Scala analysis: edo-27
27 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44.444 cents 44.444444 2: 88.889 cents 88.888889 3: 133.333 cents 133.333333 4: 177.778 cents 177.777778 5: 222.222 cents 222.222222 6: 266.667 cents 266.666667 7: 311.111 cents 311.111111 8: 355.556 cents 355.555556 9: 400.000 cents 400.000000 10: 444.444 cents 444.444444 11: 488.889 cents 488.888889 12: 533.333 cents 533.333333 13: 577.778 cents 577.777778 14: 622.222 cents 622.222222 15: 666.667 cents 666.666667 16: 711.111 cents 711.111111 17: 755.556 cents 755.555556 18: 800.000 cents 800.000000 19: 844.444 cents 844.444444 20: 888.889 cents 888.888889 21: 933.333 cents 933.333333 22: 977.778 cents 977.777778 23: 1022.222 cents 1022.222222 24: 1066.667 cents 1066.666667 25: 1111.111 cents 1111.111111 26: 1155.556 cents 1155.555556 27: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 44.4444 cents 44.4444 1: 44.4444 cents 44.4444 2: 44.4444 cents 44.4444 3: 44.4444 cents 44.4444 4: 44.4444 cents 44.4444 5: 44.4444 cents 44.4444 6: 44.4444 cents 44.4444 7: 44.4444 cents 44.4444 8: 44.4444 cents 44.4444 9: 44.4444 cents 44.4444 10: 44.4444 cents 44.4444 11: 44.4444 cents 44.4444 12: 44.4444 cents 44.4444 13: 44.4444 cents 44.4444 14: 44.4444 cents 44.4444 15: 44.4444 cents 44.4444 16: 44.4444 cents 44.4444 17: 44.4444 cents 44.4444 18: 44.4444 cents 44.4444 19: 44.4444 cents 44.4444 20: 44.4444 cents 44.4444 21: 44.4444 cents 44.4444 22: 44.4444 cents 44.4444 23: 44.4444 cents 44.4444 24: 44.4444 cents 44.4444 25: 44.4444 cents 44.4444 26: 44.4444 cents 44.4444 27: 44.4444 cents 44.4444
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 27 44.44444 cents 2: 27 88.88889 cents 3: 27 133.33333 cents 4: 27 177.77778 cents 5: 27 222.22222 cents 6: 27 266.66667 cents 7: 27 311.11111 cents 8: 27 355.55556 cents 9: 27 400.00000 cents 10: 27 444.44444 cents 11: 27 488.88889 cents 12: 27 533.33333 cents 13: 27 577.77778 cents 14: 27 622.22222 cents 15: 27 666.66667 cents 16: 27 711.11111 cents 17: 27 755.55556 cents 18: 27 800.00000 cents 19: 27 844.44444 cents 20: 27 888.88889 cents 21: 27 933.33333 cents 22: 27 977.77778 cents 23: 27 1022.22222 cents 24: 27 1066.66667 cents 25: 27 1111.11111 cents 26: 27 1155.55556 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 27 0.0 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 44.4 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 88.9 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 133.3 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 177.8 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 222.2 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 266.7 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 311.1 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 355.6 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 400.0 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 444.4 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 488.9 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 533.3 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 577.8 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 622.2 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 666.7 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 711.1 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 755.6 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 800.0 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 844.4 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 888.9 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 933.3 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 977.8 : 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 1022.2: 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 1066.7: 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 1111.1: 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 1155.6: 44.4 88.9 133.3 177.8 222.2 266.7 311.1 355.6 400.0 444.4 488.9 533.3 577.8 622.2 666.7 711.1 755.6 800.0 844.4 888.9 933.3 977.8 1022.2 1066.7 1111.1 1155.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 44.4444 cents 1/1, 0.0000 cents 44.44444 cents 2: 88.8889 .. 88.8889 cents 1/1, 0.0000 cents 44.44444 cents 3: 133.3333 .. 133.3333 cents 1/1, 0.0000 cents 44.44444 cents 4: 177.7778 .. 177.7778 cents 1/1, 0.0000 cents 44.44445 cents 5: 222.2222 .. 222.2222 cents 1/1, 0.0000 cents 44.44444 cents 6: 266.6667 .. 266.6667 cents 1/1, 0.0000 cents 44.44444 cents 7: 311.1111 .. 311.1111 cents 1/1, 0.0000 cents 44.44444 cents 8: 355.5556 .. 355.5556 cents 1/1, 0.0000 cents 44.44445 cents 9: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 44.44444 cents 10: 444.4444 .. 444.4444 cents 1/1, 0.0000 cents 44.44444 cents 11: 488.8889 .. 488.8889 cents 1/1, 0.0000 cents 44.44444 cents 12: 533.3333 .. 533.3333 cents 1/1, 0.0000 cents 44.44444 cents 13: 577.7778 .. 577.7778 cents 1/1, 0.0000 cents 44.44444 cents 14: 622.2222 .. 622.2222 cents 1/1, 0.0000 cents 44.44444 cents 15: 666.6667 .. 666.6667 cents 1/1, 0.0000 cents 44.44444 cents 16: 711.1111 .. 711.1111 cents 1/1, 0.0000 cents 44.44444 cents 17: 755.5556 .. 755.5556 cents 1/1, 0.0000 cents 44.44444 cents 18: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 44.44444 cents 19: 844.4444 .. 844.4444 cents 1/1, 0.0000 cents 44.44444 cents 20: 888.8889 .. 888.8889 cents 1/1, 0.0000 cents 44.44444 cents 21: 933.3333 .. 933.3333 cents 1/1, 0.0000 cents 44.44444 cents 22: 977.7778 .. 977.7778 cents 1/1, 0.0000 cents 44.44444 cents 23: 1022.2222 .. 1022.2222 cents 1/1, 0.0000 cents 44.44444 cents 24: 1066.6667 .. 1066.6667 cents 1/1, 0.0000 cents 44.44444 cents 25: 1111.1111 .. 1111.1111 cents 1/1, 0.0000 cents 44.44444 cents 26: 1155.5556 .. 1155.5556 cents 1/1, 0.0000 cents 44.44444 cents
SHOW DATA
Number of notes : 27 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 44.4444 cents Largest one step interval : 44.44444 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 44.44444 cents, amount: 27 Most common interval of one step : 44.44444 cents, amount: 27 Least squares average step : 44.44444 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 44.44444 cents Ratio Whole / Half tone : 5.000000 ( 5 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.037037 redundancy: 0.962963 Efficiency x scale size : 1.000000 Number of different interval sizes : 26 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 27, average 711.1111 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
27: 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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.5781 cents 3 .. 6 match: 3 H SD: 3.4052 cents 4 .. 8 match: 4 H SD: 4.6856 cents 5 .. 10 match: 5 H SD: 3.1727 cents 6 .. 12 match: 6 H SD: 3.6805 cents 7 .. 14 match: 7 H SD: 3.2642 cents 8 .. 16 match: 8 H SD: 4.8284 cents 9 .. 18 match: 9 H SD: 3.3768 cents 10 .. 20 match: 10 H SD: 2.8460 cents 11 .. 22 match: 11 H SD: 3.9528 cents 12 .. 24 match: 12 H SD: 3.1214 cents 13 .. 26 match: 13 H SD: 3.8021 cents 14 .. 28 match: 14 H SD: 3.2773 cents 15 .. 30 match: 15 H SD: 2.9422 cents 16 .. 32 match: 16 H SD: 3.4483 cents 17 .. 34 match: 17 H SD: 3.0161 cents 18 .. 36 match: 18 H SD: 2.6332 cents 19 .. 38 match: 19 H SD: 2.6930 cents 20 .. 40 match: 20 H SD: 2.5560 cents 21 .. 42 match: 21 H SD: 2.2843 cents 22 .. 44 match: 22 H SD: 2.4679 cents 23 .. 46 match: 22 S SD: 3.0757 cents 24 .. 48 match: 23 S SD: 2.4465 cents 25 .. 50 match: 24 S SD: 2.3556 cents 26 .. 52 match: 24 SD: 2.6010 cents 27 .. 54 match: 25 SD: 2.1974 cents 28 .. 56 match: 25 SD: 2.2158 cents 29 .. 58 match: 25 SD: 2.7121 cents 30 .. 60 match: 26 SD: 1.9204 cents 31 .. 62 match: 26 SD: 2.0447 cents 32 .. 64 match: 26 SD: 2.4427 cents 33 .. 66 match: 26 SD: 2.4717 cents 34 .. 68 match: 27 SD: 1.8961 cents 35 .. 70 match: 27 SD: 1.6832 cents 36 .. 72 match: 27 SD: 1.5257 cents 42 .. 84 match: 27 SD: 1.5214 cents 46 .. 92 match: 27 SD: 1.4570 cents 49 .. 98 match: 27 SD: 1.2987 cents 53 .. 106 match: 27 SD: 1.1899 cents 58 .. 116 match: 27 SD: 1.1329 cents 61 .. 122 match: 27 SD: 0.9726 cents 71 .. 142 match: 27 SD: 0.9059 cents 73 .. 146 match: 27 SD: 0.7391 cents 88 .. 176 match: 27 SD: 0.7162 cents 92 .. 184 match: 27 SD: 0.6600 cents 100 .. 200 match: 27 SD: 0.6317 cents 102 .. 204 match: 27 SD: 0.5762 cents 111 .. 222 match: 27 SD: 0.5549 cents 113 .. 226 match: 27 SD: 0.4911 cents 132 .. 264 match: 27 SD: 0.4875 cents 137 .. 274 match: 27 SD: 0.4646 cents 138 .. 276 match: 27 SD: 0.4597 cents 139 .. 278 match: 27 SD: 0.4595 cents 146 .. 292 match: 27 SD: 0.4375 cents 148 .. 296 match: 27 SD: 0.4295 cents 150 .. 300 match: 27 SD: 0.3852 cents 157 .. 314 match: 27 SD: 0.3837 cents 174 .. 348 match: 27 SD: 0.3400 cents 185 .. 370 match: 27 SD: 0.3280 cents 188 .. 376 match: 27 SD: 0.3278 cents 189 .. 378 match: 27 SD: 0.3079 cents 192 .. 384 match: 27 SD: 0.3027 cents 197 .. 394 match: 27 SD: 0.3007 cents 203 .. 406 match: 27 SD: 0.2999 cents 211 .. 422 match: 27 SD: 0.2954 cents 223 .. 446 match: 27 SD: 0.2841 cents 224 .. 448 match: 27 SD: 0.2616 cents 228 .. 456 match: 27 SD: 0.2503 cents 240 .. 480 match: 27 SD: 0.2472 cents 250 .. 500 match: 27 SD: 0.2357 cents 264 .. 528 match: 27 SD: 0.2293 cents 270 .. 540 match: 27 SD: 0.1998 cents 300 .. 600 match: 27 SD: 0.1964 cents 307 .. 614 match: 27 SD: 0.1859 cents 335 .. 670 match: 27 SD: 0.1844 cents 341 .. 682 match: 27 SD: 0.1817 cents 342 .. 684 match: 27 SD: 0.1801 cents 349 .. 698 match: 27 SD: 0.1588 cents 377 .. 754 match: 27 SD: 0.1517 cents 386 .. 772 match: 27 SD: 0.1324 cents 451 .. 902 match: 27 SD: 0.1155 cents 499 .. 998 match: 27 SD: 0.1131 cents 512 .. 1024 match: 27 SD: 0.1125 cents 527 .. 1054 match: 27 SD: 0.1114 cents 534 .. 1068 match: 27 SD: 0.1100 cents 535 .. 1070 match: 27 SD: 0.1096 cents 539 .. 1078 match: 27 SD: 0.1059 cents 547 .. 1094 match: 27 SD: 0.1052 cents 571 .. 1142 match: 27 SD: 0.1046 cents 574 .. 1148 match: 27 SD: 0.0987 cents 585 .. 1170 match: 27 SD: 0.0962 cents