Scala analysis: edo-23
23 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52.174 cents 52.173913 2: 104.348 cents 104.347826 3: 156.522 cents 156.521739 4: 208.696 cents 208.695652 5: 260.870 cents 260.869565 6: 313.043 cents 313.043478 7: 365.217 cents 365.217391 8: 417.391 cents 417.391304 9: 469.565 cents 469.565217 10: 521.739 cents 521.739130 11: 573.913 cents 573.913043 12: 626.087 cents 626.086957 13: 678.261 cents 678.260870 14: 730.435 cents 730.434783 15: 782.609 cents 782.608696 16: 834.783 cents 834.782609 17: 886.957 cents 886.956522 18: 939.130 cents 939.130435 19: 991.304 cents 991.304348 20: 1043.478 cents 1043.478261 21: 1095.652 cents 1095.652174 22: 1147.826 cents 1147.826087 23: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 52.1739 cents 52.1739 1: 52.1739 cents 52.1739 2: 52.1739 cents 52.1739 3: 52.1739 cents 52.1739 4: 52.1739 cents 52.1739 5: 52.1739 cents 52.1739 6: 52.1739 cents 52.1739 7: 52.1739 cents 52.1739 8: 52.1739 cents 52.1739 9: 52.1739 cents 52.1739 10: 52.1739 cents 52.1739 11: 52.1739 cents 52.1739 12: 52.1739 cents 52.1739 13: 52.1739 cents 52.1739 14: 52.1739 cents 52.1739 15: 52.1739 cents 52.1739 16: 52.1739 cents 52.1739 17: 52.1739 cents 52.1739 18: 52.1739 cents 52.1739 19: 52.1739 cents 52.1739 20: 52.1739 cents 52.1739 21: 52.1739 cents 52.1739 22: 52.1739 cents 52.1739 23: 52.1739 cents 52.1739
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 23 52.17391 cents 2: 23 104.34783 cents 3: 23 156.52174 cents 4: 23 208.69565 cents 5: 23 260.86957 cents 6: 23 313.04348 cents 7: 23 365.21739 cents 8: 23 417.39130 cents 9: 23 469.56522 cents 10: 23 521.73913 cents 11: 23 573.91304 cents 12: 23 626.08696 cents 13: 23 678.26087 cents 14: 23 730.43478 cents 15: 23 782.60870 cents 16: 23 834.78261 cents 17: 23 886.95652 cents 18: 23 939.13044 cents 19: 23 991.30435 cents 20: 23 1043.47826 cents 21: 23 1095.65217 cents 22: 23 1147.82609 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 23 0.0 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 52.2 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 104.3 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 156.5 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 208.7 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 260.9 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 313.0 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 365.2 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 417.4 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 469.6 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 521.7 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 573.9 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 626.1 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 678.3 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 730.4 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 782.6 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 834.8 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 887.0 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 939.1 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 991.3 : 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 1043.5: 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 1095.7: 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 1147.8: 52.2 104.3 156.5 208.7 260.9 313.0 365.2 417.4 469.6 521.7 573.9 626.1 678.3 730.4 782.6 834.8 887.0 939.1 991.3 1043.5 1095.7 1147.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.1739 .. 52.1739 cents 1/1, 0.0000 cents 52.17391 cents 2: 104.3478 .. 104.3478 cents 1/1, 0.0000 cents 52.17391 cents 3: 156.5217 .. 156.5217 cents 1/1, 0.0000 cents 52.17391 cents 4: 208.6957 .. 208.6957 cents 1/1, 0.0000 cents 52.17391 cents 5: 260.8696 .. 260.8696 cents 1/1, 0.0000 cents 52.17391 cents 6: 313.0435 .. 313.0435 cents 1/1, 0.0000 cents 52.17391 cents 7: 365.2174 .. 365.2174 cents 1/1, 0.0000 cents 52.17391 cents 8: 417.3913 .. 417.3913 cents 1/1, 0.0000 cents 52.17391 cents 9: 469.5652 .. 469.5652 cents 1/1, 0.0000 cents 52.17391 cents 10: 521.7391 .. 521.7391 cents 1/1, 0.0000 cents 52.17391 cents 11: 573.9130 .. 573.9130 cents 1/1, 0.0000 cents 52.17391 cents 12: 626.0870 .. 626.0870 cents 1/1, 0.0000 cents 52.17391 cents 13: 678.2609 .. 678.2609 cents 1/1, 0.0000 cents 52.17391 cents 14: 730.4348 .. 730.4348 cents 1/1, 0.0000 cents 52.17391 cents 15: 782.6087 .. 782.6087 cents 1/1, 0.0000 cents 52.17391 cents 16: 834.7826 .. 834.7826 cents 1/1, 0.0000 cents 52.17391 cents 17: 886.9565 .. 886.9565 cents 1/1, 0.0000 cents 52.17391 cents 18: 939.1304 .. 939.1304 cents 1/1, 0.0000 cents 52.17391 cents 19: 991.3043 .. 991.3043 cents 1/1, 0.0000 cents 52.17391 cents 20: 1043.4783 .. 1043.4783 cents 1/1, 0.0000 cents 52.17391 cents 21: 1095.6522 .. 1095.6522 cents 1/1, 0.0000 cents 52.17391 cents 22: 1147.8261 .. 1147.8261 cents 1/1, 0.0000 cents 52.17391 cents
SHOW DATA
Number of notes : 23 -- Interval properties -- Smallest interval : 52.17391 cents, class 1 Average step (divided formal octave): 52.1739 cents Largest one step interval : 52.17391 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 52.17391 cents, amount: 23 Most common interval of one step : 52.17391 cents, amount: 23 Least squares average step : 52.17391 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 52.17391 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.043478 redundancy: 0.956522 Efficiency x scale size : 1.000000 Number of different interval sizes : 22 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Scale contains two identical disjunct "tetrachords" of 11 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
23: 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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 11.8471 cents 3 .. 6 match: 3 H SD: 7.9454 cents 4 .. 8 match: 4 H SD: 9.7203 cents 5 .. 10 match: 5 H SD: 6.9156 cents 6 .. 12 match: 6 H SD: 5.7740 cents 7 .. 14 match: 7 H SD: 5.5364 cents 8 .. 16 match: 8 H SD: 5.7727 cents 9 .. 18 match: 9 H SD: 5.0076 cents 10 .. 20 match: 10 H SD: 5.2213 cents 11 .. 22 match: 11 H SD: 4.8863 cents 12 .. 24 match: 12 H SD: 5.0249 cents 13 .. 26 match: 13 H SD: 4.0524 cents 14 .. 28 match: 14 H SD: 4.3761 cents 15 .. 30 match: 15 H SD: 3.4732 cents 16 .. 32 match: 16 H SD: 3.4453 cents 17 .. 34 match: 17 H SD: 3.2627 cents 18 .. 36 match: 18 H SD: 3.0189 cents 19 .. 38 match: 19 H SD: 3.0056 cents 20 .. 40 match: 19 SD: 3.9258 cents 21 .. 42 match: 20 S SD: 2.8970 cents 22 .. 44 match: 21 SD: 3.4775 cents 23 .. 46 match: 21 SD: 2.6977 cents 24 .. 48 match: 21 SD: 3.5597 cents 25 .. 50 match: 22 SD: 2.4180 cents 26 .. 52 match: 22 SD: 2.7078 cents 27 .. 54 match: 22 SD: 3.2691 cents 28 .. 56 match: 23 SD: 2.9164 cents 29 .. 58 match: 23 SD: 2.2415 cents 30 .. 60 match: 23 SD: 1.9885 cents 31 .. 62 match: 23 SD: 1.9540 cents 36 .. 72 match: 23 SD: 1.9216 cents 39 .. 78 match: 23 SD: 1.8501 cents 42 .. 84 match: 23 SD: 1.7470 cents 44 .. 88 match: 23 SD: 1.6403 cents 46 .. 92 match: 23 SD: 1.6343 cents 48 .. 96 match: 23 SD: 1.5119 cents 51 .. 102 match: 23 SD: 1.3186 cents 54 .. 108 match: 23 SD: 1.2868 cents 60 .. 120 match: 23 SD: 1.1793 cents 61 .. 122 match: 23 SD: 1.0092 cents 63 .. 126 match: 23 SD: 0.9739 cents 71 .. 142 match: 23 SD: 0.9671 cents 76 .. 152 match: 23 SD: 0.9036 cents 84 .. 168 match: 23 SD: 0.8584 cents 85 .. 170 match: 23 SD: 0.7933 cents 86 .. 172 match: 23 SD: 0.7897 cents 92 .. 184 match: 23 SD: 0.7281 cents 94 .. 188 match: 23 SD: 0.6147 cents 110 .. 220 match: 23 SD: 0.5679 cents 125 .. 250 match: 23 SD: 0.5618 cents 127 .. 254 match: 23 SD: 0.5382 cents 128 .. 256 match: 23 SD: 0.4532 cents 140 .. 280 match: 23 SD: 0.4526 cents 157 .. 314 match: 23 SD: 0.4171 cents 158 .. 316 match: 23 SD: 0.3833 cents 161 .. 322 match: 23 SD: 0.3817 cents 173 .. 346 match: 23 SD: 0.3674 cents 179 .. 358 match: 23 SD: 0.3448 cents 190 .. 380 match: 23 SD: 0.3269 cents 196 .. 392 match: 23 SD: 0.3102 cents 208 .. 416 match: 23 SD: 0.3090 cents 221 .. 442 match: 23 SD: 0.2331 cents 257 .. 514 match: 23 SD: 0.2074 cents 289 .. 578 match: 23 SD: 0.2054 cents 308 .. 616 match: 23 SD: 0.2013 cents 318 .. 636 match: 23 SD: 0.1926 cents 336 .. 672 match: 23 SD: 0.1917 cents 352 .. 704 match: 23 SD: 0.1844 cents 353 .. 706 match: 23 SD: 0.1719 cents 358 .. 716 match: 23 SD: 0.1677 cents 369 .. 738 match: 23 SD: 0.1498 cents 392 .. 784 match: 23 SD: 0.1319 cents 455 .. 910 match: 23 SD: 0.1149 cents 484 .. 968 match: 23 SD: 0.1122 cents 529 .. 1058 match: 23 SD: 0.1085 cents 549 .. 1098 match: 23 SD: 0.1077 cents 583 .. 1166 match: 23 SD: 0.1046 cents