Scala analysis: edo-20
20 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60.000 cents 60.000000 2: 120.000 cents 120.000000 3: 180.000 cents 180.000000 4: 240.000 cents 240.000000 5: 300.000 cents 300.000000 6: 360.000 cents 360.000000 7: 420.000 cents 420.000000 8: 480.000 cents 480.000000 9: 540.000 cents 540.000000 10: 600.000 cents 600.000000 11: 660.000 cents 660.000000 12: 720.000 cents 720.000000 13: 780.000 cents 780.000000 14: 840.000 cents 840.000000 15: 900.000 cents 900.000000 16: 960.000 cents 960.000000 17: 1020.000 cents 1020.000000 18: 1080.000 cents 1080.000000 19: 1140.000 cents 1140.000000 20: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 60.0000 cents 60.0000 1: 60.0000 cents 60.0000 2: 60.0000 cents 60.0000 3: 60.0000 cents 60.0000 4: 60.0000 cents 60.0000 5: 60.0000 cents 60.0000 6: 60.0000 cents 60.0000 7: 60.0000 cents 60.0000 8: 60.0000 cents 60.0000 9: 60.0000 cents 60.0000 10: 60.0000 cents 60.0000 11: 60.0000 cents 60.0000 12: 60.0000 cents 60.0000 13: 60.0000 cents 60.0000 14: 60.0000 cents 60.0000 15: 60.0000 cents 60.0000 16: 60.0000 cents 60.0000 17: 60.0000 cents 60.0000 18: 60.0000 cents 60.0000 19: 60.0000 cents 60.0000 20: 60.0000 cents 60.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 20 60.00000 cents 2: 20 120.00000 cents 3: 20 180.00000 cents 4: 20 240.00000 cents 5: 20 300.00000 cents 6: 20 360.00000 cents 7: 20 420.00000 cents 8: 20 480.00000 cents 9: 20 540.00000 cents 10: 20 600.00000 cents 11: 20 660.00000 cents 12: 20 720.00000 cents 13: 20 780.00000 cents 14: 20 840.00000 cents 15: 20 900.00000 cents 16: 20 960.00000 cents 17: 20 1020.00000 cents 18: 20 1080.00000 cents 19: 20 1140.00000 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 0.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 60.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 120.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 180.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 240.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 300.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 360.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 420.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 480.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 540.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 600.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 660.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 720.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 780.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 840.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 900.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 960.0 : 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 1020.0: 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 1080.0: 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 1140.0: 60.0 120.0 180.0 240.0 300.0 360.0 420.0 480.0 540.0 600.0 660.0 720.0 780.0 840.0 900.0 960.0 1020.0 1080.0 1140.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 60.0000 .. 60.0000 cents 1/1, 0.0000 cents 60.00000 cents 2: 120.0000 .. 120.0000 cents 1/1, 0.0000 cents 60.00000 cents 3: 180.0000 .. 180.0000 cents 1/1, 0.0000 cents 60.00000 cents 4: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 60.00000 cents 5: 300.0000 .. 300.0000 cents 1/1, 0.0000 cents 60.00000 cents 6: 360.0000 .. 360.0000 cents 1/1, 0.0000 cents 60.00000 cents 7: 420.0000 .. 420.0000 cents 1/1, 0.0000 cents 60.00000 cents 8: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 60.00000 cents 9: 540.0000 .. 540.0000 cents 1/1, 0.0000 cents 60.00000 cents 10: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 60.00000 cents 11: 660.0000 .. 660.0000 cents 1/1, 0.0000 cents 60.00000 cents 12: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 60.00000 cents 13: 780.0000 .. 780.0000 cents 1/1, 0.0000 cents 60.00000 cents 14: 840.0000 .. 840.0000 cents 1/1, 0.0000 cents 60.00000 cents 15: 900.0000 .. 900.0000 cents 1/1, 0.0000 cents 60.00000 cents 16: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 60.00000 cents 17: 1020.0000 .. 1020.0000 cents 1/1, 0.0000 cents 60.00000 cents 18: 1080.0000 .. 1080.0000 cents 1/1, 0.0000 cents 60.00000 cents 19: 1140.0000 .. 1140.0000 cents 1/1, 0.0000 cents 60.00000 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 60.00000 cents, class 1 Average step (divided formal octave): 60.0000 cents Largest one step interval : 60.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 60.00000 cents, amount: 20 Most common interval of one step : 60.00000 cents, amount: 20 Least squares average step : 60.00000 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 60.00000 cents Ratio Whole / Half tone : infinite Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.050000 redundancy: 0.950000 Efficiency x scale size : 1.000000 Number of different interval sizes : 19 = 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 9 notes Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
20: 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: 9.0225 cents 3 .. 6 match: 3 H SD: 7.9601 cents 4 .. 8 match: 4 H SD: 8.2762 cents 5 .. 10 match: 5 H SD: 7.0673 cents 6 .. 12 match: 6 H SD: 8.3001 cents 7 .. 14 match: 7 H SD: 5.3612 cents 8 .. 16 match: 8 H SD: 5.3973 cents 9 .. 18 match: 9 H SD: 5.5816 cents 10 .. 20 match: 10 H SD: 6.0341 cents 11 .. 22 match: 11 H SD: 4.8216 cents 12 .. 24 match: 12 H SD: 5.2925 cents 13 .. 26 match: 13 H SD: 4.1999 cents 14 .. 28 match: 14 H SD: 3.9651 cents 15 .. 30 match: 15 H SD: 3.6624 cents 16 .. 32 match: 16 H SD: 3.5284 cents 17 .. 34 match: 17 H SD: 4.2095 cents 18 .. 36 match: 17 S SD: 4.4797 cents 19 .. 38 match: 18 SD: 3.3262 cents 20 .. 40 match: 18 SD: 4.2386 cents 21 .. 42 match: 19 SD: 3.2278 cents 22 .. 44 match: 19 SD: 3.2064 cents 23 .. 46 match: 19 SD: 4.0253 cents 24 .. 48 match: 20 SD: 3.7097 cents 25 .. 50 match: 20 SD: 2.7345 cents 26 .. 52 match: 20 SD: 2.4105 cents 35 .. 70 match: 20 SD: 2.1959 cents 38 .. 76 match: 20 SD: 2.1119 cents 39 .. 78 match: 20 SD: 1.9847 cents 43 .. 86 match: 20 SD: 1.7868 cents 44 .. 88 match: 20 SD: 1.7789 cents 46 .. 92 match: 20 SD: 1.6076 cents 47 .. 94 match: 20 SD: 1.4170 cents 53 .. 106 match: 20 SD: 1.2927 cents 54 .. 108 match: 20 SD: 1.1642 cents 65 .. 130 match: 20 SD: 1.1224 cents 69 .. 138 match: 20 SD: 1.0605 cents 73 .. 146 match: 20 SD: 0.9905 cents 74 .. 148 match: 20 SD: 0.9512 cents 81 .. 162 match: 20 SD: 0.8654 cents 82 .. 164 match: 20 SD: 0.7917 cents 91 .. 182 match: 20 SD: 0.7813 cents 95 .. 190 match: 20 SD: 0.7496 cents 101 .. 202 match: 20 SD: 0.6732 cents 107 .. 214 match: 20 SD: 0.6490 cents 109 .. 218 match: 20 SD: 0.5968 cents 112 .. 224 match: 20 SD: 0.5296 cents 128 .. 256 match: 20 SD: 0.5228 cents 138 .. 276 match: 20 SD: 0.5035 cents 142 .. 284 match: 20 SD: 0.4171 cents 174 .. 348 match: 20 SD: 0.4107 cents 181 .. 362 match: 20 SD: 0.3438 cents 194 .. 388 match: 20 SD: 0.2998 cents 207 .. 414 match: 20 SD: 0.2972 cents 222 .. 444 match: 20 SD: 0.2971 cents 229 .. 458 match: 20 SD: 0.2732 cents 237 .. 474 match: 20 SD: 0.2516 cents 248 .. 496 match: 20 SD: 0.2103 cents 336 .. 672 match: 20 SD: 0.1835 cents 338 .. 676 match: 20 SD: 0.1806 cents 364 .. 728 match: 20 SD: 0.1398 cents 429 .. 858 match: 20 SD: 0.1321 cents 485 .. 970 match: 20 SD: 0.1110 cents 572 .. 1144 match: 20 SD: 0.1110 cents 597 .. 1194 match: 20 SD: 0.1061 cents