Scala analysis: edo-18
18 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666667 2: 133.333 cents 133.333333 3: 200.000 cents 200.000000 4: 266.667 cents 266.666667 5: 333.333 cents 333.333333 6: 400.000 cents 400.000000 7: 466.667 cents 466.666667 8: 533.333 cents 533.333333 9: 600.000 cents 600.000000 10: 666.667 cents 666.666667 11: 733.333 cents 733.333333 12: 800.000 cents 800.000000 13: 866.667 cents 866.666667 14: 933.333 cents 933.333333 15: 1000.000 cents 1000.000000 16: 1066.667 cents 1066.666667 17: 1133.333 cents 1133.333333 18: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 66.6667 cents 66.6667 1: 66.6667 cents 66.6667 2: 66.6667 cents 66.6667 3: 66.6667 cents 66.6667 4: 66.6667 cents 66.6667 5: 66.6667 cents 66.6667 6: 66.6667 cents 66.6667 7: 66.6667 cents 66.6667 8: 66.6667 cents 66.6667 9: 66.6667 cents 66.6667 10: 66.6667 cents 66.6667 11: 66.6667 cents 66.6667 12: 66.6667 cents 66.6667 13: 66.6667 cents 66.6667 14: 66.6667 cents 66.6667 15: 66.6667 cents 66.6667 16: 66.6667 cents 66.6667 17: 66.6667 cents 66.6667 18: 66.6667 cents 66.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 18 66.66667 cents 2: 18 133.33333 cents 3: 18 200.00000 cents 4: 18 266.66667 cents 5: 18 333.33333 cents 6: 18 400.00000 cents 7: 18 466.66667 cents 8: 18 533.33333 cents 9: 18 600.00000 cents 10: 18 666.66667 cents 11: 18 733.33333 cents 12: 18 800.00000 cents 13: 18 866.66667 cents 14: 18 933.33333 cents 15: 18 1000.00000 cents 16: 18 1066.66667 cents 17: 18 1133.33333 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 0.0 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 66.7 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 133.3 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 200.0 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 266.7 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 333.3 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 400.0 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 466.7 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 533.3 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 600.0 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 666.7 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 733.3 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 800.0 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 866.7 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 933.3 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 1000.0: 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 1066.7: 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 1133.3: 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 66.6667 cents 1/1, 0.0000 cents 66.66667 cents 2: 133.3333 .. 133.3333 cents 1/1, 0.0000 cents 66.66667 cents 3: 200.0000 .. 200.0000 cents 1/1, 0.0000 cents 66.66667 cents 4: 266.6667 .. 266.6667 cents 1/1, 0.0000 cents 66.66667 cents 5: 333.3333 .. 333.3333 cents 1/1, 0.0000 cents 66.66667 cents 6: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 66.66667 cents 7: 466.6667 .. 466.6667 cents 1/1, 0.0000 cents 66.66667 cents 8: 533.3333 .. 533.3333 cents 1/1, 0.0000 cents 66.66667 cents 9: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 66.66667 cents 10: 666.6667 .. 666.6667 cents 1/1, 0.0000 cents 66.66667 cents 11: 733.3333 .. 733.3333 cents 1/1, 0.0000 cents 66.66667 cents 12: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 66.66667 cents 13: 866.6667 .. 866.6667 cents 1/1, 0.0000 cents 66.66667 cents 14: 933.3333 .. 933.3333 cents 1/1, 0.0000 cents 66.66667 cents 15: 1000.0000 .. 1000.0000 cents 1/1, 0.0000 cents 66.66667 cents 16: 1066.6667 .. 1066.6667 cents 1/1, 0.0000 cents 66.66667 cents 17: 1133.3333 .. 1133.3333 cents 1/1, 0.0000 cents 66.66667 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 66.66667 cents, class 1 Average step (divided formal octave): 66.6667 cents Largest one step interval : 66.66667 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 66.66667 cents, amount: 18 Most common interval of one step : 66.66667 cents, amount: 18 Least squares average step : 66.66667 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 66.66667 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.055556 redundancy: 0.944444 Efficiency x scale size : 1.000000 Number of different interval sizes : 17 = 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 8 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
18: 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: 15.6892 cents 3 .. 6 match: 3 H SD: 12.0074 cents 4 .. 8 match: 4 H SD: 11.5751 cents 5 .. 10 match: 5 H SD: 6.6806 cents 6 .. 12 match: 6 H SD: 8.4684 cents 7 .. 14 match: 7 H SD: 7.2942 cents 8 .. 16 match: 8 H SD: 7.5336 cents 9 .. 18 match: 9 H SD: 7.6687 cents 10 .. 20 match: 10 H SD: 6.2962 cents 11 .. 22 match: 11 H SD: 5.3179 cents 12 .. 24 match: 12 H SD: 5.1681 cents 13 .. 26 match: 13 H SD: 4.7581 cents 14 .. 28 match: 14 H SD: 4.4574 cents 15 .. 30 match: 15 H SD: 4.1720 cents 16 .. 32 match: 15 SD: 5.8686 cents 17 .. 34 match: 16 SD: 4.0463 cents 18 .. 36 match: 16 SD: 5.3565 cents 19 .. 38 match: 17 SD: 3.3101 cents 20 .. 40 match: 17 SD: 4.3542 cents 21 .. 42 match: 17 SD: 4.9242 cents 22 .. 44 match: 18 SD: 3.4328 cents 23 .. 46 match: 18 SD: 2.9742 cents 24 .. 48 match: 18 SD: 2.7322 cents 32 .. 64 match: 18 SD: 2.4459 cents 34 .. 68 match: 18 SD: 2.2649 cents 36 .. 72 match: 18 SD: 2.1425 cents 38 .. 76 match: 18 SD: 2.1090 cents 41 .. 82 match: 18 SD: 1.8480 cents 42 .. 84 match: 18 SD: 1.6080 cents 48 .. 96 match: 18 SD: 1.5474 cents 49 .. 98 match: 18 SD: 1.2610 cents 55 .. 110 match: 18 SD: 1.2609 cents 65 .. 130 match: 18 SD: 1.2243 cents 66 .. 132 match: 18 SD: 1.0685 cents 72 .. 144 match: 18 SD: 0.9571 cents 74 .. 148 match: 18 SD: 0.8951 cents 77 .. 154 match: 18 SD: 0.8811 cents 80 .. 160 match: 18 SD: 0.8751 cents 89 .. 178 match: 18 SD: 0.8624 cents 96 .. 192 match: 18 SD: 0.8369 cents 97 .. 194 match: 18 SD: 0.6841 cents 100 .. 200 match: 18 SD: 0.6594 cents 108 .. 216 match: 18 SD: 0.6545 cents 122 .. 244 match: 18 SD: 0.6136 cents 123 .. 246 match: 18 SD: 0.5076 cents 150 .. 300 match: 18 SD: 0.4601 cents 155 .. 310 match: 18 SD: 0.3875 cents 174 .. 348 match: 18 SD: 0.3091 cents 203 .. 406 match: 18 SD: 0.2793 cents 235 .. 470 match: 18 SD: 0.2693 cents 277 .. 554 match: 18 SD: 0.1843 cents 311 .. 622 match: 18 SD: 0.1717 cents 377 .. 754 match: 18 SD: 0.1697 cents 385 .. 770 match: 18 SD: 0.1302 cents 485 .. 970 match: 18 SD: 0.1195 cents 565 .. 1130 match: 18 SD: 0.1003 cents 588 .. 1176 match: 18 SD: 0.0956 cents