Scala analysis: edo-22
22 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54.545 cents 54.545455 2: 109.091 cents 109.090909 3: 163.636 cents 163.636364 4: 218.182 cents 218.181818 5: 272.727 cents 272.727273 6: 327.273 cents 327.272727 7: 381.818 cents 381.818182 8: 436.364 cents 436.363636 9: 490.909 cents 490.909091 10: 545.455 cents 545.454545 11: 600.000 cents 600.000000 12: 654.545 cents 654.545455 13: 709.091 cents 709.090909 14: 763.636 cents 763.636364 15: 818.182 cents 818.181818 16: 872.727 cents 872.727273 17: 927.273 cents 927.272727 18: 981.818 cents 981.818182 19: 1036.364 cents 1036.363636 20: 1090.909 cents 1090.909091 21: 1145.455 cents 1145.454545 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 54.5455 cents 54.5455 1: 54.5455 cents 54.5455 2: 54.5455 cents 54.5455 3: 54.5455 cents 54.5455 4: 54.5455 cents 54.5455 5: 54.5455 cents 54.5455 6: 54.5455 cents 54.5455 7: 54.5455 cents 54.5455 8: 54.5455 cents 54.5455 9: 54.5455 cents 54.5455 10: 54.5455 cents 54.5455 11: 54.5455 cents 54.5455 12: 54.5455 cents 54.5455 13: 54.5455 cents 54.5455 14: 54.5455 cents 54.5455 15: 54.5455 cents 54.5455 16: 54.5455 cents 54.5455 17: 54.5455 cents 54.5455 18: 54.5455 cents 54.5455 19: 54.5455 cents 54.5455 20: 54.5455 cents 54.5455 21: 54.5455 cents 54.5455 22: 54.5455 cents 54.5455
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 22 54.54545 cents 2: 22 109.09091 cents 3: 22 163.63636 cents 4: 22 218.18182 cents 5: 22 272.72727 cents 6: 22 327.27273 cents 7: 22 381.81818 cents 8: 22 436.36364 cents 9: 22 490.90909 cents 10: 22 545.45454 cents 11: 22 600.00000 cents 12: 22 654.54545 cents 13: 22 709.09091 cents 14: 22 763.63636 cents 15: 22 818.18182 cents 16: 22 872.72727 cents 17: 22 927.27273 cents 18: 22 981.81818 cents 19: 22 1036.36364 cents 20: 22 1090.90909 cents 21: 22 1145.45455 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
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 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 54.5 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 109.1 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 163.6 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 218.2 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 272.7 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 327.3 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 381.8 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 436.4 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 490.9 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 545.5 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 600.0 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 654.5 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 709.1 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 763.6 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 818.2 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 872.7 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 927.3 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 981.8 : 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 1036.4: 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 1090.9: 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 1145.5: 54.5 109.1 163.6 218.2 272.7 327.3 381.8 436.4 490.9 545.5 600.0 654.5 709.1 763.6 818.2 872.7 927.3 981.8 1036.4 1090.9 1145.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.5455 .. 54.5455 cents 1/1, 0.0000 cents 54.54545 cents 2: 109.0909 .. 109.0909 cents 1/1, 0.0000 cents 54.54545 cents 3: 163.6364 .. 163.6364 cents 1/1, 0.0000 cents 54.54545 cents 4: 218.1818 .. 218.1818 cents 1/1, 0.0000 cents 54.54545 cents 5: 272.7273 .. 272.7273 cents 1/1, 0.0000 cents 54.54546 cents 6: 327.2727 .. 327.2727 cents 1/1, 0.0000 cents 54.54545 cents 7: 381.8182 .. 381.8182 cents 1/1, 0.0000 cents 54.54545 cents 8: 436.3636 .. 436.3636 cents 1/1, 0.0000 cents 54.54545 cents 9: 490.9091 .. 490.9091 cents 1/1, 0.0000 cents 54.54545 cents 10: 545.4545 .. 545.4545 cents 1/1, 0.0000 cents 54.54545 cents 11: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 54.54545 cents 12: 654.5455 .. 654.5455 cents 1/1, 0.0000 cents 54.54545 cents 13: 709.0909 .. 709.0909 cents 1/1, 0.0000 cents 54.54545 cents 14: 763.6364 .. 763.6364 cents 1/1, 0.0000 cents 54.54545 cents 15: 818.1818 .. 818.1818 cents 1/1, 0.0000 cents 54.54545 cents 16: 872.7273 .. 872.7273 cents 1/1, 0.0000 cents 54.54545 cents 17: 927.2727 .. 927.2727 cents 1/1, 0.0000 cents 54.54545 cents 18: 981.8182 .. 981.8182 cents 1/1, 0.0000 cents 54.54545 cents 19: 1036.3636 .. 1036.3636 cents 1/1, 0.0000 cents 54.54545 cents 20: 1090.9091 .. 1090.9091 cents 1/1, 0.0000 cents 54.54545 cents 21: 1145.4545 .. 1145.4545 cents 1/1, 0.0000 cents 54.54545 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 54.54545 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 54.54545 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 54.54545 cents, amount: 22 Most common interval of one step : 54.54545 cents, amount: 22 Least squares average step : 54.54545 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 54.54545 cents Ratio Whole / Half tone : 4.000000 ( 4 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.045455 redundancy: 0.954545 Efficiency x scale size : 1.000000 Number of different interval sizes : 21 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 22, average 709.0909 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- 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: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 3.5680 cents 3 .. 6 match: 3 H SD: 4.5486 cents 4 .. 8 match: 4 H SD: 3.8724 cents 5 .. 10 match: 5 H SD: 5.7045 cents 6 .. 12 match: 6 H SD: 3.4977 cents 7 .. 14 match: 7 H SD: 5.0204 cents 8 .. 16 match: 8 H SD: 3.9217 cents 9 .. 18 match: 9 H SD: 4.4072 cents 10 .. 20 match: 10 H SD: 4.0880 cents 11 .. 22 match: 11 H SD: 4.4941 cents 12 .. 24 match: 12 H SD: 3.8592 cents 13 .. 26 match: 13 H SD: 4.9248 cents 14 .. 28 match: 14 H SD: 3.5593 cents 15 .. 30 match: 15 H SD: 3.7261 cents 16 .. 32 match: 16 H SD: 3.5884 cents 17 .. 34 match: 17 H SD: 3.2151 cents 18 .. 36 match: 18 H SD: 3.0600 cents 19 .. 38 match: 18 S SD: 4.2761 cents 20 .. 40 match: 19 S SD: 3.3297 cents 21 .. 42 match: 20 SD: 3.3215 cents 22 .. 44 match: 20 SD: 3.1459 cents 23 .. 46 match: 21 SD: 3.6202 cents 24 .. 48 match: 21 SD: 2.5416 cents 25 .. 50 match: 21 SD: 3.1072 cents 26 .. 52 match: 21 SD: 3.5343 cents 27 .. 54 match: 22 SD: 2.8052 cents 28 .. 56 match: 22 SD: 2.2543 cents 29 .. 58 match: 22 SD: 2.1634 cents 30 .. 60 match: 22 SD: 2.0717 cents 38 .. 76 match: 22 SD: 2.0066 cents 40 .. 80 match: 22 SD: 1.9727 cents 41 .. 82 match: 22 SD: 1.8508 cents 43 .. 86 match: 22 SD: 1.6014 cents 48 .. 96 match: 22 SD: 1.4962 cents 49 .. 98 match: 22 SD: 1.4663 cents 52 .. 104 match: 22 SD: 1.2845 cents 58 .. 116 match: 22 SD: 1.1293 cents 59 .. 118 match: 22 SD: 1.0751 cents 61 .. 122 match: 22 SD: 1.0549 cents 63 .. 126 match: 22 SD: 1.0474 cents 65 .. 130 match: 22 SD: 1.0455 cents 72 .. 144 match: 22 SD: 1.0293 cents 73 .. 146 match: 22 SD: 0.9505 cents 76 .. 152 match: 22 SD: 0.9350 cents 81 .. 162 match: 22 SD: 0.7846 cents 89 .. 178 match: 22 SD: 0.7017 cents 101 .. 202 match: 22 SD: 0.6741 cents 111 .. 222 match: 22 SD: 0.5980 cents 119 .. 238 match: 22 SD: 0.5373 cents 121 .. 242 match: 22 SD: 0.5251 cents 122 .. 244 match: 22 SD: 0.5137 cents 140 .. 280 match: 22 SD: 0.4791 cents 150 .. 300 match: 22 SD: 0.4290 cents 154 .. 308 match: 22 SD: 0.3997 cents 164 .. 328 match: 22 SD: 0.3930 cents 181 .. 362 match: 22 SD: 0.3632 cents 182 .. 364 match: 22 SD: 0.3430 cents 189 .. 378 match: 22 SD: 0.3381 cents 195 .. 390 match: 22 SD: 0.3353 cents 210 .. 420 match: 22 SD: 0.3268 cents 211 .. 422 match: 22 SD: 0.3173 cents 215 .. 430 match: 22 SD: 0.3015 cents 222 .. 444 match: 22 SD: 0.2891 cents 240 .. 480 match: 22 SD: 0.2862 cents 244 .. 488 match: 22 SD: 0.2505 cents 275 .. 550 match: 22 SD: 0.2060 cents 292 .. 584 match: 22 SD: 0.2024 cents 311 .. 622 match: 22 SD: 0.1853 cents 342 .. 684 match: 22 SD: 0.1838 cents 351 .. 702 match: 22 SD: 0.1798 cents 370 .. 740 match: 22 SD: 0.1692 cents 381 .. 762 match: 22 SD: 0.1406 cents 433 .. 866 match: 22 SD: 0.1189 cents 505 .. 1010 match: 22 SD: 0.1150 cents 534 .. 1068 match: 22 SD: 0.1102 cents 586 .. 1172 match: 22 SD: 0.0980 cents 597 .. 1194 match: 22 SD: 0.0956 cents