Scala analysis: edo-26
26 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46.154 cents 46.153846 2: 92.308 cents 92.307692 3: 138.462 cents 138.461538 4: 184.615 cents 184.615385 5: 230.769 cents 230.769231 6: 276.923 cents 276.923077 7: 323.077 cents 323.076923 8: 369.231 cents 369.230769 9: 415.385 cents 415.384615 10: 461.538 cents 461.538462 11: 507.692 cents 507.692308 12: 553.846 cents 553.846154 13: 600.000 cents 600.000000 14: 646.154 cents 646.153846 15: 692.308 cents 692.307692 16: 738.462 cents 738.461538 17: 784.615 cents 784.615385 18: 830.769 cents 830.769231 19: 876.923 cents 876.923077 20: 923.077 cents 923.076923 21: 969.231 cents 969.230769 22: 1015.385 cents 1015.384615 23: 1061.538 cents 1061.538462 24: 1107.692 cents 1107.692308 25: 1153.846 cents 1153.846154 26: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 46.1538 cents 46.1538 1: 46.1538 cents 46.1538 2: 46.1538 cents 46.1538 3: 46.1538 cents 46.1538 4: 46.1538 cents 46.1538 5: 46.1538 cents 46.1538 6: 46.1538 cents 46.1538 7: 46.1538 cents 46.1538 8: 46.1538 cents 46.1538 9: 46.1538 cents 46.1538 10: 46.1538 cents 46.1538 11: 46.1538 cents 46.1538 12: 46.1538 cents 46.1538 13: 46.1538 cents 46.1538 14: 46.1538 cents 46.1538 15: 46.1538 cents 46.1538 16: 46.1538 cents 46.1538 17: 46.1538 cents 46.1538 18: 46.1538 cents 46.1538 19: 46.1538 cents 46.1538 20: 46.1538 cents 46.1538 21: 46.1538 cents 46.1538 22: 46.1538 cents 46.1538 23: 46.1538 cents 46.1538 24: 46.1538 cents 46.1538 25: 46.1538 cents 46.1538 26: 46.1538 cents 46.1538
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 26 46.15385 cents 2: 26 92.30769 cents 3: 26 138.46154 cents 4: 26 184.61539 cents 5: 26 230.76923 cents 6: 26 276.92308 cents 7: 26 323.07692 cents 8: 26 369.23077 cents 9: 26 415.38462 cents 10: 26 461.53846 cents 11: 26 507.69231 cents 12: 26 553.84615 cents 13: 26 600.00000 cents 14: 26 646.15385 cents 15: 26 692.30769 cents 16: 26 738.46154 cents 17: 26 784.61538 cents 18: 26 830.76923 cents 19: 26 876.92308 cents 20: 26 923.07692 cents 21: 26 969.23077 cents 22: 26 1015.38462 cents 23: 26 1061.53846 cents 24: 26 1107.69231 cents 25: 26 1153.84615 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 24 25 26 0.0 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 46.2 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 92.3 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 138.5 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 184.6 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 230.8 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 276.9 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 323.1 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 369.2 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 415.4 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 461.5 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 507.7 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 553.8 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 600.0 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 646.2 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 692.3 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 738.5 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 784.6 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 830.8 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 876.9 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 923.1 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 969.2 : 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 1015.4: 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 1061.5: 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 1107.7: 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 1153.8: 46.2 92.3 138.5 184.6 230.8 276.9 323.1 369.2 415.4 461.5 507.7 553.8 600.0 646.2 692.3 738.5 784.6 830.8 876.9 923.1 969.2 1015.4 1061.5 1107.7 1153.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.1538 .. 46.1538 cents 1/1, 0.0000 cents 46.15385 cents 2: 92.3077 .. 92.3077 cents 1/1, 0.0000 cents 46.15385 cents 3: 138.4615 .. 138.4615 cents 1/1, 0.0000 cents 46.15385 cents 4: 184.6154 .. 184.6154 cents 1/1, 0.0000 cents 46.15385 cents 5: 230.7692 .. 230.7692 cents 1/1, 0.0000 cents 46.15385 cents 6: 276.9231 .. 276.9231 cents 1/1, 0.0000 cents 46.15385 cents 7: 323.0769 .. 323.0769 cents 1/1, 0.0000 cents 46.15385 cents 8: 369.2308 .. 369.2308 cents 1/1, 0.0000 cents 46.15385 cents 9: 415.3846 .. 415.3846 cents 1/1, 0.0000 cents 46.15385 cents 10: 461.5385 .. 461.5385 cents 1/1, 0.0000 cents 46.15385 cents 11: 507.6923 .. 507.6923 cents 1/1, 0.0000 cents 46.15385 cents 12: 553.8462 .. 553.8462 cents 1/1, 0.0000 cents 46.15385 cents 13: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 46.15385 cents 14: 646.1538 .. 646.1538 cents 1/1, 0.0000 cents 46.15385 cents 15: 692.3077 .. 692.3077 cents 1/1, 0.0000 cents 46.15385 cents 16: 738.4615 .. 738.4615 cents 1/1, 0.0000 cents 46.15385 cents 17: 784.6154 .. 784.6154 cents 1/1, 0.0000 cents 46.15385 cents 18: 830.7692 .. 830.7692 cents 1/1, 0.0000 cents 46.15385 cents 19: 876.9231 .. 876.9231 cents 1/1, 0.0000 cents 46.15385 cents 20: 923.0769 .. 923.0769 cents 1/1, 0.0000 cents 46.15385 cents 21: 969.2308 .. 969.2308 cents 1/1, 0.0000 cents 46.15385 cents 22: 1015.3846 .. 1015.3846 cents 1/1, 0.0000 cents 46.15385 cents 23: 1061.5385 .. 1061.5385 cents 1/1, 0.0000 cents 46.15385 cents 24: 1107.6923 .. 1107.6923 cents 1/1, 0.0000 cents 46.15385 cents 25: 1153.8462 .. 1153.8462 cents 1/1, 0.0000 cents 46.15385 cents
SHOW DATA
Number of notes : 26 -- Interval properties -- Smallest interval : 46.15385 cents, class 1 Average step (divided formal octave): 46.1538 cents Largest one step interval : 46.15385 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 46.15385 cents, amount: 26 Most common interval of one step : 46.15385 cents, amount: 26 Least squares average step : 46.15385 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 46.15385 cents Ratio Whole / Half tone : 1.333333 ( 4/3 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.038462 redundancy: 0.961538 Efficiency x scale size : 1.000000 Number of different interval sizes : 25 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 26, average 692.3077 cents Scale contains two identical disjunct "tetrachords" of 12 notes Best fifths 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
26: 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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.8237 cents 3 .. 6 match: 3 H SD: 4.0601 cents 4 .. 8 match: 4 H SD: 4.9057 cents 5 .. 10 match: 5 H SD: 5.1296 cents 6 .. 12 match: 6 H SD: 3.6920 cents 7 .. 14 match: 7 H SD: 4.2926 cents 8 .. 16 match: 8 H SD: 4.3950 cents 9 .. 18 match: 9 H SD: 4.3390 cents 10 .. 20 match: 10 H SD: 3.4944 cents 11 .. 22 match: 11 H SD: 4.4125 cents 12 .. 24 match: 12 H SD: 2.9562 cents 13 .. 26 match: 13 H SD: 3.1937 cents 14 .. 28 match: 14 H SD: 3.7052 cents 15 .. 30 match: 15 H SD: 3.3428 cents 16 .. 32 match: 16 H SD: 3.3913 cents 17 .. 34 match: 17 H SD: 2.8703 cents 18 .. 36 match: 18 H SD: 2.7941 cents 19 .. 38 match: 19 H SD: 2.7386 cents 20 .. 40 match: 20 H SD: 2.4373 cents 21 .. 42 match: 21 H SD: 2.5147 cents 22 .. 44 match: 21 SD: 3.1810 cents 23 .. 46 match: 22 S SD: 2.7793 cents 24 .. 48 match: 23 S SD: 2.3312 cents 25 .. 50 match: 23 SD: 2.9551 cents 26 .. 52 match: 24 SD: 2.1489 cents 27 .. 54 match: 24 SD: 2.5493 cents 28 .. 56 match: 25 SD: 2.6564 cents 29 .. 58 match: 25 SD: 1.9953 cents 30 .. 60 match: 25 SD: 2.3008 cents 31 .. 62 match: 25 SD: 2.6672 cents 32 .. 64 match: 26 SD: 2.4359 cents 33 .. 66 match: 26 SD: 1.8575 cents 34 .. 68 match: 26 SD: 1.7318 cents 35 .. 70 match: 26 SD: 1.6929 cents 36 .. 72 match: 26 SD: 1.6506 cents 44 .. 88 match: 26 SD: 1.5649 cents 45 .. 90 match: 26 SD: 1.4950 cents 47 .. 94 match: 26 SD: 1.4068 cents 51 .. 102 match: 26 SD: 1.3151 cents 53 .. 106 match: 26 SD: 1.2760 cents 55 .. 110 match: 26 SD: 1.2436 cents 58 .. 116 match: 26 SD: 1.1261 cents 59 .. 118 match: 26 SD: 1.0687 cents 68 .. 136 match: 26 SD: 0.9423 cents 70 .. 140 match: 26 SD: 0.8481 cents 71 .. 142 match: 26 SD: 0.7895 cents 79 .. 158 match: 26 SD: 0.7829 cents 85 .. 170 match: 26 SD: 0.7466 cents 88 .. 176 match: 26 SD: 0.7168 cents 92 .. 184 match: 26 SD: 0.6958 cents 96 .. 192 match: 26 SD: 0.6668 cents 97 .. 194 match: 26 SD: 0.6296 cents 104 .. 208 match: 26 SD: 0.6050 cents 106 .. 212 match: 26 SD: 0.5537 cents 108 .. 216 match: 26 SD: 0.5338 cents 122 .. 244 match: 26 SD: 0.5328 cents 132 .. 264 match: 26 SD: 0.4395 cents 143 .. 286 match: 26 SD: 0.3870 cents 167 .. 334 match: 26 SD: 0.3596 cents 177 .. 354 match: 26 SD: 0.3350 cents 185 .. 370 match: 26 SD: 0.3341 cents 190 .. 380 match: 26 SD: 0.3339 cents 196 .. 392 match: 26 SD: 0.3054 cents 203 .. 406 match: 26 SD: 0.2821 cents 214 .. 428 match: 26 SD: 0.2801 cents 220 .. 440 match: 26 SD: 0.2717 cents 232 .. 464 match: 26 SD: 0.2472 cents 252 .. 504 match: 26 SD: 0.2244 cents 258 .. 516 match: 26 SD: 0.2172 cents 287 .. 574 match: 26 SD: 0.1919 cents 311 .. 622 match: 26 SD: 0.1891 cents 321 .. 642 match: 26 SD: 0.1885 cents 328 .. 656 match: 26 SD: 0.1703 cents 364 .. 728 match: 26 SD: 0.1586 cents 399 .. 798 match: 26 SD: 0.1419 cents 420 .. 840 match: 26 SD: 0.1360 cents 443 .. 886 match: 26 SD: 0.1269 cents 478 .. 956 match: 26 SD: 0.1158 cents 513 .. 1026 match: 26 SD: 0.1050 cents 517 .. 1034 match: 26 SD: 0.1033 cents 560 .. 1120 match: 26 SD: 0.0967 cents 589 .. 1178 match: 26 SD: 0.0955 cents