Scala analysis: edo-24
24 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.000 cents 50.000000 2: 100.000 cents 100.000000 3: 150.000 cents 150.000000 4: 200.000 cents 200.000000 5: 250.000 cents 250.000000 6: 300.000 cents 300.000000 7: 350.000 cents 350.000000 8: 400.000 cents 400.000000 9: 450.000 cents 450.000000 10: 500.000 cents 500.000000 11: 550.000 cents 550.000000 12: 600.000 cents 600.000000 13: 650.000 cents 650.000000 14: 700.000 cents 700.000000 15: 750.000 cents 750.000000 16: 800.000 cents 800.000000 17: 850.000 cents 850.000000 18: 900.000 cents 900.000000 19: 950.000 cents 950.000000 20: 1000.000 cents 1000.000000 21: 1050.000 cents 1050.000000 22: 1100.000 cents 1100.000000 23: 1150.000 cents 1150.000000 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 50.0000 cents 50.0000 1: 50.0000 cents 50.0000 2: 50.0000 cents 50.0000 3: 50.0000 cents 50.0000 4: 50.0000 cents 50.0000 5: 50.0000 cents 50.0000 6: 50.0000 cents 50.0000 7: 50.0000 cents 50.0000 8: 50.0000 cents 50.0000 9: 50.0000 cents 50.0000 10: 50.0000 cents 50.0000 11: 50.0000 cents 50.0000 12: 50.0000 cents 50.0000 13: 50.0000 cents 50.0000 14: 50.0000 cents 50.0000 15: 50.0000 cents 50.0000 16: 50.0000 cents 50.0000 17: 50.0000 cents 50.0000 18: 50.0000 cents 50.0000 19: 50.0000 cents 50.0000 20: 50.0000 cents 50.0000 21: 50.0000 cents 50.0000 22: 50.0000 cents 50.0000 23: 50.0000 cents 50.0000 24: 50.0000 cents 50.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 24 50.00000 cents 2: 24 100.00000 cents 3: 24 150.00000 cents 4: 24 200.00000 cents 5: 24 250.00000 cents 6: 24 300.00000 cents 7: 24 350.00000 cents 8: 24 400.00000 cents 9: 24 450.00000 cents 10: 24 500.00000 cents 11: 24 550.00000 cents 12: 24 600.00000 cents 13: 24 650.00000 cents 14: 24 700.00000 cents 15: 24 750.00000 cents 16: 24 800.00000 cents 17: 24 850.00000 cents 18: 24 900.00000 cents 19: 24 950.00000 cents 20: 24 1000.00000 cents 21: 24 1050.00000 cents 22: 24 1100.00000 cents 23: 24 1150.00000 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 21 22 23 24 0.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 50.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 100.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 150.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 200.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 250.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 300.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 350.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 400.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 450.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 500.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 550.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 600.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 650.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 700.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 750.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 800.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 850.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 900.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 950.0 : 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 1000.0: 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 1050.0: 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 1100.0: 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 1150.0: 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0 800.0 850.0 900.0 950.0 1000.0 1050.0 1100.0 1150.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 50.0000 cents 1/1, 0.0000 cents 50.00000 cents 2: 100.0000 .. 100.0000 cents 1/1, 0.0000 cents 50.00000 cents 3: 150.0000 .. 150.0000 cents 1/1, 0.0000 cents 50.00000 cents 4: 200.0000 .. 200.0000 cents 1/1, 0.0000 cents 50.00000 cents 5: 250.0000 .. 250.0000 cents 1/1, 0.0000 cents 50.00000 cents 6: 300.0000 .. 300.0000 cents 1/1, 0.0000 cents 50.00000 cents 7: 350.0000 .. 350.0000 cents 1/1, 0.0000 cents 50.00000 cents 8: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 50.00000 cents 9: 450.0000 .. 450.0000 cents 1/1, 0.0000 cents 50.00000 cents 10: 500.0000 .. 500.0000 cents 1/1, 0.0000 cents 50.00000 cents 11: 550.0000 .. 550.0000 cents 1/1, 0.0000 cents 50.00000 cents 12: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 50.00000 cents 13: 650.0000 .. 650.0000 cents 1/1, 0.0000 cents 50.00000 cents 14: 700.0000 .. 700.0000 cents 1/1, 0.0000 cents 50.00000 cents 15: 750.0000 .. 750.0000 cents 1/1, 0.0000 cents 50.00000 cents 16: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 50.00000 cents 17: 850.0000 .. 850.0000 cents 1/1, 0.0000 cents 50.00000 cents 18: 900.0000 .. 900.0000 cents 1/1, 0.0000 cents 50.00000 cents 19: 950.0000 .. 950.0000 cents 1/1, 0.0000 cents 50.00000 cents 20: 1000.0000 .. 1000.0000 cents 1/1, 0.0000 cents 50.00000 cents 21: 1050.0000 .. 1050.0000 cents 1/1, 0.0000 cents 50.00000 cents 22: 1100.0000 .. 1100.0000 cents 1/1, 0.0000 cents 50.00000 cents 23: 1150.0000 .. 1150.0000 cents 1/1, 0.0000 cents 50.00000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 50.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 50.00000 cents, amount: 24 Most common interval of one step : 50.00000 cents, amount: 24 Least squares average step : 50.00000 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 50.00000 cents Ratio Whole / Half tone : 2.000000 ( 2 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.041667 redundancy: 0.958333 Efficiency x scale size : 1.000000 Number of different interval sizes : 23 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 24, average 700.0000 cents Scale contains two identical disjunct "tetrachords" of 11 notes Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
24: 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: 0.9775 cents 3 .. 6 match: 3 H SD: 5.2543 cents 4 .. 8 match: 4 H SD: 5.8393 cents 5 .. 10 match: 5 H SD: 6.4728 cents 6 .. 12 match: 6 H SD: 3.8634 cents 7 .. 14 match: 7 H SD: 6.3001 cents 8 .. 16 match: 8 H SD: 3.5132 cents 9 .. 18 match: 9 H SD: 3.4832 cents 10 .. 20 match: 10 H SD: 4.2036 cents 11 .. 22 match: 11 H SD: 3.1932 cents 12 .. 24 match: 12 H SD: 3.5347 cents 13 .. 26 match: 13 H SD: 3.5477 cents 14 .. 28 match: 14 H SD: 4.0689 cents 15 .. 30 match: 15 H SD: 3.3508 cents 16 .. 32 match: 16 H SD: 3.2552 cents 17 .. 34 match: 17 H SD: 3.1920 cents 18 .. 36 match: 18 H SD: 3.0066 cents 19 .. 38 match: 19 H SD: 2.8270 cents 20 .. 40 match: 20 H SD: 3.0290 cents 21 .. 42 match: 20 SD: 3.5557 cents 22 .. 44 match: 21 S SD: 2.5873 cents 23 .. 46 match: 21 SD: 3.5449 cents 24 .. 48 match: 22 SD: 2.3812 cents 25 .. 50 match: 22 SD: 3.2419 cents 26 .. 52 match: 23 SD: 2.4157 cents 27 .. 54 match: 23 SD: 2.3815 cents 28 .. 56 match: 23 SD: 2.9242 cents 29 .. 58 match: 23 SD: 2.9700 cents 30 .. 60 match: 24 SD: 2.2881 cents 31 .. 62 match: 24 SD: 1.8965 cents 32 .. 64 match: 24 SD: 1.8441 cents 38 .. 76 match: 24 SD: 1.8352 cents 41 .. 82 match: 24 SD: 1.6536 cents 44 .. 88 match: 24 SD: 1.5699 cents 46 .. 92 match: 24 SD: 1.4253 cents 53 .. 106 match: 24 SD: 1.2897 cents 54 .. 108 match: 24 SD: 1.2288 cents 57 .. 114 match: 24 SD: 1.2026 cents 63 .. 126 match: 24 SD: 1.0062 cents 65 .. 130 match: 24 SD: 0.9623 cents 66 .. 132 match: 24 SD: 0.9052 cents 68 .. 136 match: 24 SD: 0.8842 cents 81 .. 162 match: 24 SD: 0.8837 cents 84 .. 168 match: 24 SD: 0.8386 cents 85 .. 170 match: 24 SD: 0.8173 cents 88 .. 176 match: 24 SD: 0.7897 cents 89 .. 178 match: 24 SD: 0.7456 cents 90 .. 180 match: 24 SD: 0.6581 cents 99 .. 198 match: 24 SD: 0.6400 cents 101 .. 202 match: 24 SD: 0.5505 cents 123 .. 246 match: 24 SD: 0.5214 cents 131 .. 262 match: 24 SD: 0.4379 cents 147 .. 294 match: 24 SD: 0.4354 cents 155 .. 310 match: 24 SD: 0.3953 cents 164 .. 328 match: 24 SD: 0.3891 cents 169 .. 338 match: 24 SD: 0.3276 cents 201 .. 402 match: 24 SD: 0.3040 cents 205 .. 410 match: 24 SD: 0.2957 cents 219 .. 438 match: 24 SD: 0.2915 cents 232 .. 464 match: 24 SD: 0.2653 cents 253 .. 506 match: 24 SD: 0.2650 cents 263 .. 526 match: 24 SD: 0.2582 cents 265 .. 530 match: 24 SD: 0.2364 cents 276 .. 552 match: 24 SD: 0.2234 cents 301 .. 602 match: 24 SD: 0.1993 cents 334 .. 668 match: 24 SD: 0.1670 cents 353 .. 706 match: 24 SD: 0.1590 cents 367 .. 734 match: 24 SD: 0.1583 cents 374 .. 748 match: 24 SD: 0.1474 cents 417 .. 834 match: 24 SD: 0.1446 cents 439 .. 878 match: 24 SD: 0.1144 cents 508 .. 1016 match: 24 SD: 0.1133 cents 522 .. 1044 match: 24 SD: 0.1033 cents 540 .. 1080 match: 24 SD: 0.0955 cents