Scala analysis: met24-canonical
Smoothed MET-24 in 2048-EDO, generators (2/1, 703.711c, 57.422c)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.422 cents 57.421880 2: 125.977 cents 125.976560 3: 183.398 cents 183.398440 4: 207.422 cents 207.421880 5: 264.844 cents 264.843750 6: 288.867 cents 288.867190 7: 346.289 cents 346.289060 8: 414.844 cents 414.843750 9: 472.266 cents 472.265630 10: 496.289 cents 496.289060 11: 553.711 cents 553.710940 12: 622.266 cents 622.265630 13: 679.688 cents 679.687500 14: 703.711 cents 703.710940 15: 761.133 cents 761.132810 16: 829.687 cents 829.687500 17: 887.109 cents 887.109380 18: 911.133 cents 911.132810 19: 968.555 cents 968.554690 20: 992.578 cents 992.578120 21: 1050.000 cents 1050.000000 22: 1118.555 cents 1118.554690 23: 1175.977 cents 1175.976560 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 24.0234 cents 24.0234 1: 57.4219 cents 57.4219 2: 68.5547 cents 68.5547 3: 57.4219 cents 57.4219 4: 24.0234 cents 24.0234 5: 57.4219 cents 57.4219 6: 24.0234 cents 24.0234 7: 57.4219 cents 57.4219 8: 68.5547 cents 68.5547 9: 57.4219 cents 57.4219 10: 24.0234 cents 24.0234 11: 57.4219 cents 57.4219 12: 68.5547 cents 68.5547 13: 57.4219 cents 57.4219 14: 24.0234 cents 24.0234 15: 57.4219 cents 57.4219 16: 68.5547 cents 68.5547 17: 57.4219 cents 57.4219 18: 24.0234 cents 24.0234 19: 57.4219 cents 57.4219 20: 24.0234 cents 24.0234 21: 57.4219 cents 57.4219 22: 68.5547 cents 68.5547 23: 57.4219 cents 57.4219 24: 24.0234 cents 24.0234
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 24.02344 cents 1: 12 57.42188 cents 1: 5 68.55468 cents 2: 14 81.44532 cents 2: 10 125.97656 cents 3: 2 105.46875 cents 3: 7 138.86719 cents 3: 10 150.00000 cents 3: 5 183.39844 cents 4: 4 162.89063 cents 4: 20 207.42188 cents 5: 2 220.31250 cents 5: 9 231.44531 cents 5: 10 264.84375 cents 5: 3 275.97657 cents 6: 18 288.86719 cents 6: 6 333.39844 cents 7: 4 312.89062 cents 7: 9 346.28906 cents 7: 8 357.42187 cents 7: 3 390.82031 cents 8: 8 370.31250 cents 8: 16 414.84375 cents 9: 4 427.73438 cents 9: 11 438.86718 cents 9: 8 472.26563 cents 9: 1 483.39844 cents 10: 22 496.28906 cents 10: 2 540.82031 cents 11: 6 520.31250 cents 11: 11 553.71094 cents 11: 6 564.84375 cents 11: 1 598.24219 cents 12: 12 577.73438 cents 12: 12 622.26563 cents 13: 1 601.75781 cents 13: 6 635.15625 cents 13: 11 646.28906 cents 13: 6 679.68750 cents 14: 2 659.17969 cents 14: 22 703.71094 cents 15: 1 716.60156 cents 15: 8 727.73437 cents 15: 11 761.13281 cents 15: 4 772.26562 cents 16: 16 785.15625 cents 16: 8 829.68750 cents 17: 3 809.17968 cents 17: 8 842.57813 cents 17: 9 853.71093 cents 17: 4 887.10938 cents 18: 6 866.60156 cents 18: 18 911.13281 cents 19: 3 924.02344 cents 19: 10 935.15624 cents 19: 9 968.55469 cents 19: 2 979.68750 cents 20: 20 992.57812 cents 20: 4 1037.10937 cents 21: 5 1016.60156 cents 21: 10 1050.00000 cents 21: 7 1061.13281 cents 21: 2 1094.53125 cents 22: 10 1074.02344 cents 22: 14 1118.55469 cents 23: 5 1131.44532 cents 23: 12 1142.57812 cents 23: 7 1175.97656 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 : 57.4 126.0 183.4 207.4 264.8 288.9 346.3 414.8 472.3 496.3 553.7 622.3 679.7 703.7 761.1 829.7 887.1 911.1 968.6 992.6 1050.0 1118.6 1176.0 1200.0 57.4 : 68.6 126.0 150.0 207.4 231.4 288.9 357.4 414.8 438.9 496.3 564.8 622.3 646.3 703.7 772.3 829.7 853.7 911.1 935.2 992.6 1061.1 1118.6 1142.6 1200.0 126.0 : 57.4 81.4 138.9 162.9 220.3 288.9 346.3 370.3 427.7 496.3 553.7 577.7 635.2 703.7 761.1 785.2 842.6 866.6 924.0 992.6 1050.0 1074.0 1131.4 1200.0 183.4 : 24.0 81.4 105.5 162.9 231.4 288.9 312.9 370.3 438.9 496.3 520.3 577.7 646.3 703.7 727.7 785.2 809.2 866.6 935.2 992.6 1016.6 1074.0 1142.6 1200.0 207.4 : 57.4 81.4 138.9 207.4 264.8 288.9 346.3 414.8 472.3 496.3 553.7 622.3 679.7 703.7 761.1 785.2 842.6 911.1 968.6 992.6 1050.0 1118.6 1176.0 1200.0 264.8 : 24.0 81.4 150.0 207.4 231.4 288.9 357.4 414.8 438.9 496.3 564.8 622.3 646.3 703.7 727.7 785.2 853.7 911.1 935.2 992.6 1061.1 1118.6 1142.6 1200.0 288.9 : 57.4 126.0 183.4 207.4 264.8 333.4 390.8 414.8 472.3 540.8 598.2 622.3 679.7 703.7 761.1 829.7 887.1 911.1 968.6 1037.1 1094.5 1118.6 1176.0 1200.0 346.3 : 68.6 126.0 150.0 207.4 276.0 333.4 357.4 414.8 483.4 540.8 564.8 622.3 646.3 703.7 772.3 829.7 853.7 911.1 979.7 1037.1 1061.1 1118.6 1142.6 1200.0 414.8 : 57.4 81.4 138.9 207.4 264.8 288.9 346.3 414.8 472.3 496.3 553.7 577.7 635.2 703.7 761.1 785.2 842.6 911.1 968.6 992.6 1050.0 1074.0 1131.4 1200.0 472.3 : 24.0 81.4 150.0 207.4 231.4 288.9 357.4 414.8 438.9 496.3 520.3 577.7 646.3 703.7 727.7 785.2 853.7 911.1 935.2 992.6 1016.6 1074.0 1142.6 1200.0 496.3 : 57.4 126.0 183.4 207.4 264.8 333.4 390.8 414.8 472.3 496.3 553.7 622.3 679.7 703.7 761.1 829.7 887.1 911.1 968.6 992.6 1050.0 1118.6 1176.0 1200.0 553.7 : 68.6 126.0 150.0 207.4 276.0 333.4 357.4 414.8 438.9 496.3 564.8 622.3 646.3 703.7 772.3 829.7 853.7 911.1 935.2 992.6 1061.1 1118.6 1142.6 1200.0 622.3 : 57.4 81.4 138.9 207.4 264.8 288.9 346.3 370.3 427.7 496.3 553.7 577.7 635.2 703.7 761.1 785.2 842.6 866.6 924.0 992.6 1050.0 1074.0 1131.4 1200.0 679.7 : 24.0 81.4 150.0 207.4 231.4 288.9 312.9 370.3 438.9 496.3 520.3 577.7 646.3 703.7 727.7 785.2 809.2 866.6 935.2 992.6 1016.6 1074.0 1142.6 1200.0 703.7 : 57.4 126.0 183.4 207.4 264.8 288.9 346.3 414.8 472.3 496.3 553.7 622.3 679.7 703.7 761.1 785.2 842.6 911.1 968.6 992.6 1050.0 1118.6 1176.0 1200.0 761.1 : 68.6 126.0 150.0 207.4 231.4 288.9 357.4 414.8 438.9 496.3 564.8 622.3 646.3 703.7 727.7 785.2 853.7 911.1 935.2 992.6 1061.1 1118.6 1142.6 1200.0 829.7 : 57.4 81.4 138.9 162.9 220.3 288.9 346.3 370.3 427.7 496.3 553.7 577.7 635.2 659.2 716.6 785.2 842.6 866.6 924.0 992.6 1050.0 1074.0 1131.4 1200.0 887.1 : 24.0 81.4 105.5 162.9 231.4 288.9 312.9 370.3 438.9 496.3 520.3 577.7 601.8 659.2 727.7 785.2 809.2 866.6 935.2 992.6 1016.6 1074.0 1142.6 1200.0 911.1 : 57.4 81.4 138.9 207.4 264.8 288.9 346.3 414.8 472.3 496.3 553.7 577.7 635.2 703.7 761.1 785.2 842.6 911.1 968.6 992.6 1050.0 1118.6 1176.0 1200.0 968.6 : 24.0 81.4 150.0 207.4 231.4 288.9 357.4 414.8 438.9 496.3 520.3 577.7 646.3 703.7 727.7 785.2 853.7 911.1 935.2 992.6 1061.1 1118.6 1142.6 1200.0 992.6 : 57.4 126.0 183.4 207.4 264.8 333.4 390.8 414.8 472.3 496.3 553.7 622.3 679.7 703.7 761.1 829.7 887.1 911.1 968.6 1037.1 1094.5 1118.6 1176.0 1200.0 1050.0: 68.6 126.0 150.0 207.4 276.0 333.4 357.4 414.8 438.9 496.3 564.8 622.3 646.3 703.7 772.3 829.7 853.7 911.1 979.7 1037.1 1061.1 1118.6 1142.6 1200.0 1118.6: 57.4 81.4 138.9 207.4 264.8 288.9 346.3 370.3 427.7 496.3 553.7 577.7 635.2 703.7 761.1 785.2 842.6 911.1 968.6 992.6 1050.0 1074.0 1131.4 1200.0 1176.0: 24.0 81.4 150.0 207.4 231.4 288.9 312.9 370.3 438.9 496.3 520.3 577.7 646.3 703.7 727.7 785.2 853.7 911.1 935.2 992.6 1016.6 1074.0 1142.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0234 .. 68.5547 cents 44.53124 cents 24.02344 cents 2: 81.4453 .. 125.9766 cents 44.53124 cents 12.89064 cents 3: 105.4687 .. 183.3984 cents 77.92969 cents -20.50781 cents 4: 162.8906 .. 207.4219 cents 44.53125 cents -20.50781 cents 5: 220.3125 .. 275.9766 cents 55.66407 cents 12.89062 cents 6: 288.8672 .. 333.3984 cents 44.53125 cents 12.89062 cents 7: 312.8906 .. 390.8203 cents 77.92969 cents -20.50782 cents 8: 370.3125 .. 414.8438 cents 44.53125 cents -20.50781 cents 9: 427.7344 .. 483.3984 cents 55.66406 cents 12.89063 cents 10: 496.2891 .. 540.8203 cents 44.53125 cents 12.89062 cents 11: 520.3125 .. 598.2422 cents 77.92969 cents -20.50781 cents 12: 577.7344 .. 622.2656 cents 44.53125 cents -20.50781 cents 13: 601.7578 .. 679.6875 cents 77.92969 cents -20.50782 cents 14: 659.1797 .. 703.7109 cents 44.53125 cents -20.50781 cents 15: 716.6016 .. 772.2656 cents 55.66406 cents 12.89062 cents 16: 785.1562 .. 829.6875 cents 44.53125 cents 12.89063 cents 17: 809.1797 .. 887.1094 cents 77.92970 cents -20.50782 cents 18: 866.6016 .. 911.1328 cents 44.53125 cents -20.50782 cents 19: 924.0234 .. 979.6875 cents 55.66406 cents 12.89063 cents 20: 992.5781 .. 1037.1094 cents 44.53125 cents 12.89062 cents 21: 1016.6016 .. 1094.5313 cents 77.92969 cents -20.50781 cents 22: 1074.0234 .. 1118.5547 cents 44.53125 cents -20.50781 cents 23: 1131.4453 .. 1175.9766 cents 44.53124 cents 12.89063 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 24.02343 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 68.55468 cents Average / Smallest step : 2.081301 Largest / Average step : 1.371094 Largest / Smallest step : 2.853659 Median interval of one step : 57.42188 cents, amount: 12 Most common interval of one step : 57.42188 cents, amount: 12 Least squares average step : 50.79217 cents, oct.: 1219.01212 cents Scale is not proper Scale is a mode of a 2048-tone equal temperament with octave 2/1 degrees: 98 215 313 354 452 493 591 708 806 847 945 1062 1160 1201 1299 1416 1514 1555 1653 1694 1792 1909 2007 2048 Least number of segments generator : 1025 of 600.586 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1201 of 703.711 cents and inv. generated superset size: 266 = 242 more = 1108.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACACABACABACABACACABAC Step pattern size order : MLMSMSMLMSMLMSMLMSMSMLMS Scale is a Constant Structure, by a margin of 3.51562 cents Scale diversity : 1.284200 Lumma stability : 0.147461 Lumma impropriety factor : 0.205078 Number of different interval sizes : 68 = 2.95652 / 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 : 3.51562 cents Most common intervals : 496.28906 cents & inv., amount: 22 Most common triad is 0.0 496.289 703.711 cents, amount: 20 Number of recognisable fifths : 23, average 704.2714 cents Number of appreciable fifths : 22, average 703.7109 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 7 = 29.1667% Limited inverse transpositions : 23 Inversional symmetry on intervals : 11-12 23-24 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
24: 1 1 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: 18.6164 c. M: 37.1094 c. 26: 1 2 1 0 2 0 1 2 1 1 1 1 2 0 1 2 1 1 1 0 2 1 1 1 N SD: 14.0094 c. M: 23.3474 c. 27: 1 2 1 0 2 0 2 1 1 1 1 2 1 1 1 1 2 0 2 0 1 2 1 1 N SD: 16.2816 c. M: 29.6875 c. 29: 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 P D3 SD: 11.8520 c. M: 18.1439 c. 30: 1 2 2 0 2 0 2 1 2 0 2 2 1 1 1 2 1 1 1 1 1 2 1 1 N SD: 11.2799 c. M:-17.7344 c. 31: 1 2 2 0 2 0 2 2 1 1 1 2 2 0 2 1 2 1 1 1 1 2 1 1 N SD: 11.2767 c. M: 18.7122 c. 33: 2 1 2 1 1 1 2 1 2 1 1 2 2 0 2 2 1 1 2 0 2 2 1 1 N SD: 10.4291 c. M:-17.3473 c. 35: 2 2 1 1 2 0 2 2 2 0 2 2 2 1 1 2 2 1 1 1 2 2 1 1 N SD: 9.6547 c. M: 16.2891 c. 37: 2 2 2 0 2 1 2 2 2 0 2 2 2 1 1 3 1 1 2 1 1 3 1 1 N SD: 9.6251 c. M:-16.5804 c. 38: 2 2 2 1 1 1 2 2 2 1 2 2 2 0 2 2 2 1 2 0 2 2 2 1 N SD: 8.7656 c. M:-15.0493 c. 39: 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 0 2 1 2 2 2 1 N SD: 9.0641 c. M: 18.8251 c. 41: 2 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 1 P D3 SD: 5.1445 c. M: 10.1753 c. 46: 2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1 N SD: 3.5754 c. M: 7.1586 c. 58: 3 3 3 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 1 3 3 3 1 N D3 SD: 2.9999 c. M:-5.4351 c. 87: 4 5 4 2 4 2 4 5 4 2 4 5 4 2 4 5 4 2 4 2 4 5 4 2 N SD: 2.2936 c. M: 4.3508 c. 104: 5 6 5 2 5 2 5 6 5 2 5 6 5 2 5 6 5 2 5 2 5 6 5 2 N SD: 0.6783 c. M:-1.3522 c. 191: 9 11 9 4 9 4 9 11 9 4 9 11 9 4 9 11 9 4 9 4 9 11 9 4 N SD: 0.7241 c. M: 1.2455 c. 249: 12 14 12 5 12 5 12 14 12 5 12 14 12 5 12 14 12 5 12 5 12 14 12 5 N SD: 0.3926 c. M: 0.7718 c. 295: 14 17 14 6 14 6 14 17 14 6 14 17 14 6 14 17 14 6 14 6 14 17 14 6 N SD: 0.3105 c. M: 0.5263 c. 353: 17 20 17 7 17 7 17 20 17 7 17 20 17 7 17 20 17 7 17 7 17 20 17 7 N SD: 0.2374 c. M:-0.4531 c. 399: 19 23 19 8 19 8 19 23 19 8 19 23 19 8 19 23 19 8 19 8 19 23 19 8 N SD: 0.2186 c. M: 0.4244 c. 457: 22 26 22 9 22 9 22 26 22 9 22 26 22 9 22 26 22 9 22 9 22 26 22 9 N SD: 0.2630 c. M:-0.4180 c. 503: 24 29 24 10 24 10 24 29 24 10 24 29 24 10 24 29 24 10 24 10 24 29 24 10 N SD: 0.2575 c. M:-0.5312 c. 544: 26 31 26 11 26 11 26 31 26 11 26 31 26 11 26 31 26 11 26 11 26 31 26 11 N SD: 0.1729 c. M: 0.3447 c. 648: 31 37 31 13 31 13 31 37 31 13 31 37 31 13 31 37 31 13 31 13 31 37 31 13 N SD: 0.0363 c. M: 0.0723 c. 1400: 67 80 67 28 67 28 67 80 67 28 67 80 67 28 67 80 67 28 67 28 67 80 67 28 N SD: 0.0168 c. M:-0.0335 c. 2048: 98 117 98 41 98 41 98 117 98 41 98 117 98 41 98 117 98 41 98 41 98 117 98 41 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.8780 cents 3 .. 6 match: 3 H SD: 1.0878 cents 4 .. 8 match: 4 H SD: 7.1463 cents 5 .. 10 match: 5 H SD: 9.8556 cents 6 .. 12 match: 6 H SD: 0.7120 cents 7 .. 14 match: 7 H SD: 7.0097 cents 8 .. 16 match: 8 H SD: 5.4053 cents 9 .. 18 match: 9 H SD: 2.6107 cents 10 .. 20 match: 10 H SD: 5.6622 cents 11 .. 22 match: 11 H SD: 4.8963 cents 12 .. 24 match: 12 H SD: 4.2387 cents 13 .. 26 match: 13 H SD: 3.1860 cents 14 .. 28 match: 14 H SD: 4.7464 cents 15 .. 30 match: 15 H SD: 4.8071 cents 16 .. 32 match: 15 SD: 3.5187 cents 17 .. 34 match: 16 S SD: 4.9910 cents 18 .. 36 match: 17 S SD: 3.0521 cents 19 .. 38 match: 18 SD: 3.6100 cents 20 .. 40 match: 19 SD: 4.2957 cents 21 .. 42 match: 20 SD: 3.7199 cents 22 .. 44 match: 19 S SD: 3.3107 cents 23 .. 46 match: 22 S SD: 2.6697 cents 24 .. 48 match: 20 SD: 2.6932 cents 25 .. 50 match: 20 S SD: 3.0780 cents 26 .. 52 match: 22 SD: 2.3711 cents 27 .. 54 match: 23 SD: 2.4817 cents 28 .. 56 match: 21 SD: 2.6606 cents 29 .. 58 match: 22 SD: 2.3415 cents 30 .. 60 match: 23 SD: 2.2594 cents 31 .. 62 match: 22 SD: 2.3260 cents 32 .. 64 match: 23 SD: 1.9602 cents 33 .. 66 match: 23 SD: 2.2837 cents 34 .. 68 match: 21 SD: 2.2276 cents 35 .. 70 match: 22 SD: 2.0602 cents 36 .. 72 match: 24 SD: 1.7622 cents 37 .. 74 match: 23 SD: 1.7040 cents 40 .. 80 match: 22 SD: 1.6306 cents 41 .. 82 match: 22 SD: 1.7828 cents 42 .. 84 match: 23 SD: 1.5819 cents 43 .. 86 match: 23 SD: 1.8755 cents 44 .. 88 match: 24 SD: 1.6315 cents 46 .. 92 match: 23 SD: 1.7898 cents 48 .. 96 match: 24 SD: 1.4009 cents 50 .. 100 match: 23 SD: 1.5723 cents 51 .. 102 match: 23 SD: 1.4565 cents 52 .. 104 match: 23 SD: 1.4150 cents 53 .. 106 match: 24 SD: 1.3774 cents 54 .. 108 match: 24 SD: 0.9913 cents 67 .. 134 match: 24 SD: 0.9437 cents 72 .. 144 match: 24 SD: 0.9276 cents 78 .. 156 match: 24 SD: 0.8347 cents 81 .. 162 match: 24 SD: 0.8268 cents 85 .. 170 match: 24 SD: 0.7881 cents 88 .. 176 match: 24 SD: 0.7603 cents 90 .. 180 match: 24 SD: 0.7195 cents 96 .. 192 match: 24 SD: 0.6483 cents 108 .. 216 match: 24 SD: 0.5563 cents 117 .. 234 match: 24 SD: 0.5269 cents 127 .. 254 match: 24 SD: 0.4473 cents 143 .. 286 match: 24 SD: 0.4034 cents 150 .. 300 match: 24 SD: 0.4029 cents 159 .. 318 match: 24 SD: 0.3930 cents 172 .. 344 match: 24 SD: 0.3461 cents 181 .. 362 match: 24 SD: 0.2696 cents 236 .. 472 match: 24 SD: 0.2543 cents 241 .. 482 match: 24 SD: 0.2429 cents 265 .. 530 match: 24 SD: 0.2375 cents 266 .. 532 match: 24 SD: 0.2240 cents 291 .. 582 match: 24 SD: 0.2231 cents 293 .. 586 match: 24 SD: 0.2068 cents 303 .. 606 match: 24 SD: 0.1875 cents 329 .. 658 match: 24 SD: 0.1698 cents 358 .. 716 match: 24 SD: 0.1593 cents 385 .. 770 match: 24 SD: 0.1534 cents 393 .. 786 match: 24 SD: 0.1530 cents 411 .. 822 match: 24 SD: 0.1382 cents 424 .. 848 match: 24 SD: 0.1333 cents 447 .. 894 match: 24 SD: 0.1186 cents 478 .. 956 match: 24 SD: 0.1157 cents 501 .. 1002 match: 24 SD: 0.1035 cents 599 .. 1198 match: 24 SD: 0.0945 cents