Scala analysis: mag22
22 note magic temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.512 cents 58.512100 2: 117.024 cents 117.024201 3: 158.083 cents 158.083059 4: 204.960 cents 204.959665 5: 263.472 cents 263.471766 6: 321.984 cents 321.983866 7: 380.496 cents 380.495967 8: 439.008 cents 439.008067 9: 497.520 cents 497.520167 10: 544.397 cents 544.396773 11: 585.456 cents 585.455632 12: 643.968 cents 643.967732 13: 702.480 cents 702.479833 14: 760.992 cents 760.991933 15: 819.504 cents 819.504033 16: 878.016 cents 878.016134 17: 930.710 cents 930.710487 18: 971.769 cents 971.769345 19: 1024.464 cents 1024.463699 20: 1082.976 cents 1082.975799 21: 1141.488 cents 1141.487900 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 58.5121 cents 58.5121 1: 58.5121 cents 58.5121 2: 58.5121 cents 58.5121 3: 41.0589 cents 41.0589 4: 46.8766 cents 46.8766 5: 58.5121 cents 58.5121 6: 58.5121 cents 58.5121 7: 58.5121 cents 58.5121 8: 58.5121 cents 58.5121 9: 58.5121 cents 58.5121 10: 46.8766 cents 46.8766 11: 41.0589 cents 41.0589 12: 58.5121 cents 58.5121 13: 58.5121 cents 58.5121 14: 58.5121 cents 58.5121 15: 58.5121 cents 58.5121 16: 58.5121 cents 58.5121 17: 52.6944 cents 52.6944 18: 41.0589 cents 41.0589 19: 52.6944 cents 52.6944 20: 58.5121 cents 58.5121 21: 58.5121 cents 58.5121 22: 58.5121 cents 58.5121
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 41.05886 cents 1: 2 46.87661 cents 1: 2 52.69435 cents 1: 15 58.51210 cents 2: 2 87.93546 cents 2: 2 93.75321 cents 2: 2 99.57096 cents 2: 2 105.38871 cents 2: 2 111.20645 cents 2: 12 117.02420 cents 3: 5 146.44757 cents 3: 2 152.26531 cents 3: 2 158.08306 cents 3: 2 163.90081 cents 3: 2 169.71855 cents 3: 9 175.53630 cents 4: 8 204.95966 cents 4: 2 210.77741 cents 4: 2 216.59516 cents 4: 2 222.41291 cents 4: 2 228.23065 cents 4: 6 234.04840 cents 5: 11 263.47177 cents 5: 2 269.28951 cents 5: 2 275.10726 cents 5: 2 280.92501 cents 5: 2 286.74276 cents 5: 3 292.56050 cents 6: 14 321.98387 cents 6: 2 327.80161 cents 6: 2 333.61936 cents 6: 2 339.43711 cents 6: 2 345.25485 cents 7: 17 380.49597 cents 7: 5 386.31371 cents 8: 4 427.37257 cents 8: 2 433.19032 cents 8: 16 439.00807 cents 9: 1 468.43143 cents 9: 2 474.24918 cents 9: 2 480.06693 cents 9: 2 485.88467 cents 9: 2 491.70242 cents 9: 13 497.52017 cents 10: 4 526.94353 cents 10: 2 532.76128 cents 10: 2 538.57903 cents 10: 2 544.39677 cents 10: 2 550.21452 cents 10: 10 556.03227 cents 11: 7 585.45563 cents 11: 2 591.27338 cents 11: 2 597.09113 cents 11: 2 602.90887 cents 11: 2 608.72662 cents 11: 7 614.54437 cents 12: 10 643.96773 cents 12: 2 649.78548 cents 12: 2 655.60323 cents 12: 2 661.42097 cents 12: 2 667.23872 cents 12: 4 673.05647 cents 13: 13 702.47983 cents 13: 2 708.29758 cents 13: 2 714.11533 cents 13: 2 719.93308 cents 13: 2 725.75082 cents 13: 1 731.56857 cents 14: 16 760.99193 cents 14: 2 766.80968 cents 14: 4 772.62743 cents 15: 5 813.68629 cents 15: 17 819.50403 cents 16: 2 854.74514 cents 16: 2 860.56289 cents 16: 2 866.38064 cents 16: 2 872.19839 cents 16: 14 878.01613 cents 17: 3 907.43950 cents 17: 2 913.25725 cents 17: 2 919.07499 cents 17: 2 924.89274 cents 17: 2 930.71049 cents 17: 11 936.52823 cents 18: 6 965.95160 cents 18: 2 971.76934 cents 18: 2 977.58709 cents 18: 2 983.40484 cents 18: 2 989.22259 cents 18: 8 995.04033 cents 19: 9 1024.46370 cents 19: 2 1030.28145 cents 19: 2 1036.09919 cents 19: 2 1041.91694 cents 19: 2 1047.73469 cents 19: 5 1053.55243 cents 20: 12 1082.97580 cents 20: 2 1088.79355 cents 20: 2 1094.61129 cents 20: 2 1100.42904 cents 20: 2 1106.24679 cents 20: 2 1112.06454 cents 21: 15 1141.48790 cents 21: 2 1147.30565 cents 21: 2 1153.12339 cents 21: 3 1158.94114 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.04762 = 106/21
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 0.0 : 58.5 117.0 158.1 205.0 263.5 322.0 380.5 439.0 497.5 544.4 585.5 644.0 702.5 761.0 819.5 878.0 930.7 971.8 1024.5 1083.0 1141.5 1200.0 58.5 : 58.5 99.6 146.4 205.0 263.5 322.0 380.5 439.0 485.9 526.9 585.5 644.0 702.5 761.0 819.5 872.2 913.3 966.0 1024.5 1083.0 1141.5 1200.0 117.0 : 41.1 87.9 146.4 205.0 263.5 322.0 380.5 427.4 468.4 526.9 585.5 644.0 702.5 761.0 813.7 854.7 907.4 966.0 1024.5 1083.0 1141.5 1200.0 158.1 : 46.9 105.4 163.9 222.4 280.9 339.4 386.3 427.4 485.9 544.4 602.9 661.4 719.9 772.6 813.7 866.4 924.9 983.4 1041.9 1100.4 1158.9 1200.0 205.0 : 58.5 117.0 175.5 234.0 292.6 339.4 380.5 439.0 497.5 556.0 614.5 673.1 725.8 766.8 819.5 878.0 936.5 995.0 1053.6 1112.1 1153.1 1200.0 263.5 : 58.5 117.0 175.5 234.0 280.9 322.0 380.5 439.0 497.5 556.0 614.5 667.2 708.3 761.0 819.5 878.0 936.5 995.0 1053.6 1094.6 1141.5 1200.0 322.0 : 58.5 117.0 175.5 222.4 263.5 322.0 380.5 439.0 497.5 556.0 608.7 649.8 702.5 761.0 819.5 878.0 936.5 995.0 1036.1 1083.0 1141.5 1200.0 380.5 : 58.5 117.0 163.9 205.0 263.5 322.0 380.5 439.0 497.5 550.2 591.3 644.0 702.5 761.0 819.5 878.0 936.5 977.6 1024.5 1083.0 1141.5 1200.0 439.0 : 58.5 105.4 146.4 205.0 263.5 322.0 380.5 439.0 491.7 532.8 585.5 644.0 702.5 761.0 819.5 878.0 919.1 966.0 1024.5 1083.0 1141.5 1200.0 497.5 : 46.9 87.9 146.4 205.0 263.5 322.0 380.5 433.2 474.2 526.9 585.5 644.0 702.5 761.0 819.5 860.6 907.4 966.0 1024.5 1083.0 1141.5 1200.0 544.4 : 41.1 99.6 158.1 216.6 275.1 333.6 386.3 427.4 480.1 538.6 597.1 655.6 714.1 772.6 813.7 860.6 919.1 977.6 1036.1 1094.6 1153.1 1200.0 585.5 : 58.5 117.0 175.5 234.0 292.6 345.3 386.3 439.0 497.5 556.0 614.5 673.1 731.6 772.6 819.5 878.0 936.5 995.0 1053.6 1112.1 1158.9 1200.0 644.0 : 58.5 117.0 175.5 234.0 286.7 327.8 380.5 439.0 497.5 556.0 614.5 673.1 714.1 761.0 819.5 878.0 936.5 995.0 1053.6 1100.4 1141.5 1200.0 702.5 : 58.5 117.0 175.5 228.2 269.3 322.0 380.5 439.0 497.5 556.0 614.5 655.6 702.5 761.0 819.5 878.0 936.5 995.0 1041.9 1083.0 1141.5 1200.0 761.0 : 58.5 117.0 169.7 210.8 263.5 322.0 380.5 439.0 497.5 556.0 597.1 644.0 702.5 761.0 819.5 878.0 936.5 983.4 1024.5 1083.0 1141.5 1200.0 819.5 : 58.5 111.2 152.3 205.0 263.5 322.0 380.5 439.0 497.5 538.6 585.5 644.0 702.5 761.0 819.5 878.0 924.9 966.0 1024.5 1083.0 1141.5 1200.0 878.0 : 52.7 93.8 146.4 205.0 263.5 322.0 380.5 439.0 480.1 526.9 585.5 644.0 702.5 761.0 819.5 866.4 907.4 966.0 1024.5 1083.0 1141.5 1200.0 930.7 : 41.1 93.8 152.3 210.8 269.3 327.8 386.3 427.4 474.2 532.8 591.3 649.8 708.3 766.8 813.7 854.7 913.3 971.8 1030.3 1088.8 1147.3 1200.0 971.8 : 52.7 111.2 169.7 228.2 286.7 345.3 386.3 433.2 491.7 550.2 608.7 667.2 725.8 772.6 813.7 872.2 930.7 989.2 1047.7 1106.2 1158.9 1200.0 1024.5: 58.5 117.0 175.5 234.0 292.6 333.6 380.5 439.0 497.5 556.0 614.5 673.1 719.9 761.0 819.5 878.0 936.5 995.0 1053.6 1106.2 1147.3 1200.0 1083.0: 58.5 117.0 175.5 234.0 275.1 322.0 380.5 439.0 497.5 556.0 614.5 661.4 702.5 761.0 819.5 878.0 936.5 995.0 1047.7 1088.8 1141.5 1200.0 1141.5: 58.5 117.0 175.5 216.6 263.5 322.0 380.5 439.0 497.5 556.0 602.9 644.0 702.5 761.0 819.5 878.0 936.5 989.2 1030.3 1083.0 1141.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 58.5121 cents 17.45324 cents 41.05886 cents 2: 87.9355 .. 117.0242 cents 29.08874 cents 29.42336 cents 3: 146.4476 .. 175.5363 cents 29.08874 cents 29.42336 cents 4: 204.9597 .. 234.0484 cents 29.08874 cents 29.42336 cents 5: 263.4718 .. 292.5605 cents 29.08874 cents 29.42336 cents 6: 321.9839 .. 345.2549 cents 23.27099 cents 29.42336 cents 7: 380.4960 .. 386.3137 cents 5.81775 cents 35.24111 cents 8: 427.3726 .. 439.0081 cents 11.63549 cents 41.05886 cents 9: 468.4314 .. 497.5202 cents 29.08874 cents 29.42336 cents 10: 526.9435 .. 556.0323 cents 29.08874 cents 29.42337 cents 11: 585.4556 .. 614.5444 cents 29.08874 cents 29.42336 cents 12: 643.9677 .. 673.0565 cents 29.08874 cents 29.42336 cents 13: 702.4798 .. 731.5686 cents 29.08874 cents 29.42336 cents 14: 760.9919 .. 772.6274 cents 11.63550 cents 29.42336 cents 15: 813.6863 .. 819.5040 cents 5.81775 cents 41.05886 cents 16: 854.7451 .. 878.0161 cents 23.27099 cents 35.24111 cents 17: 907.4395 .. 936.5282 cents 29.08874 cents 29.42336 cents 18: 965.9516 .. 995.0403 cents 29.08874 cents 29.42336 cents 19: 1024.4637 .. 1053.5524 cents 29.08874 cents 29.42336 cents 20: 1082.9758 .. 1112.0645 cents 29.08874 cents 29.42336 cents 21: 1141.4879 .. 1158.9411 cents 17.45324 cents 29.42336 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 41.05886 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 58.51210 cents Average / Smallest step : 1.328470 Largest / Average step : 1.072722 Largest / Smallest step : 1.425079 Median interval of one step : 58.51210 cents, amount: 15 Most common interval of one step : 58.51210 cents, amount: 15 Least squares average step : 54.29174 cents, oct.: 1194.41834 cents Scale is strictly proper Step pattern alph. order: AABCAAAAACBAAAAADBDAAA Step pattern size order : DDABDDDDDBADDDDDCACDDD Scale is a Constant Structure, by a margin of 29.42336 cents Scale diversity : 1.299238 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.587910 Number of different interval sizes : 106 = 5.04762 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 5.04762 = 106/21 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 5.81775 cents Most common intervals : 380.49597 cents & inv., amount: 17 Most common triad is 0.0 380.496 819.504 cents, amount: 16 Number of recognisable fifths : 19, average 706.1542 cents Number of appreciable fifths : 17, average 704.5332 cents Best major thirds form a closed circle Formal octave complements present : 13 = 59.0909% Limited transpositions with margin 29.0887 cents: 7 15 Limited inverse transpositions : 13 Inversional symmetry on intervals : 6-7 17-18 -- Rational properties --
FIT/MODE
22: 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: 7.3499 c. M:-14.5444 c. 41: 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 P M ME SD: 3.9561 c. M: 11.7416 c. 48: 2 3 1 2 3 2 2 3 2 2 1 3 2 2 3 2 2 2 2 2 3 2 P D3 SD: 6.9018 c. M:-11.5282 c. 49: 2 3 1 2 3 2 3 2 2 2 2 2 3 2 2 3 2 2 2 2 3 2 P D3 SD: 6.9350 c. M: 11.3408 c. 53: 3 2 2 2 3 2 3 2 3 2 2 2 3 3 2 3 2 2 2 3 2 3 P SD: 5.5296 c. M: 10.0055 c. 60: 3 3 2 2 3 3 3 3 3 2 2 3 3 3 3 3 2 3 2 3 3 3 SP D3 SD: 4.0018 c. M: 10.7105 c. 62: 3 3 2 3 3 3 3 3 3 2 2 3 3 3 3 3 3 2 3 3 3 3 SP D3 S SD: 4.9398 c. M:-7.9436 c. 63: 3 3 2 3 3 3 3 3 3 3 2 3 3 3 3 3 3 2 3 3 3 3 SP M ME SD: 3.2166 c. M:-7.9842 c. 70: 3 4 2 3 3 4 3 4 3 3 2 4 3 3 4 3 3 3 3 3 4 3 SP SD: 4.5935 c. M:-7.4608 c. 75: 4 3 3 3 3 4 4 3 4 3 3 3 4 4 3 4 3 3 3 4 3 4 SP SD: 4.2583 c. M: 7.4718 c. 79: 4 4 2 3 4 4 4 4 4 3 2 4 4 4 4 4 3 3 3 4 4 4 SP SD: 4.2449 c. M: 8.2404 c. 82: 4 4 3 3 4 4 4 4 4 3 3 4 4 4 4 4 4 2 4 4 4 4 SP D3 SD: 1.9831 c. M: 5.9157 c. 94: 5 4 3 4 5 4 5 4 5 4 3 4 5 5 4 5 4 3 4 5 4 5 SP SD: 3.4328 c. M: 5.6699 c. 99: 5 5 3 4 5 5 4 5 5 4 3 5 5 5 5 4 5 3 5 4 5 5 SP SD: 3.2541 c. M:-5.8393 c. 100: 5 5 3 4 5 5 5 5 4 4 4 5 5 4 5 5 5 3 4 5 5 5 SP SD: 3.4455 c. M: 5.5202 c. 101: 5 5 3 4 5 5 5 5 5 4 3 5 5 5 5 5 4 4 4 5 5 5 SP SD: 2.0532 c. M: 3.9778 c. 104: 5 5 4 4 5 5 5 5 5 4 4 5 5 5 5 5 5 3 5 5 5 5 SP D3 SD: 1.9374 c. M:-3.9049 c. 123: 6 6 4 5 6 6 6 6 6 5 4 6 6 6 6 6 5 5 5 6 6 6 SP SD: 1.3069 c. M: 3.8812 c. 142: 7 7 5 5 7 7 7 7 7 5 5 7 7 7 7 7 6 5 6 7 7 7 SP SD: 1.4688 c. M: 3.5517 c. 144: 7 7 5 6 7 7 7 7 7 5 5 7 7 7 7 7 7 5 6 7 7 7 SP SD: 2.3116 c. M:-3.3737 c. 145: 7 7 5 6 7 7 7 7 7 6 5 7 7 7 7 7 6 5 7 7 7 7 SP SD: 1.5541 c. M: 3.8139 c. 164: 8 8 6 6 8 8 8 8 8 6 6 8 8 8 8 8 7 6 7 8 8 8 SP SD: 0.9783 c. M: 2.9334 c. 183: 9 9 6 7 9 9 9 9 9 7 6 9 9 9 9 9 8 6 8 9 9 9 SP SD: 0.9344 c. M: 1.8491 c. 205: 10 10 7 8 10 10 10 10 10 8 7 10 10 10 10 10 9 7 9 10 10 10 SP SD: 0.0454 c. M: 0.0898 c. 1867: 91 91 64 73 91 91 91 91 91 73 64 91 91 91 91 91 82 64 82 91 91 91 SP SD: 0.0418 c. M:-0.0827 c. 2072: 101 101 71 81 101 101 101 101 101 81 71 101 101 101 101 101 91 71 91 101 101 101 SP SD: 0.0332 c. M:-0.0656 c. 2277: 111 111 78 89 111 111 111 111 111 89 78 111 111 111 111 111 100 78 100 111 111 111 SP SD: 0.0261 c. M:-0.0516 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.2624 cents 3 .. 6 match: 3 H SD: 2.1214 cents 4 .. 8 match: 4 H SD: 1.6353 cents 5 .. 10 match: 5 H SD: 2.2795 cents 6 .. 12 match: 6 H SD: 4.3215 cents 7 .. 14 match: 7 H SD: 6.3871 cents 8 .. 16 match: 8 H SD: 2.9628 cents 9 .. 18 match: 9 H SD: 5.1915 cents 10 .. 20 match: 10 H SD: 3.6763 cents 11 .. 22 match: 11 H SD: 4.8054 cents 12 .. 24 match: 12 H SD: 3.9147 cents 13 .. 26 match: 13 H SD: 4.5793 cents 14 .. 28 match: 14 H SD: 4.0680 cents 15 .. 30 match: 15 H SD: 3.2342 cents 16 .. 32 match: 16 H SD: 3.4567 cents 17 .. 34 match: 17 H SD: 3.7238 cents 18 .. 36 match: 18 H SD: 3.5570 cents 19 .. 38 match: 17 SD: 4.9267 cents 20 .. 40 match: 19 SD: 2.8268 cents 21 .. 42 match: 19 SD: 3.5494 cents 22 .. 44 match: 20 SD: 3.4882 cents 23 .. 46 match: 20 SD: 3.4761 cents 24 .. 48 match: 21 SD: 2.2250 cents 25 .. 50 match: 21 SD: 2.4922 cents 26 .. 52 match: 20 SD: 3.2367 cents 27 .. 54 match: 21 SD: 2.8615 cents 28 .. 56 match: 22 SD: 2.7356 cents 29 .. 58 match: 22 SD: 2.3519 cents 30 .. 60 match: 22 SD: 1.9851 cents 32 .. 64 match: 22 SD: 1.9464 cents 36 .. 72 match: 21 SD: 2.2291 cents 38 .. 76 match: 22 SD: 1.8111 cents 40 .. 80 match: 22 SD: 1.7781 cents 42 .. 84 match: 22 SD: 1.7007 cents 45 .. 90 match: 22 SD: 1.6063 cents 48 .. 96 match: 22 SD: 1.4615 cents 49 .. 98 match: 22 SD: 1.4409 cents 53 .. 106 match: 22 SD: 1.3206 cents 54 .. 108 match: 22 SD: 1.1922 cents 56 .. 112 match: 22 SD: 1.1592 cents 60 .. 120 match: 22 SD: 1.0561 cents 62 .. 124 match: 22 SD: 0.9240 cents 73 .. 146 match: 22 SD: 0.8559 cents 84 .. 168 match: 22 SD: 0.7388 cents 94 .. 188 match: 22 SD: 0.6873 cents 97 .. 194 match: 22 SD: 0.6781 cents 104 .. 208 match: 22 SD: 0.6768 cents 111 .. 222 match: 22 SD: 0.6416 cents 114 .. 228 match: 22 SD: 0.4397 cents 146 .. 292 match: 22 SD: 0.3998 cents 166 .. 332 match: 22 SD: 0.3992 cents 167 .. 334 match: 22 SD: 0.3974 cents 170 .. 340 match: 22 SD: 0.3700 cents 176 .. 352 match: 22 SD: 0.3442 cents 198 .. 396 match: 22 SD: 0.3185 cents 200 .. 400 match: 22 SD: 0.3088 cents 201 .. 402 match: 22 SD: 0.3045 cents 228 .. 456 match: 22 SD: 0.2911 cents 229 .. 458 match: 22 SD: 0.2838 cents 230 .. 460 match: 22 SD: 0.2805 cents 231 .. 462 match: 22 SD: 0.2743 cents 239 .. 478 match: 22 SD: 0.2574 cents 260 .. 520 match: 22 SD: 0.2400 cents 268 .. 536 match: 22 SD: 0.2252 cents 284 .. 568 match: 22 SD: 0.2050 cents 312 .. 624 match: 22 SD: 0.2026 cents 316 .. 632 match: 22 SD: 0.2016 cents 328 .. 656 match: 22 SD: 0.1998 cents 333 .. 666 match: 22 SD: 0.1864 cents 342 .. 684 match: 22 SD: 0.1815 cents 357 .. 714 match: 22 SD: 0.1475 cents 406 .. 812 match: 22 SD: 0.1312 cents 430 .. 860 match: 22 SD: 0.1236 cents 468 .. 936 match: 22 SD: 0.1224 cents 524 .. 1048 match: 22 SD: 0.1210 cents 542 .. 1084 match: 22 SD: 0.1196 cents 544 .. 1088 match: 22 SD: 0.1176 cents 558 .. 1116 match: 22 SD: 0.1139 cents 574 .. 1148 match: 22 SD: 0.1114 cents 582 .. 1164 match: 22 SD: 0.1085 cents 586 .. 1172 match: 22 SD: 0.1055 cents