Scala analysis: xen18-schulter-pure-11-14-24
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: 52.524 cents 52.524000 2: 78.115 cents 78.115000 3: 130.639 cents 130.639000 4: 208.754 cents 208.754000 5: 261.278 cents 261.278000 6: 286.869 cents 286.869000 7: 339.393 cents 339.393000 8: 364.984 cents 364.984000 9: 417.508 cents 417.508000 10: 495.623 cents 495.623000 11: 548.147 cents 548.147000 12: 573.738 cents 573.738000 13: 626.262 cents 626.262000 14: 704.377 cents 704.377000 15: 756.901 cents 756.901000 16: 782.492 cents 782.492000 17: 835.016 cents 835.016000 18: 860.607 cents 860.607000 19: 913.131 cents 913.131000 20: 991.246 cents 991.246000 21: 1043.770 cents 1043.770000 22: 1069.361 cents 1069.361000 23: 1121.885 cents 1121.885000 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.1150 cents 78.1150 1: 52.5240 cents 52.5240 2: 25.5910 cents 25.5910 3: 52.5240 cents 52.5240 4: 78.1150 cents 78.1150 5: 52.5240 cents 52.5240 6: 25.5910 cents 25.5910 7: 52.5240 cents 52.5240 8: 25.5910 cents 25.5910 9: 52.5240 cents 52.5240 10: 78.1150 cents 78.1150 11: 52.5240 cents 52.5240 12: 25.5910 cents 25.5910 13: 52.5240 cents 52.5240 14: 78.1150 cents 78.1150 15: 52.5240 cents 52.5240 16: 25.5910 cents 25.5910 17: 52.5240 cents 52.5240 18: 25.5910 cents 25.5910 19: 52.5240 cents 52.5240 20: 78.1150 cents 78.1150 21: 52.5240 cents 52.5240 22: 25.5910 cents 25.5910 23: 52.5240 cents 52.5240 24: 78.1150 cents 78.1150
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 25.59100 cents 1: 12 52.52400 cents 1: 5 78.11500 cents 2: 14 78.11500 cents 2: 10 130.63900 cents 3: 2 103.70600 cents 3: 7 130.63900 cents 3: 10 156.23000 cents 3: 5 183.16300 cents 4: 4 156.23000 cents 4: 20 208.75400 cents 5: 2 208.75400 cents 5: 9 234.34500 cents 5: 10 261.27800 cents 5: 3 286.86900 cents 6: 18 286.86900 cents 6: 6 339.39300 cents 7: 4 312.46000 cents 7: 9 339.39300 cents 7: 8 364.98400 cents 7: 3 391.91700 cents 8: 8 364.98400 cents 8: 16 417.50800 cents 9: 4 417.50800 cents 9: 11 443.09900 cents 9: 8 470.03200 cents 9: 1 495.62300 cents 10: 22 495.62300 cents 10: 2 548.14700 cents 11: 6 521.21400 cents 11: 11 548.14700 cents 11: 6 573.73800 cents 11: 1 600.67100 cents 12: 12 573.73800 cents 12: 12 626.26200 cents 13: 1 599.32900 cents 13: 6 626.26200 cents 13: 11 651.85300 cents 13: 6 678.78600 cents 14: 2 651.85300 cents 14: 22 704.37700 cents 15: 1 704.37700 cents 15: 8 729.96800 cents 15: 11 756.90100 cents 15: 4 782.49200 cents 16: 16 782.49200 cents 16: 8 835.01600 cents 17: 3 808.08300 cents 17: 8 835.01600 cents 17: 9 860.60700 cents 17: 4 887.54000 cents 18: 6 860.60700 cents 18: 18 913.13100 cents 19: 3 913.13100 cents 19: 10 938.72200 cents 19: 9 965.65500 cents 19: 2 991.24600 cents 20: 20 991.24600 cents 20: 4 1043.77000 cents 21: 5 1016.83700 cents 21: 10 1043.77000 cents 21: 7 1069.36100 cents 21: 2 1096.29400 cents 22: 10 1069.36100 cents 22: 14 1121.88500 cents 23: 5 1121.88500 cents 23: 12 1147.47600 cents 23: 7 1174.40900 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.95652 = 68/23
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 23 24 0.0 : 52.5 78.1 130.6 208.8 261.3 286.9 339.4 365.0 417.5 495.6 548.1 573.7 626.3 704.4 756.9 782.5 835.0 860.6 913.1 991.2 1043.8 1069.4 1121.9 1200.0 52.5 : 25.6 78.1 156.2 208.8 234.3 286.9 312.5 365.0 443.1 495.6 521.2 573.7 651.9 704.4 730.0 782.5 808.1 860.6 938.7 991.2 1016.8 1069.4 1147.5 1200.0 78.1 : 52.5 130.6 183.2 208.8 261.3 286.9 339.4 417.5 470.0 495.6 548.1 626.3 678.8 704.4 756.9 782.5 835.0 913.1 965.7 991.2 1043.8 1121.9 1174.4 1200.0 130.6 : 78.1 130.6 156.2 208.8 234.3 286.9 365.0 417.5 443.1 495.6 573.7 626.3 651.9 704.4 730.0 782.5 860.6 913.1 938.7 991.2 1069.4 1121.9 1147.5 1200.0 208.8 : 52.5 78.1 130.6 156.2 208.8 286.9 339.4 365.0 417.5 495.6 548.1 573.7 626.3 651.9 704.4 782.5 835.0 860.6 913.1 991.2 1043.8 1069.4 1121.9 1200.0 261.3 : 25.6 78.1 103.7 156.2 234.3 286.9 312.5 365.0 443.1 495.6 521.2 573.7 599.3 651.9 730.0 782.5 808.1 860.6 938.7 991.2 1016.8 1069.4 1147.5 1200.0 286.9 : 52.5 78.1 130.6 208.8 261.3 286.9 339.4 417.5 470.0 495.6 548.1 573.7 626.3 704.4 756.9 782.5 835.0 913.1 965.7 991.2 1043.8 1121.9 1174.4 1200.0 339.4 : 25.6 78.1 156.2 208.8 234.3 286.9 365.0 417.5 443.1 495.6 521.2 573.7 651.9 704.4 730.0 782.5 860.6 913.1 938.7 991.2 1069.4 1121.9 1147.5 1200.0 365.0 : 52.5 130.6 183.2 208.8 261.3 339.4 391.9 417.5 470.0 495.6 548.1 626.3 678.8 704.4 756.9 835.0 887.5 913.1 965.7 1043.8 1096.3 1121.9 1174.4 1200.0 417.5 : 78.1 130.6 156.2 208.8 286.9 339.4 365.0 417.5 443.1 495.6 573.7 626.3 651.9 704.4 782.5 835.0 860.6 913.1 991.2 1043.8 1069.4 1121.9 1147.5 1200.0 495.6 : 52.5 78.1 130.6 208.8 261.3 286.9 339.4 365.0 417.5 495.6 548.1 573.7 626.3 704.4 756.9 782.5 835.0 913.1 965.7 991.2 1043.8 1069.4 1121.9 1200.0 548.1 : 25.6 78.1 156.2 208.8 234.3 286.9 312.5 365.0 443.1 495.6 521.2 573.7 651.9 704.4 730.0 782.5 860.6 913.1 938.7 991.2 1016.8 1069.4 1147.5 1200.0 573.7 : 52.5 130.6 183.2 208.8 261.3 286.9 339.4 417.5 470.0 495.6 548.1 626.3 678.8 704.4 756.9 835.0 887.5 913.1 965.7 991.2 1043.8 1121.9 1174.4 1200.0 626.3 : 78.1 130.6 156.2 208.8 234.3 286.9 365.0 417.5 443.1 495.6 573.7 626.3 651.9 704.4 782.5 835.0 860.6 913.1 938.7 991.2 1069.4 1121.9 1147.5 1200.0 704.4 : 52.5 78.1 130.6 156.2 208.8 286.9 339.4 365.0 417.5 495.6 548.1 573.7 626.3 704.4 756.9 782.5 835.0 860.6 913.1 991.2 1043.8 1069.4 1121.9 1200.0 756.9 : 25.6 78.1 103.7 156.2 234.3 286.9 312.5 365.0 443.1 495.6 521.2 573.7 651.9 704.4 730.0 782.5 808.1 860.6 938.7 991.2 1016.8 1069.4 1147.5 1200.0 782.5 : 52.5 78.1 130.6 208.8 261.3 286.9 339.4 417.5 470.0 495.6 548.1 626.3 678.8 704.4 756.9 782.5 835.0 913.1 965.7 991.2 1043.8 1121.9 1174.4 1200.0 835.0 : 25.6 78.1 156.2 208.8 234.3 286.9 365.0 417.5 443.1 495.6 573.7 626.3 651.9 704.4 730.0 782.5 860.6 913.1 938.7 991.2 1069.4 1121.9 1147.5 1200.0 860.6 : 52.5 130.6 183.2 208.8 261.3 339.4 391.9 417.5 470.0 548.1 600.7 626.3 678.8 704.4 756.9 835.0 887.5 913.1 965.7 1043.8 1096.3 1121.9 1174.4 1200.0 913.1 : 78.1 130.6 156.2 208.8 286.9 339.4 365.0 417.5 495.6 548.1 573.7 626.3 651.9 704.4 782.5 835.0 860.6 913.1 991.2 1043.8 1069.4 1121.9 1147.5 1200.0 991.2 : 52.5 78.1 130.6 208.8 261.3 286.9 339.4 417.5 470.0 495.6 548.1 573.7 626.3 704.4 756.9 782.5 835.0 913.1 965.7 991.2 1043.8 1069.4 1121.9 1200.0 1043.8: 25.6 78.1 156.2 208.8 234.3 286.9 365.0 417.5 443.1 495.6 521.2 573.7 651.9 704.4 730.0 782.5 860.6 913.1 938.7 991.2 1016.8 1069.4 1147.5 1200.0 1069.4: 52.5 130.6 183.2 208.8 261.3 339.4 391.9 417.5 470.0 495.6 548.1 626.3 678.8 704.4 756.9 835.0 887.5 913.1 965.7 991.2 1043.8 1121.9 1174.4 1200.0 1121.9: 78.1 130.6 156.2 208.8 286.9 339.4 365.0 417.5 443.1 495.6 573.7 626.3 651.9 704.4 782.5 835.0 860.6 913.1 938.7 991.2 1069.4 1121.9 1147.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.5910 .. 78.1150 cents 52.52400 cents 25.59100 cents 2: 78.1150 .. 130.6390 cents 52.52400 cents 1/1, 0.0000 cents 3: 103.7060 .. 183.1630 cents 79.45700 cents -26.93300 cents 4: 156.2300 .. 208.7540 cents 52.52400 cents -26.93300 cents 5: 208.7540 .. 286.8690 cents 78.11500 cents 1/1, 0.0000 cents 6: 286.8690 .. 339.3930 cents 52.52400 cents 1/1, 0.0000 cents 7: 312.4600 .. 391.9170 cents 79.45700 cents -26.93300 cents 8: 364.9840 .. 417.5080 cents 52.52400 cents -26.93300 cents 9: 417.5080 .. 495.6230 cents 78.11500 cents 1/1, 0.0000 cents 10: 495.6230 .. 548.1470 cents 52.52400 cents 1/1, 0.0000 cents 11: 521.2140 .. 600.6710 cents 79.45700 cents -26.93300 cents 12: 573.7380 .. 626.2620 cents 52.52400 cents -26.93300 cents 13: 599.3290 .. 678.7860 cents 79.45700 cents -26.93300 cents 14: 651.8530 .. 704.3770 cents 52.52400 cents -26.93300 cents 15: 704.3770 .. 782.4920 cents 78.11500 cents 1/1, 0.0000 cents 16: 782.4920 .. 835.0160 cents 52.52400 cents 1/1, 0.0000 cents 17: 808.0830 .. 887.5400 cents 79.45700 cents -26.93300 cents 18: 860.6070 .. 913.1310 cents 52.52400 cents -26.93300 cents 19: 913.1310 .. 991.2460 cents 78.11500 cents 1/1, 0.0000 cents 20: 991.2460 .. 1043.7700 cents 52.52400 cents 1/1, 0.0000 cents 21: 1016.8370 .. 1096.2940 cents 79.45700 cents -26.93300 cents 22: 1069.3610 .. 1121.8850 cents 52.52400 cents -26.93300 cents 23: 1121.8850 .. 1174.4090 cents 52.52400 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 25.59100 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 78.11500 cents Average / Smallest step : 1.953812 Largest / Average step : 1.562300 Largest / Smallest step : 3.052440 Median interval of one step : 52.52400 cents, amount: 12 Most common interval of one step : 52.52400 cents, amount: 12 Least squares average step : 49.01476 cents, oct.: 1176.35429 cents Scale is not proper Scale is a mode of a 891-tone equal temperament with octave 1200.000 cents degrees: 39 58 97 155 194 213 252 271 310 368 407 426 465 523 562 581 620 639 678 736 775 794 833 891 Least number of segments generator : 446 of 600.673 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 523 of 704.377 cents and inv. generated superset size: 24 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABABACABACABABACABAC Step pattern size order : MSMLMSMSMLMSMLMSMSMLMSML Scale is not a Constant Structure Scale diversity : 1.205209 Lumma stability : 0.042652 Lumma impropriety factor : 0.268212 Rothenberg efficiency : 0.694444 redundancy: 0.305556 Efficiency x scale size : 16.666667 Number of different interval sizes : 46 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.95652 = 68/23 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1.34200 cents Most common intervals : 495.62300 cents & inv., amount: 23 Scale has Generated (pseudo-Myhill) property, generator: 704.377 cents and inv. Scale is a chain of 12 triads 0.0 52.524 704.377 cents Most common triad is 0.0 495.623 704.377 cents, amount: 22 Number of recognisable fifths : 23, average 704.3770 cents Scale contains two identical conjunct "tetrachords" of 11 notes Formal octave complements present : 19 = 79.1667% Limited inverse transpositions : 23 Inversional symmetry on intervals : 11-12 23-24 -- Rational properties --
FIT/MODE
24: 1 0 1 2 1 0 2 0 1 2 1 0 1 2 1 0 1 1 1 2 1 0 1 2 N T3 SD: 19.1712 c. M: 36.8690 c. 25: 1 0 1 2 1 1 1 0 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 N D3 SD: 21.6459 c. M: 36.9010 c. 27: 1 1 1 1 2 0 1 1 1 2 1 1 1 2 1 0 2 0 1 2 1 1 1 2 N SD: 15.2173 c. M: 30.9762 c. 28: 1 1 1 2 1 1 1 1 1 2 1 0 2 1 2 0 1 1 1 2 1 1 1 2 N SD: 12.1437 c. M: 20.7303 c. 29: 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 2 P D3 SD: 6.8352 c. M: 13.0021 c. 46: 2 1 2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1 2 3 N SD: 0.2147 c. M: 0.4084 c. 477: 21 10 21 31 21 10 21 10 21 31 21 10 21 31 21 10 21 10 21 31 21 10 21 31 N G SD: 0.1878 c. M:-0.3572 c. 523: 23 11 23 34 23 11 23 11 23 34 23 11 23 34 23 11 23 11 23 34 23 11 23 34 N G SD: 0.1524 c. M:-0.2899 c. 569: 25 12 25 37 25 12 25 12 25 37 25 12 25 37 25 12 25 12 25 37 25 12 25 37 N G SD: 0.1227 c. M:-0.2334 c. 615: 27 13 27 40 27 13 27 13 27 40 27 13 27 40 27 13 27 13 27 40 27 13 27 40 N G SD: 0.0975 c. M:-0.1854 c. 661: 29 14 29 43 29 14 29 14 29 43 29 14 29 43 29 14 29 14 29 43 29 14 29 43 N G SD: 0.0757 c. M:-0.1441 c. 707: 31 15 31 46 31 15 31 15 31 46 31 15 31 46 31 15 31 15 31 46 31 15 31 46 N G SD: 0.0568 c. M:-0.1081 c. 753: 33 16 33 49 33 16 33 16 33 49 33 16 33 49 33 16 33 16 33 49 33 16 33 49 N G SD: 0.0403 c. M:-0.0766 c. 799: 35 17 35 52 35 17 35 17 35 52 35 17 35 52 35 17 35 17 35 52 35 17 35 52 N G SD: 0.0256 c. M:-0.0487 c. 845: 37 18 37 55 37 18 37 18 37 55 37 18 37 55 37 18 37 18 37 55 37 18 37 55 N G SD: 0.0125 c. M:-0.0238 c. 891: 39 19 39 58 39 19 39 19 39 58 39 19 39 58 39 19 39 19 39 58 39 19 39 58 N G SD: 0.0008 c. M:-0.0015 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: 7.9583 cents 4 .. 8 match: 4 H SD: 7.7600 cents 5 .. 10 match: 5 H SD: 8.4407 cents 6 .. 12 match: 6 H SD: 4.2112 cents 7 .. 14 match: 7 H SD: 5.1388 cents 8 .. 16 match: 8 H SD: 4.6518 cents 9 .. 18 match: 9 H SD: 4.9164 cents 10 .. 20 match: 10 H SD: 6.6782 cents 11 .. 22 match: 11 H SD: 4.3450 cents 12 .. 24 match: 12 H SD: 4.0744 cents 13 .. 26 match: 13 H SD: 3.9032 cents 14 .. 28 match: 14 H SD: 3.3527 cents 15 .. 30 match: 14 SD: 5.0413 cents 16 .. 32 match: 16 H SD: 3.7845 cents 17 .. 34 match: 16 S SD: 4.4588 cents 18 .. 36 match: 17 S SD: 3.3325 cents 19 .. 38 match: 16 SD: 3.9711 cents 20 .. 40 match: 17 SD: 4.0424 cents 21 .. 42 match: 19 S SD: 3.3345 cents 22 .. 44 match: 20 SD: 2.6752 cents 23 .. 46 match: 19 SD: 2.4006 cents 24 .. 48 match: 20 SD: 2.8197 cents 25 .. 50 match: 20 S SD: 2.8337 cents 26 .. 52 match: 20 SD: 2.3939 cents 27 .. 54 match: 20 SD: 2.8230 cents 28 .. 56 match: 22 SD: 2.5688 cents 29 .. 58 match: 21 SD: 2.4708 cents 30 .. 60 match: 20 SD: 1.9169 cents 31 .. 62 match: 20 SD: 2.6582 cents 32 .. 64 match: 22 SD: 2.3721 cents 33 .. 66 match: 24 SD: 2.1804 cents 34 .. 68 match: 21 SD: 2.1327 cents 35 .. 70 match: 22 SD: 2.2553 cents 36 .. 72 match: 22 SD: 1.7917 cents 37 .. 74 match: 24 SD: 1.7549 cents 38 .. 76 match: 23 SD: 1.8153 cents 39 .. 78 match: 23 SD: 1.6890 cents 40 .. 80 match: 22 SD: 1.4363 cents 41 .. 82 match: 23 SD: 1.8735 cents 42 .. 84 match: 24 SD: 1.6683 cents 44 .. 88 match: 23 SD: 1.6953 cents 45 .. 90 match: 24 SD: 1.6916 cents 46 .. 92 match: 24 SD: 1.6168 cents 47 .. 94 match: 22 SD: 1.6634 cents 48 .. 96 match: 24 SD: 1.3880 cents 49 .. 98 match: 23 SD: 1.5193 cents 50 .. 100 match: 23 SD: 1.4980 cents 51 .. 102 match: 23 SD: 1.3271 cents 52 .. 104 match: 23 SD: 1.5984 cents 53 .. 106 match: 23 SD: 1.5451 cents 54 .. 108 match: 23 SD: 1.3209 cents 55 .. 110 match: 24 SD: 1.3162 cents 56 .. 112 match: 24 SD: 1.1613 cents 60 .. 120 match: 24 SD: 1.0858 cents 61 .. 122 match: 24 SD: 1.0630 cents 62 .. 124 match: 24 SD: 1.0184 cents 66 .. 132 match: 24 SD: 1.0115 cents 68 .. 136 match: 24 SD: 0.9945 cents 69 .. 138 match: 24 SD: 0.9195 cents 78 .. 156 match: 24 SD: 0.8665 cents 84 .. 168 match: 24 SD: 0.7986 cents 87 .. 174 match: 24 SD: 0.7422 cents 88 .. 176 match: 24 SD: 0.7163 cents 99 .. 198 match: 24 SD: 0.6990 cents 102 .. 204 match: 24 SD: 0.5711 cents 110 .. 220 match: 24 SD: 0.5387 cents 115 .. 230 match: 24 SD: 0.5324 cents 124 .. 248 match: 24 SD: 0.4190 cents 157 .. 314 match: 24 SD: 0.4133 cents 166 .. 332 match: 24 SD: 0.3180 cents 193 .. 386 match: 24 SD: 0.2944 cents 217 .. 434 match: 24 SD: 0.2758 cents 239 .. 478 match: 24 SD: 0.2269 cents 282 .. 564 match: 24 SD: 0.1951 cents 295 .. 590 match: 24 SD: 0.1937 cents 344 .. 688 match: 24 SD: 0.1857 cents 366 .. 732 match: 24 SD: 0.1744 cents 374 .. 748 match: 24 SD: 0.1694 cents 383 .. 766 match: 24 SD: 0.1668 cents 384 .. 768 match: 24 SD: 0.1662 cents 387 .. 774 match: 24 SD: 0.1587 cents 392 .. 784 match: 24 SD: 0.1231 cents 494 .. 988 match: 24 SD: 0.1205 cents 498 .. 996 match: 24 SD: 0.1154 cents 516 .. 1032 match: 24 SD: 0.1056 cents 521 .. 1042 match: 24 SD: 0.1044 cents 576 .. 1152 match: 24 SD: 0.1027 cents 583 .. 1166 match: 24 SD: 0.1004 cents