Scala analysis: mostly-elevens-scale-tempered-to-72-EDO
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.000 cents 50.000000 2: 150.000 cents 150.000000 3: 216.667 cents 216.667000 4: 283.333 cents 283.333000 5: 350.000 cents 350.000000 6: 416.667 cents 416.667000 7: 500.000 cents 500.000000 8: 583.333 cents 583.333000 9: 650.000 cents 650.000000 10: 700.000 cents 700.000000 11: 783.333 cents 783.333000 12: 850.000 cents 850.000000 13: 916.667 cents 916.667000 14: 1000.000 cents 1000.000000 15: 1050.000 cents 1050.000000 16: 1116.667 cents 1116.667000 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 83.3330 cents 83.3330 1: 50.0000 cents 50.0000 2: 100.0000 cents 100.0000 3: 66.6670 cents 66.6670 4: 66.6660 cents 66.6660 5: 66.6670 cents 66.6670 6: 66.6670 cents 66.6670 7: 83.3330 cents 83.3330 8: 83.3330 cents 83.3330 9: 66.6670 cents 66.6670 10: 50.0000 cents 50.0000 11: 83.3330 cents 83.3330 12: 66.6670 cents 66.6670 13: 66.6670 cents 66.6670 14: 83.3330 cents 83.3330 15: 50.0000 cents 50.0000 16: 66.6670 cents 66.6670 17: 83.3330 cents 83.3330
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 50.00000 cents 1: 1 66.66600 cents 1: 7 66.66700 cents 1: 5 83.33300 cents 1: 1 100.00000 cents 2: 2 116.66700 cents 2: 5 133.33300 cents 2: 2 133.33400 cents 2: 6 150.00000 cents 2: 1 166.66600 cents 2: 1 166.66700 cents 3: 9 200.00000 cents 3: 4 216.66700 cents 3: 4 233.33300 cents 4: 1 250.00000 cents 4: 5 266.66700 cents 4: 5 283.33300 cents 4: 6 300.00000 cents 5: 1 333.33300 cents 5: 2 333.33400 cents 5: 8 350.00000 cents 5: 3 366.66600 cents 5: 3 366.66700 cents 6: 2 400.00000 cents 6: 7 416.66700 cents 6: 7 433.33300 cents 6: 1 450.00000 cents 7: 3 466.66700 cents 7: 2 483.33300 cents 7: 11 500.00000 cents 7: 1 533.33300 cents 8: 1 533.33400 cents 8: 5 550.00000 cents 8: 2 566.66600 cents 8: 5 566.66700 cents 8: 3 583.33300 cents 8: 1 600.00000 cents 9: 1 600.00000 cents 9: 3 616.66700 cents 9: 5 633.33300 cents 9: 2 633.33400 cents 9: 5 650.00000 cents 9: 1 666.66600 cents 10: 1 666.66700 cents 10: 11 700.00000 cents 10: 2 716.66700 cents 10: 3 733.33300 cents 11: 1 750.00000 cents 11: 7 766.66700 cents 11: 7 783.33300 cents 11: 2 800.00000 cents 12: 3 833.33300 cents 12: 3 833.33400 cents 12: 8 850.00000 cents 12: 2 866.66600 cents 12: 1 866.66700 cents 13: 6 900.00000 cents 13: 5 916.66700 cents 13: 5 933.33300 cents 13: 1 950.00000 cents 14: 4 966.66700 cents 14: 4 983.33300 cents 14: 9 1000.00000 cents 15: 1 1033.33300 cents 15: 1 1033.33400 cents 15: 6 1050.00000 cents 15: 2 1066.66600 cents 15: 5 1066.66700 cents 15: 2 1083.33300 cents 16: 1 1100.00000 cents 16: 5 1116.66700 cents 16: 7 1133.33300 cents 16: 1 1133.33400 cents 16: 3 1150.00000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.62500 = 37/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 50.0 150.0 216.7 283.3 350.0 416.7 500.0 583.3 650.0 700.0 783.3 850.0 916.7 1000.0 1050.0 1116.7 1200.0 50.0 : 100.0 166.7 233.3 300.0 366.7 450.0 533.3 600.0 650.0 733.3 800.0 866.7 950.0 1000.0 1066.7 1150.0 1200.0 150.0 : 66.7 133.3 200.0 266.7 350.0 433.3 500.0 550.0 633.3 700.0 766.7 850.0 900.0 966.7 1050.0 1100.0 1200.0 216.7 : 66.7 133.3 200.0 283.3 366.7 433.3 483.3 566.7 633.3 700.0 783.3 833.3 900.0 983.3 1033.3 1133.3 1200.0 283.3 : 66.7 133.3 216.7 300.0 366.7 416.7 500.0 566.7 633.3 716.7 766.7 833.3 916.7 966.7 1066.7 1133.3 1200.0 350.0 : 66.7 150.0 233.3 300.0 350.0 433.3 500.0 566.7 650.0 700.0 766.7 850.0 900.0 1000.0 1066.7 1133.3 1200.0 416.7 : 83.3 166.7 233.3 283.3 366.7 433.3 500.0 583.3 633.3 700.0 783.3 833.3 933.3 1000.0 1066.7 1133.3 1200.0 500.0 : 83.3 150.0 200.0 283.3 350.0 416.7 500.0 550.0 616.7 700.0 750.0 850.0 916.7 983.3 1050.0 1116.7 1200.0 583.3 : 66.7 116.7 200.0 266.7 333.3 416.7 466.7 533.3 616.7 666.7 766.7 833.3 900.0 966.7 1033.3 1116.7 1200.0 650.0 : 50.0 133.3 200.0 266.7 350.0 400.0 466.7 550.0 600.0 700.0 766.7 833.3 900.0 966.7 1050.0 1133.3 1200.0 700.0 : 83.3 150.0 216.7 300.0 350.0 416.7 500.0 550.0 650.0 716.7 783.3 850.0 916.7 1000.0 1083.3 1150.0 1200.0 783.3 : 66.7 133.3 216.7 266.7 333.3 416.7 466.7 566.7 633.3 700.0 766.7 833.3 916.7 1000.0 1066.7 1116.7 1200.0 850.0 : 66.7 150.0 200.0 266.7 350.0 400.0 500.0 566.7 633.3 700.0 766.7 850.0 933.3 1000.0 1050.0 1133.3 1200.0 916.7 : 83.3 133.3 200.0 283.3 333.3 433.3 500.0 566.7 633.3 700.0 783.3 866.7 933.3 983.3 1066.7 1133.3 1200.0 1000.0: 50.0 116.7 200.0 250.0 350.0 416.7 483.3 550.0 616.7 700.0 783.3 850.0 900.0 983.3 1050.0 1116.7 1200.0 1050.0: 66.7 150.0 200.0 300.0 366.7 433.3 500.0 566.7 650.0 733.3 800.0 850.0 933.3 1000.0 1066.7 1150.0 1200.0 1116.7: 83.3 133.3 233.3 300.0 366.7 433.3 500.0 583.3 666.7 733.3 783.3 866.7 933.3 1000.0 1083.3 1133.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 100.0000 cents 50.00000 cents 50.00000 cents 2: 116.6670 .. 166.6670 cents 50.00000 cents 16.66700 cents 3: 200.0000 .. 233.3330 cents 33.33300 cents 33.33300 cents 4: 250.0000 .. 300.0000 cents 50.00000 cents 16.66700 cents 5: 333.3330 .. 366.6670 cents 33.33400 cents 33.33300 cents 6: 400.0000 .. 450.0000 cents 50.00000 cents 33.33300 cents 7: 466.6670 .. 533.3330 cents 66.66600 cents 16.66700 cents 8: 533.3340 .. 600.0000 cents 66.66600 cents 0.00100 cents 9: 600.0000 .. 666.6660 cents 66.66600 cents 1/1, 0.0000 cents 10: 666.6670 .. 733.3330 cents 66.66600 cents 0.00100 cents 11: 750.0000 .. 800.0000 cents 50.00000 cents 16.66700 cents 12: 833.3330 .. 866.6670 cents 33.33400 cents 33.33300 cents 13: 900.0000 .. 950.0000 cents 50.00000 cents 33.33300 cents 14: 966.6670 .. 1000.0000 cents 33.33300 cents 16.66700 cents 15: 1033.3330 .. 1083.3330 cents 50.00000 cents 33.33300 cents 16: 1100.0000 .. 1150.0000 cents 50.00000 cents 16.66700 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 100.00000 cents Average / Smallest step : 1.411765 Largest / Average step : 1.416667 Largest / Smallest step : 2.000000 Median interval of one step : 66.66700 cents, amount: 7 Most common interval of one step : 66.66700 cents, amount: 7 Least squares average step : 70.67227 cents, oct.: 1201.42862 cents Scale is proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 3 9 13 17 21 25 30 35 39 42 47 51 55 60 63 67 72 Least number of segments generator : 43 of 716.667 cents and inv. number of contiguous generator circle segments: 3 Shortest superset generator : 55 of 916.667 cents and inv. generated superset size: 41 = 24 more = 241.176% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCCEECAECCEACE Step pattern size order : AECBCCDDCADCCDACD Interval vector is [ 0 0 3 7 5 1 2 2 6 1 0 9 4 4 1 5 5 6 0 2 8 3 0 2 7 7 1 3 2 11 0 1 5 5 3 1 ] Scale is not a Constant Structure Scale diversity : 1.393535 Rothenberg stability : 0.992647 = 135/136 Lumma stability : 0.333335 Number of different interval sizes : 73 = 4.56250 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.62500 = 37/8 Median interval variety : 3.5 Lowest interval variety : 3 Smallest interval difference : 0.00100 cents Most common intervals : 500.00000 cents & inv., amount: 11 Most common triad is 0.0 500.000 700.000 cents, amount: 7 Number of recognisable fifths : 13, average 702.5642 cents Number of appreciable fifths : 11, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 11 = 64.7059% -- 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: 9.8527 c. M:-20.5882 c. 24: 1 2 1 2 1 1 2 2 1 1 2 1 1 2 1 1 2 N D3 SD: 10.6950 c. M:-16.6670 c. 29: 1 3 1 2 1 2 2 2 2 1 2 1 2 2 1 2 2 N D3 SD: 10.4132 c. M: 22.4138 c. 31: 1 3 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 N D3 SD: 7.9154 c. M:-15.5911 c. 38: 2 3 2 2 2 2 3 2 3 1 3 2 2 3 1 2 3 P T3 SD: 8.0424 c. M: 14.9119 c. 41: 2 3 2 3 2 2 3 3 2 2 3 2 2 3 2 2 3 P D3 SD: 5.9851 c. M: 11.7890 c. 46: 2 4 2 3 2 3 3 3 3 2 3 3 2 3 2 3 3 P D3 SD: 6.1813 c. M: 10.8696 c. 48: 2 4 3 2 3 3 3 3 3 2 3 3 3 3 2 3 3 P D3 SD: 5.3472 c. M:-8.3330 c. 55: 2 5 3 3 3 3 4 4 3 2 4 3 3 4 2 3 4 N SD: 3.0455 c. M: 6.3636 c. 72: 3 6 4 4 4 4 5 5 4 3 5 4 4 5 3 4 5 P SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.9775 cents 3 .. 6 match: 3 H SD: 10.7891 cents 4 .. 8 match: 4 H SD: 10.8885 cents 5 .. 10 match: 5 H SD: 9.5403 cents 6 .. 12 match: 6 H SD: 6.0619 cents 7 .. 14 match: 7 H SD: 6.9243 cents 8 .. 16 match: 8 H SD: 7.8868 cents 9 .. 18 match: 9 H SD: 5.9649 cents 10 .. 20 match: 10 H SD: 6.2833 cents 11 .. 22 match: 11 H SD: 5.2979 cents 12 .. 24 match: 12 H SD: 5.2546 cents 13 .. 26 match: 13 H SD: 5.7521 cents 14 .. 28 match: 14 H SD: 4.9595 cents 15 .. 30 match: 13 SD: 6.2274 cents 16 .. 32 match: 14 SD: 6.0658 cents 17 .. 34 match: 15 SD: 5.4020 cents 18 .. 36 match: 16 SD: 4.6257 cents 19 .. 38 match: 15 SD: 4.9974 cents 20 .. 40 match: 16 SD: 4.8059 cents 21 .. 42 match: 16 SD: 4.3469 cents 22 .. 44 match: 17 SD: 2.8848 cents 30 .. 60 match: 17 SD: 2.0683 cents 40 .. 80 match: 17 SD: 1.8019 cents 44 .. 88 match: 17 SD: 1.4093 cents 60 .. 120 match: 17 SD: 1.3599 cents 62 .. 124 match: 17 SD: 1.2388 cents 63 .. 126 match: 17 SD: 1.1474 cents 66 .. 132 match: 17 SD: 0.8840 cents 77 .. 154 match: 17 SD: 0.8478 cents 90 .. 180 match: 17 SD: 0.8341 cents 95 .. 190 match: 17 SD: 0.8310 cents 96 .. 192 match: 17 SD: 0.7466 cents 98 .. 196 match: 17 SD: 0.7377 cents 99 .. 198 match: 17 SD: 0.7349 cents 107 .. 214 match: 17 SD: 0.5896 cents 129 .. 258 match: 17 SD: 0.5029 cents 143 .. 286 match: 17 SD: 0.4659 cents 164 .. 328 match: 17 SD: 0.4408 cents 165 .. 330 match: 17 SD: 0.4142 cents 169 .. 338 match: 17 SD: 0.4134 cents 173 .. 346 match: 17 SD: 0.3714 cents 180 .. 360 match: 17 SD: 0.3498 cents 202 .. 404 match: 17 SD: 0.3168 cents 210 .. 420 match: 17 SD: 0.3056 cents 232 .. 464 match: 17 SD: 0.2841 cents 242 .. 484 match: 17 SD: 0.2724 cents 265 .. 530 match: 17 SD: 0.2439 cents 275 .. 550 match: 17 SD: 0.2414 cents 287 .. 574 match: 17 SD: 0.2397 cents 299 .. 598 match: 17 SD: 0.2150 cents 308 .. 616 match: 17 SD: 0.2071 cents 309 .. 618 match: 17 SD: 0.2007 cents 331 .. 662 match: 17 SD: 0.1787 cents 344 .. 688 match: 17 SD: 0.1758 cents 367 .. 734 match: 17 SD: 0.1672 cents 397 .. 794 match: 17 SD: 0.1648 cents 412 .. 824 match: 17 SD: 0.1641 cents 434 .. 868 match: 17 SD: 0.1551 cents 445 .. 890 match: 17 SD: 0.1527 cents 472 .. 944 match: 17 SD: 0.1462 cents 474 .. 948 match: 17 SD: 0.1448 cents 477 .. 954 match: 17 SD: 0.1415 cents 500 .. 1000 match: 17 SD: 0.1374 cents 510 .. 1020 match: 17 SD: 0.1338 cents 517 .. 1034 match: 17 SD: 0.1279 cents 540 .. 1080 match: 17 SD: 0.0921 cents