10: 1 729.96800 cents 11: 4 756.90100 cents 11: 13 782.49200 cents 12: 9 835.01600 cents 12: 8 860.60700 cents 13: 14 913.13100 cents 13: 3 938.72200 cents 14: 2 965.65500 cents 14: 15 991.24600 cents 15: 7 1043.77000 cents 15: 10 1069.36100 cents 16: 12 1121.88500 cents 16: 5 1147.47600 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 : 78.1 130.6 208.8 286.9 339.4 417.5 495.6 573.7 626.3 704.4 782.5 835.0 913.1 991.2 1043.8 1121.9 1200.0 78.1 : 52.5 130.6 208.8 261.3 339.4 417.5 495.6 548.1 626.3 704.4 756.9 835.0 913.1 965.7 1043.8 1121.9 1200.0 130.6 : 78.1 156.2 208.8 286.9 365.0 443.1 495.6 573.7 651.9 704.4 782.5 860.6 913.1 991.2 1069.4 1147.5 1200.0 208.8 : 78.1 130.6 208.8 286.9 365.0 417.5 495.6 573.7 626.3 704.4 782.5 835.0 913.1 991.2 1069.4 1121.9 1200.0 286.9 : 52.5 130.6 208.8 286.9 339.4 417.5 495.6 548.1 626.3 704.4 756.9 835.0 913.1 991.2 1043.8 1121.9 1200.0 339.4 : 78.1 156.2 234.3 286.9 365.0 443.1 495.6 573.7 651.9 704.4 782.5 860.6 938.7 991.2 1069.4 1147.5 1200.0 417.5 : 78.1 156.2 208.8 286.9 365.0 417.5 495.6 573.7 626.3 704.4 782.5 860.6 913.1 991.2 1069.4 1121.9 1200.0 495.6 : 78.1 130.6 208.8 286.9 339.4 417.5 495.6 548.1 626.3 704.4 782.5 835.0 913.1 991.2 1043.8 1121.9 1200.0 573.7 : 52.5 130.6 208.8 261.3 339.4 417.5 470.0 548.1 626.3 704.4 756.9 835.0 913.1 965.7 1043.8 1121.9 1200.0 626.3 : 78.1 156.2 208.8 286.9 365.0 417.5 495.6 573.7 651.9 704.4 782.5 860.6 913.1 991.2 1069.4 1147.5 1200.0 704.4 : 78.1 130.6 208.8 286.9 339.4 417.5 495.6 573.7 626.3 704.4 782.5 835.0 913.1 991.2 1069.4 1121.9 1200.0 782.5 : 52.5 130.6 208.8 261.3 339.4 417.5 495.6 548.1 626.3 704.4 756.9 835.0 913.1 991.2 1043.8 1121.9 1200.0 835.0 : 78.1 156.2 208.8 286.9 365.0 443.1 495.6 573.7 651.9 704.4 782.5 860.6 938.7 991.2 1069.4 1147.5 1200.0 913.1 : 78.1 130.6 208.8 286.9 365.0 417.5 495.6 573.7 626.3 704.4 782.5 860.6 913.1 991.2 1069.4 1121.9 1200.0 991.2 : 52.5 130.6 208.8 286.9 339.4 417.5 495.6 548.1 626.3 704.4 782.5 835.0 913.1 991.2 1043.8 1121.9 1200.0 1043.8: 78.1 156.2 234.3 286.9 365.0 443.1 495.6 573.7 651.9 730.0 782.5 860.6 938.7 991.2 1069.4 1147.5 1200.0 1121.9: 78.1 156.2 208.8 286.9 365.0 417.5 495.6 573.7 651.9 704.4 782.5 860.6 913.1 991.2 1069.4 1121.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.5240 .. 78.1150 cents 25.59100 cents 52.52400 cents 2: 130.6390 .. 156.2300 cents 25.59100 cents 52.52400 cents 3: 208.7540 .. 234.3450 cents 25.59100 cents 52.52400 cents 4: 261.2780 .. 286.8690 cents 25.59100 cents 26.93300 cents 5: 339.3930 .. 364.9840 cents 25.59100 cents 52.52400 cents 6: 417.5080 .. 443.0990 cents 25.59100 cents 52.52400 cents 7: 470.0320 .. 495.6230 cents 25.59100 cents 26.93300 cents 8: 548.1470 .. 573.7380 cents 25.59100 cents 52.52400 cents 9: 626.2620 .. 651.8530 cents 25.59100 cents 52.52400 cents 10: 704.3770 .. 729.9680 cents 25.59100 cents 52.52400 cents 11: 756.9010 .. 782.4920 cents 25.59100 cents 26.93300 cents 12: 835.0160 .. 860.6070 cents 25.59100 cents 52.52400 cents 13: 913.1310 .. 938.7220 cents 25.59100 cents 52.52400 cents 14: 965.6550 .. 991.2460 cents 25.59100 cents 26.93300 cents 15: 1043.7700 .. 1069.3610 cents 25.59100 cents 52.52400 cents 16: 1121.8850 .. 1147.4760 cents 25.59100 cents 52.52400 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 52.52400 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 78.11500 cents Average / Smallest step : 1.343923 Largest / Average step : 1.106629 Largest / Smallest step : 1.487225 Median interval of one step : 78.11500 cents, amount: 12 Most common interval of one step : 78.11500 cents, amount: 12 Least squares average step : 70.27283 cents, oct.: 1194.63808 cents Scale is strictly proper Scale has Myhill's property chromas: 25.59100 cents and 26.93300 cents, ratio: 1.052440 generators: 7 of 495.62300 cents and 10 of 704.37700 cents ET pair of linear temperament : 12&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 891-tone equal temperament with octave 1200.000 cents degrees: 58 97 155 213 252 310 368 426 465 523 581 620 678 736 775 833 891 generators: 368 and 523 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABAABAA Step pattern size order : LSLLSLLLSLLSLLSLL Scale is a Constant Structure, by a margin of 26.93300 cents Ratio Whole / Half tone : 2.672393 Scale diversity : 1.191443 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.658787 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 : 25.59100 cents Most common intervals : 495.62300 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 495.623 991.246 cents Most common triad is 0.0 495.623 704.377 cents, amount: 15 Number of recognisable fifths : 16, average 704.3770 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.9656 c. M:-15.0535 c. 29: 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 2 P M ME S SD: 4.9143 c. M: 9.2872 c. 46: 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 SP M ME S SD: 0.1544 c. M: 0.2917 c. 477: 31 21 31 31 21 31 31 31 21 31 31 21 31 31 21 31 31 SP M DE S SD: 0.1350 c. M:-0.2552 c. 523: 34 23 34 34 23 34 34 34 23 34 34 23 34 34 23 34 34 SP M DE S SD: 0.1096 c. M:-0.2071 c. 569: 37 25 37 37 25 37 37 37 25 37 37 25 37 37 25 37 37 SP M DE S SD: 0.0882 c. M:-0.1667 c. 615: 40 27 40 40 27 40 40 40 27 40 40 27 40 40 27 40 40 SP M DE S SD: 0.0701 c. M:-0.1324 c. 661: 43 29 43 43 29 43 43 43 29 43 43 29 43 43 29 43 43 SP M DE S SD: 0.0545 c. M:-0.1029 c. 707: 46 31 46 46 31 46 46 46 31 46 46 31 46 46 31 46 46 SP M DE S SD: 0.0409 c. M:-0.0772 c. 753: 49 33 49 49 33 49 49 49 33 49 49 33 49 49 33 49 49 SP M DE S SD: 0.0289 c. M:-0.0547 c. 799: 52 35 52 52 35 52 52 52 35 52 52 35 52 52 35 52 52 SP M DE S SD: 0.0184 c. M:-0.0348 c. 845: 55 37 55 55 37 55 55 55 37 55 55 37 55 55 37 55 55 SP M DE S SD: 0.0090 c. M:-0.0170 c. 891: 58 39 58 58 39 58 58 58 39 58 58 39 58 58 39 58 58 SP M DE S SD: 0.0006 c. M:-0.0010 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.2110 cents 3 .. 6 match: 3 H SD: 9.6247 cents 4 .. 8 match: 4 H SD: 9.6229 cents 5 .. 10 match: 5 H SD: 8.4407 cents 6 .. 12 match: 6 H SD: 5.9413 cents 7 .. 14 match: 7 H SD: 6.4975 cents 8 .. 16 match: 8 H SD: 7.0358 cents 9 .. 18 match: 9 H SD: 5.5179 cents 10 .. 20 match: 10 H SD: 6.6782 cents 11 .. 22 match: 11 H SD: 6.1516 cents 12 .. 24 match: 12 H SD: 4.9588 cents 13 .. 26 match: 13 H SD: 5.8364 cents 14 .. 28 match: 14 H SD: 4.6774 cents 15 .. 30 match: 13 SD: 6.0096 cents 16 .. 32 match: 15 SD: 4.3816 cents 17 .. 34 match: 15 SD: 5.4237 cents 18 .. 36 match: 16 SD: 3.5678 cents 19 .. 38 match: 16 SD: 4.9197 cents 20 .. 40 match: 16 SD: 5.2010 cents 21 .. 42 match: 17 S SD: 3.9253 cents 22 .. 44 match: 17 SD: 3.2335 cents 23 .. 46 match: 17 SD: 2.5047 cents 25 .. 50 match: 16 SD: 3.3485 cents 26 .. 52 match: 17 SD: 2.9408 cents 28 .. 56 match: 17 SD: 2.8729 cents 33 .. 66 match: 17 SD: 2.6939 cents 34 .. 68 match: 17 SD: 2.6733 cents 36 .. 72 match: 17 SD: 2.3231 cents 37 .. 74 match: 17 SD: 2.1552 cents 39 .. 78 match: 17 SD: 1.8822 cents 40 .. 80 match: 17 SD: 1.6952 cents 46 .. 92 match: 17 SD: 1.6814 cents 48 .. 96 match: 17 SD: 1.5161 cents 56 .. 112 match: 17 SD: 1.4824 cents 60 .. 120 match: 17 SD: 1.3279 cents 61 .. 122 match: 17 SD: 1.2547 cents 63 .. 126 match: 17 SD: 1.1680 cents 66 .. 132 match: 17 SD: 0.9820 cents 78 .. 156 match: 17 SD: 0.9448 cents 84 .. 168 match: 17 SD: 0.8711 cents 87 .. 174 match: 17 SD: 0.7478 cents 88 .. 176 match: 17 SD: 0.7465 cents 102 .. 204 match: 17 SD: 0.6878 cents 110 .. 220 match: 17 SD: 0.6223 cents 115 .. 230 match: 17 SD: 0.5817 cents 124 .. 248 match: 17 SD: 0.5351 cents 133 .. 266 match: 17 SD: 0.5230 cents 150 .. 300 match: 17 SD: 0.4734 cents 151 .. 302 match: 17 SD: 0.4691 cents 157 .. 314 match: 17 SD: 0.4572 cents 166 .. 332 match: 17 SD: 0.4325 cents 179 .. 358 match: 17 SD: 0.3694 cents 193 .. 386 match: 17 SD: 0.3201 cents 216 .. 432 match: 17 SD: 0.3101 cents 217 .. 434 match: 17 SD: 0.2966 cents 239 .. 478 match: 17 SD: 0.2723 cents 257 .. 514 match: 17 SD: 0.2668 cents 259 .. 518 match: 17 SD: 0.2623 cents 278 .. 556 match: 17 SD: 0.2534 cents 282 .. 564 match: 17 SD: 0.2134 cents 305 .. 610 match: 17 SD: 0.1426 cents 476 .. 952 match: 17 SD: 0.1233 cents 498 .. 996 match: 17 SD: 0.1101 cents 586 .. 1172 match: 17 SD: 0.1065 cents