Scala analysis: miracle41s
Miracle-41 with Secor's minimax generator of 116.7155941 cents (5:9 exact). XH5, 1976
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32.844 cents 32.844060 2: 51.027 cents 51.027480 3: 83.872 cents 83.871540 4: 116.716 cents 116.715590 5: 149.560 cents 149.559650 6: 10/9 182.403712 minor whole tone 7: 200.587 cents 200.587130 8: 233.431 cents 233.431190 9: 266.275 cents 266.275250 10: 299.119 cents 299.119310 11: 317.303 cents 317.302720 12: 350.147 cents 350.146780 13: 382.991 cents 382.990840 14: 415.835 cents 415.834900 15: 434.018 cents 434.018320 16: 466.862 cents 466.862380 17: 499.706 cents 499.706430 18: 532.550 cents 532.550490 19: 550.734 cents 550.733910 20: 583.578 cents 583.577970 21: 616.422 cents 616.422030 22: 649.266 cents 649.266090 23: 667.450 cents 667.449510 24: 700.294 cents 700.293570 25: 733.138 cents 733.137620 26: 765.982 cents 765.981680 27: 784.165 cents 784.165100 28: 817.009 cents 817.009160 29: 849.853 cents 849.853220 30: 882.697 cents 882.697280 31: 900.881 cents 900.880690 32: 933.725 cents 933.724750 33: 966.569 cents 966.568810 34: 999.413 cents 999.412870 35: 9/5 1017.596288 just minor seventh, BP seventh 36: 1050.440 cents 1050.440350 37: 1083.284 cents 1083.284410 38: 1116.128 cents 1116.128470 39: 1134.312 cents 1134.311880 40: 1167.156 cents 1167.155940 41: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32.8441 cents 32.8441 1: 32.8441 cents 32.8441 2: 18.1834 cents 18.1834 3: 32.8441 cents 32.8441 4: 32.8440 cents 32.8440 5: 32.8441 cents 32.8441 6: 32.8441 cents 32.8441 7: 18.1834 cents 18.1834 8: 32.8441 cents 32.8441 9: 32.8441 cents 32.8441 10: 32.8441 cents 32.8441 11: 18.1834 cents 18.1834 12: 32.8441 cents 32.8441 13: 32.8441 cents 32.8441 14: 32.8441 cents 32.8441 15: 18.1834 cents 18.1834 16: 32.8441 cents 32.8441 17: 32.8441 cents 32.8441 18: 32.8441 cents 32.8441 19: 18.1834 cents 18.1834 20: 32.8441 cents 32.8441 21: 32.8441 cents 32.8441 22: 32.8441 cents 32.8441 23: 18.1834 cents 18.1834 24: 32.8441 cents 32.8441 25: 32.8441 cents 32.8441 26: 32.8441 cents 32.8441 27: 18.1834 cents 18.1834 28: 32.8441 cents 32.8441 29: 32.8441 cents 32.8441 30: 32.8441 cents 32.8441 31: 18.1834 cents 18.1834 32: 32.8441 cents 32.8441 33: 32.8441 cents 32.8441 34: 32.8441 cents 32.8441 35: 18.1834 cents 18.1834 36: 32.8441 cents 32.8441 37: 32.8441 cents 32.8441 38: 32.8441 cents 32.8441 39: 18.1834 cents 18.1834 40: 32.8441 cents 32.8441 41: 32.8441 cents 32.8441
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 18.18342 cents 1: 31 32.84406 cents 2: 20 51.02748 cents 2: 21 65.68811 cents 3: 30 83.87154 cents 3: 11 98.53217 cents 4: 40 116.71559 cents 4: 1 131.37623 cents 5: 9 134.89901 cents 5: 32 149.55965 cents 6: 19 167.74307 cents 6: 22 10/9 182.404 cents minor whole tone 7: 29 200.58713 cents 7: 12 215.24777 cents 8: 39 233.43119 cents 8: 2 248.09183 cents 9: 8 251.61461 cents 9: 33 266.27525 cents 10: 18 284.45866 cents 10: 23 299.11931 cents 11: 28 317.30272 cents 11: 13 331.96336 cents 12: 38 350.14678 cents 12: 3 364.80742 cents 13: 7 368.33020 cents 13: 34 382.99084 cents 14: 17 401.17426 cents 14: 24 415.83490 cents 15: 27 434.01832 cents 15: 14 448.67895 cents 16: 37 466.86238 cents 16: 4 481.52301 cents 17: 6 485.04580 cents 17: 35 499.70643 cents 18: 16 517.88985 cents 18: 25 532.55049 cents 19: 26 550.73391 cents 19: 15 565.39455 cents 20: 36 583.57797 cents 20: 5 598.23861 cents 21: 5 601.76139 cents 21: 36 616.42203 cents 22: 15 634.60545 cents 22: 26 649.26609 cents 23: 25 667.44951 cents 23: 16 682.11014 cents 24: 35 700.29357 cents 24: 6 714.95420 cents 25: 4 718.47698 cents 25: 37 733.13762 cents 26: 14 751.32104 cents 26: 27 765.98168 cents 27: 24 784.16510 cents 27: 17 798.82574 cents 28: 34 817.00916 cents 28: 7 831.66980 cents 29: 3 81/50 835.193 cents acute minor sixth 29: 38 849.85322 cents 30: 13 868.03663 cents 30: 28 882.69728 cents 31: 23 900.88069 cents 31: 18 915.54133 cents 32: 33 933.72475 cents 32: 8 948.38539 cents 33: 2 951.90817 cents 33: 39 966.56881 cents 34: 12 984.75223 cents 34: 29 999.41287 cents 35: 22 9/5 1017.596 cents just minor seventh, BP seventh 35: 19 1032.25693 cents 36: 32 1050.44035 cents 36: 9 1065.10099 cents 37: 1 1068.62377 cents 37: 40 1083.28441 cents 38: 11 1101.46782 cents 38: 30 1116.12847 cents 39: 21 1134.31188 cents 39: 20 1148.97252 cents 40: 31 1167.15594 cents 40: 10 1181.81658 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 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 0.0 : 32.8 51.0 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 32.8 : 18.2 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 51.0 : 32.8 65.7 98.5 131.4 149.6 182.4 215.2 248.1 266.3 299.1 332.0 364.8 383.0 415.8 448.7 481.5 499.7 532.6 565.4 598.2 616.4 649.3 682.1 715.0 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 83.9 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 116.7 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 149.6 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 182.4 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 485.0 517.9 550.7 583.6 601.8 634.6 667.4 700.3 718.5 751.3 784.2 817.0 835.2 868.0 900.9 933.7 951.9 984.8 1017.6 1050.4 1068.6 1101.5 1134.3 1167.2 1200.0 200.6 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1181.8 1200.0 233.4 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 266.3 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 299.1 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 485.0 517.9 550.7 583.6 601.8 634.6 667.4 700.3 718.5 751.3 784.2 817.0 835.2 868.0 900.9 933.7 951.9 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 317.3 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 350.1 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 383.0 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 415.8 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 485.0 517.9 550.7 583.6 601.8 634.6 667.4 700.3 718.5 751.3 784.2 817.0 835.2 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 434.0 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 466.9 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 499.7 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 532.6 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 485.0 517.9 550.7 583.6 601.8 634.6 667.4 700.3 718.5 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 550.7 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 583.6 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 616.4 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 649.3 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 485.0 517.9 550.7 583.6 601.8 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 667.4 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 715.0 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 700.3 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 733.1 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 766.0 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 485.0 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 784.2 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 598.2 616.4 649.3 682.1 715.0 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 817.0 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 849.9 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 882.7 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 368.3 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 900.9 : 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 481.5 499.7 532.6 565.4 598.2 616.4 649.3 682.1 715.0 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 933.7 : 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 966.6 : 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 999.4 : 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 251.6 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 1017.6: 32.8 65.7 98.5 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 364.8 383.0 415.8 448.7 481.5 499.7 532.6 565.4 598.2 616.4 649.3 682.1 715.0 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 1050.4: 32.8 65.7 83.9 116.7 149.6 182.4 200.6 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 1083.3: 32.8 51.0 83.9 116.7 149.6 167.7 200.6 233.4 266.3 299.1 317.3 350.1 383.0 415.8 434.0 466.9 499.7 532.6 550.7 583.6 616.4 649.3 667.4 700.3 733.1 766.0 784.2 817.0 849.9 882.7 900.9 933.7 966.6 999.4 1017.6 1050.4 1083.3 1116.1 1134.3 1167.2 1200.0 1116.1: 18.2 51.0 83.9 116.7 134.9 167.7 200.6 233.4 266.3 284.5 317.3 350.1 383.0 401.2 434.0 466.9 499.7 517.9 550.7 583.6 616.4 634.6 667.4 700.3 733.1 751.3 784.2 817.0 849.9 868.0 900.9 933.7 966.6 984.8 1017.6 1050.4 1083.3 1101.5 1134.3 1167.2 1200.0 1134.3: 32.8 65.7 98.5 116.7 149.6 182.4 215.2 248.1 266.3 299.1 332.0 364.8 383.0 415.8 448.7 481.5 499.7 532.6 565.4 598.2 616.4 649.3 682.1 715.0 733.1 766.0 798.8 831.7 849.9 882.7 915.5 948.4 966.6 999.4 1032.3 1065.1 1083.3 1116.1 1149.0 1181.8 1200.0 1167.2: 32.8 65.7 83.9 116.7 149.6 182.4 215.2 233.4 266.3 299.1 332.0 350.1 383.0 415.8 448.7 466.9 499.7 532.6 565.4 583.6 616.4 649.3 682.1 700.3 733.1 766.0 798.8 817.0 849.9 882.7 915.5 933.7 966.6 999.4 1032.3 1050.4 1083.3 1116.1 1149.0 1167.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.1834 .. 32.8441 cents 14.66064 cents 18.18342 cents 2: 51.0275 .. 65.6881 cents 14.66063 cents 18.18342 cents 3: 83.8715 .. 98.5322 cents 14.66063 cents 18.18343 cents 4: 116.7156 .. 131.3762 cents 14.66064 cents 18.18342 cents 5: 134.8990 .. 149.5596 cents 14.66064 cents 3.52278 cents 6: 167.7431 .. 182.4037 cents 14.66064 cents 18.18342 cents 7: 200.5871 .. 215.2478 cents 14.66064 cents 18.18342 cents 8: 233.4312 .. 248.0918 cents 14.66064 cents 18.18342 cents 9: 251.6146 .. 266.2753 cents 14.66064 cents 3.52278 cents 10: 284.4587 .. 299.1193 cents 14.66065 cents 18.18341 cents 11: 317.3027 .. 331.9634 cents 14.66064 cents 18.18341 cents 12: 350.1468 .. 364.8074 cents 14.66064 cents 18.18342 cents 13: 368.3302 .. 382.9908 cents 14.66064 cents 3.52278 cents 14: 401.1743 .. 415.8349 cents 14.66064 cents 18.18342 cents 15: 434.0183 .. 448.6789 cents 14.66063 cents 18.18342 cents 16: 466.8624 .. 481.5230 cents 14.66063 cents 18.18343 cents 17: 485.0458 .. 499.7064 cents 14.66063 cents 3.52279 cents 18: 517.8898 .. 532.5505 cents 14.66064 cents 18.18342 cents 19: 550.7339 .. 565.3945 cents 14.66064 cents 18.18342 cents 20: 583.5780 .. 598.2386 cents 14.66064 cents 18.18342 cents 21: 601.7614 .. 616.4220 cents 14.66064 cents 3.52278 cents 22: 634.6054 .. 649.2661 cents 14.66064 cents 18.18342 cents 23: 667.4495 .. 682.1101 cents 14.66063 cents 18.18342 cents 24: 700.2936 .. 714.9542 cents 14.66063 cents 18.18343 cents 25: 718.4770 .. 733.1376 cents 14.66064 cents 3.52278 cents 26: 751.3210 .. 765.9817 cents 14.66064 cents 18.18342 cents 27: 784.1651 .. 798.8257 cents 14.66064 cents 18.18342 cents 28: 817.0092 .. 831.6698 cents 14.66064 cents 18.18342 cents 29: 835.1926 .. 849.8532 cents 14.66064 cents 3.52278 cents 30: 868.0366 .. 882.6973 cents 14.66065 cents 18.18341 cents 31: 900.8807 .. 915.5413 cents 14.66064 cents 18.18341 cents 32: 933.7247 .. 948.3854 cents 14.66064 cents 18.18342 cents 33: 951.9082 .. 966.5688 cents 14.66064 cents 3.52278 cents 34: 984.7522 .. 999.4129 cents 14.66064 cents 18.18342 cents 35: 1017.5963 .. 1032.2569 cents 14.66064 cents 18.18342 cents 36: 1050.4404 .. 1065.1010 cents 14.66064 cents 18.18342 cents 37: 1068.6238 .. 1083.2844 cents 14.66064 cents 3.52278 cents 38: 1101.4678 .. 1116.1285 cents 14.66065 cents 18.18341 cents 39: 1134.3119 .. 1148.9725 cents 14.66064 cents 18.18341 cents 40: 1167.1559 .. 1181.8166 cents 14.66064 cents 18.18342 cents
SHOW DATA
Number of notes : 41 -- Interval properties -- Smallest interval : 18.18341 cents, class 1 Average step (divided formal octave): 29.2683 cents Largest one step interval : 32.84406 cents Average / Smallest step : 1.609615 Largest / Average step : 1.122172 Largest / Smallest step : 1.806265 Median interval of one step : 32.84406 cents, amount: 31 Most common interval of one step : 32.84406 cents, amount: 31 Least squares average step : 29.24244 cents, oct.: 1198.94019 cents Scale is strictly proper Scale has Myhill's property chromas: 14.66064 cents and 3.52278 cents, ratio: 4.161668 generators: 4 of 116.71559 cents and 37 of 1083.28441 cents ET pair of linear temperament : 10&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 2046-tone equal temperament with octave 2/1 degrees: 56 87 143 199 255 311 342 398 454 510 541 597 653 709 740 796 852 908 939 995 1051 1107 1138 1194 1250 1306 1337 1393 1449 1505 1536 1592 1648 1704 1735 1791 1847 1903 1934 1990 2046 generators: 199 and 1847 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAAABAAABAAABAAABAAABAAABAAABAAABAAABAA Step pattern size order : LSLLLLSLLLSLLLSLLLSLLLSLLLSLLLSLLLSLLLSLL Scale is a Constant Structure, by a margin of 3.52278 cents Scale diversity : 1.161373 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.511312 Rothenberg efficiency : 0.682927 redundancy: 0.317073 Efficiency x scale size : 28.000000 Number of different interval sizes : 80 = 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 : 3.52278 cents Most common intervals : 116.71559 cents & inv., amount: 40 Scale is a chain of 20 triads 0.0 116.716 233.431 cents Most common triad is 0.0 116.716 1083.284 cents, amount: 39 Number of recognisable fifths : 45, average 703.8646 cents Number of appreciable fifths : 35, average 700.2936 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 9 Formal octave complements present : 39 = 95.1220% Limited inverse transpositions : 8 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 24-25 -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
41: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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: 4.2460 c. M:-7.5091 c. 72: 2 1 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 P M ME S SD: 0.5810 c. M: 1.0275 c. 185: 5 3 5 5 5 5 3 5 5 5 3 5 5 5 3 5 5 5 3 5 5 5 3 5 5 5 3 5 5 5 3 5 5 5 3 5 5 5 3 5 5 SP M DE S SD: 0.4888 c. M:-0.8644 c. 257: 7 4 7 7 7 7 4 7 7 7 4 7 7 7 4 7 7 7 4 7 7 7 4 7 7 7 4 7 7 7 4 7 7 7 4 7 7 7 4 7 7 SP M DE S SD: 0.1891 c. M:-0.3344 c. 329: 9 5 9 9 9 9 5 9 9 9 5 9 9 9 5 9 9 9 5 9 9 9 5 9 9 9 5 9 9 9 5 9 9 9 5 9 9 9 5 9 9 SP M DE S SD: 0.0206 c. M:-0.0363 c. 1059: 29 16 29 29 29 29 16 29 29 29 16 29 29 29 16 29 29 29 16 29 29 29 16 29 29 29 16 29 29 29 16 29 29 29 16 29 29 29 16 29 29 SP M DE S SD: 0.0203 c. M: 0.0360 c. 1388: 38 21 38 38 38 38 21 38 38 38 21 38 38 38 21 38 38 38 21 38 38 38 21 38 38 38 21 38 38 38 21 38 38 38 21 38 38 38 21 38 38 SP M DE S SD: 0.0106 c. M: 0.0188 c. 1717: 47 26 47 47 47 47 26 47 47 47 26 47 47 47 26 47 47 47 26 47 47 47 26 47 47 47 26 47 47 47 26 47 47 47 26 47 47 47 26 47 47 SP M DE S SD: 0.0047 c. M: 0.0083 c. 2046: 56 31 56 56 56 56 31 56 56 56 31 56 56 56 31 56 56 56 31 56 56 56 31 56 56 56 31 56 56 56 31 56 56 56 31 56 56 56 31 56 56 SP M DE S SD: 0.0006 c. M: 0.0011 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.8307 cents 3 .. 6 match: 3 H SD: 0.7832 cents 4 .. 8 match: 4 H SD: 1.0867 cents 5 .. 10 match: 5 H SD: 0.7730 cents 6 .. 12 match: 6 H SD: 0.5217 cents 7 .. 14 match: 7 H SD: 1.7183 cents 8 .. 16 match: 8 H SD: 1.4900 cents 9 .. 18 match: 9 H SD: 2.2572 cents 10 .. 20 match: 10 H SD: 2.5846 cents 11 .. 22 match: 11 H SD: 2.3826 cents 12 .. 24 match: 12 H SD: 1.9011 cents 13 .. 26 match: 13 H SD: 2.8229 cents 14 .. 28 match: 14 H SD: 1.5731 cents 15 .. 30 match: 15 H SD: 1.7329 cents 16 .. 32 match: 16 H SD: 1.7302 cents 17 .. 34 match: 17 H SD: 2.8988 cents 18 .. 36 match: 18 H SD: 1.9154 cents 19 .. 38 match: 19 H SD: 1.9264 cents 20 .. 40 match: 20 H SD: 1.9976 cents 21 .. 42 match: 21 H SD: 1.6064 cents 22 .. 44 match: 22 H SD: 1.7358 cents 23 .. 46 match: 23 H SD: 1.9513 cents 24 .. 48 match: 24 H SD: 1.5631 cents 25 .. 50 match: 25 H SD: 1.6936 cents 26 .. 52 match: 26 H SD: 1.9416 cents 27 .. 54 match: 27 H SD: 1.7789 cents 28 .. 56 match: 28 H SD: 1.4549 cents 29 .. 58 match: 29 H SD: 1.7090 cents 30 .. 60 match: 30 H SD: 1.4561 cents 31 .. 62 match: 31 H SD: 1.5921 cents 32 .. 64 match: 32 H SD: 1.2602 cents 33 .. 66 match: 32 SD: 1.5684 cents 34 .. 68 match: 30 SD: 1.8283 cents 35 .. 70 match: 33 SD: 1.3185 cents 36 .. 72 match: 34 SD: 1.2291 cents 37 .. 74 match: 32 SD: 1.6097 cents 38 .. 76 match: 35 SD: 1.3867 cents 39 .. 78 match: 35 SD: 1.5087 cents 40 .. 80 match: 36 SD: 1.1961 cents 41 .. 82 match: 35 SD: 1.2659 cents 42 .. 84 match: 38 SD: 1.0663 cents 43 .. 86 match: 35 SD: 1.3049 cents 44 .. 88 match: 38 SD: 1.1406 cents 45 .. 90 match: 39 SD: 1.1344 cents 46 .. 92 match: 36 SD: 1.3027 cents 47 .. 94 match: 38 SD: 1.1796 cents 48 .. 96 match: 40 SD: 1.1031 cents 49 .. 98 match: 38 SD: 1.1520 cents 50 .. 100 match: 38 SD: 1.2446 cents 51 .. 102 match: 39 SD: 1.2757 cents 52 .. 104 match: 36 SD: 1.1764 cents 53 .. 106 match: 41 SD: 1.0292 cents 54 .. 108 match: 39 SD: 0.9357 cents 55 .. 110 match: 41 SD: 0.9076 cents 56 .. 112 match: 40 SD: 0.8740 cents 57 .. 114 match: 39 SD: 0.9605 cents 59 .. 118 match: 40 SD: 0.8383 cents 60 .. 120 match: 39 SD: 0.8559 cents 61 .. 122 match: 38 SD: 0.8920 cents 62 .. 124 match: 40 SD: 0.9089 cents 63 .. 126 match: 41 SD: 0.8091 cents 66 .. 132 match: 41 SD: 0.7922 cents 67 .. 134 match: 40 SD: 0.8900 cents 68 .. 136 match: 40 SD: 0.7863 cents 69 .. 138 match: 40 SD: 0.8816 cents 70 .. 140 match: 41 SD: 0.7331 cents 72 .. 144 match: 40 SD: 0.7720 cents 74 .. 148 match: 41 SD: 0.7158 cents 77 .. 154 match: 39 SD: 0.7079 cents 79 .. 158 match: 40 SD: 0.7882 cents 80 .. 160 match: 40 SD: 0.6469 cents 81 .. 162 match: 40 SD: 0.6552 cents 82 .. 164 match: 40 SD: 0.7638 cents 83 .. 166 match: 40 SD: 0.7054 cents 84 .. 168 match: 41 SD: 0.6104 cents 89 .. 178 match: 41 SD: 0.6088 cents 90 .. 180 match: 41 SD: 0.5902 cents 95 .. 190 match: 41 SD: 0.5820 cents 96 .. 192 match: 41 SD: 0.5420 cents 98 .. 196 match: 41 SD: 0.4838 cents 110 .. 220 match: 41 SD: 0.4517 cents 120 .. 240 match: 41 SD: 0.4380 cents 125 .. 250 match: 41 SD: 0.4230 cents 126 .. 252 match: 41 SD: 0.4149 cents 133 .. 266 match: 41 SD: 0.3897 cents 138 .. 276 match: 41 SD: 0.3613 cents 144 .. 288 match: 41 SD: 0.3342 cents 155 .. 310 match: 41 SD: 0.3020 cents 161 .. 322 match: 41 SD: 0.2879 cents 169 .. 338 match: 41 SD: 0.2826 cents 187 .. 374 match: 41 SD: 0.2679 cents 197 .. 394 match: 41 SD: 0.2536 cents 200 .. 400 match: 41 SD: 0.2389 cents 214 .. 428 match: 41 SD: 0.2349 cents 222 .. 444 match: 41 SD: 0.2331 cents 224 .. 448 match: 41 SD: 0.2307 cents 227 .. 454 match: 41 SD: 0.2262 cents 229 .. 458 match: 41 SD: 0.2228 cents 242 .. 484 match: 41 SD: 0.1929 cents 259 .. 518 match: 41 SD: 0.1737 cents 277 .. 554 match: 41 SD: 0.1710 cents 299 .. 598 match: 41 SD: 0.1604 cents 302 .. 604 match: 41 SD: 0.1587 cents 325 .. 650 match: 41 SD: 0.1452 cents 361 .. 722 match: 41 SD: 0.1226 cents 397 .. 794 match: 41 SD: 0.1201 cents 421 .. 842 match: 41 SD: 0.1166 cents 424 .. 848 match: 41 SD: 0.1141 cents 431 .. 862 match: 41 SD: 0.1112 cents 456 .. 912 match: 41 SD: 0.1112 cents 457 .. 914 match: 41 SD: 0.1060 cents 478 .. 956 match: 41 SD: 0.1051 cents 487 .. 974 match: 41 SD: 0.1049 cents 499 .. 998 match: 41 SD: 0.1032 cents 505 .. 1010 match: 41 SD: 0.0948 cents 529 .. 1058 match: 41 SD: 0.0920 cents 561 .. 1122 match: 41 SD: 0.0811 cents