Scala analysis: edo-21
21 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.143 cents 57.142857 2: 114.286 cents 114.285714 3: 171.429 cents 171.428571 4: 228.571 cents 228.571429 5: 285.714 cents 285.714286 6: 342.857 cents 342.857143 7: 400.000 cents 400.000000 8: 457.143 cents 457.142857 9: 514.286 cents 514.285714 10: 571.429 cents 571.428571 11: 628.571 cents 628.571429 12: 685.714 cents 685.714286 13: 742.857 cents 742.857143 14: 800.000 cents 800.000000 15: 857.143 cents 857.142857 16: 914.286 cents 914.285714 17: 971.429 cents 971.428571 18: 1028.571 cents 1028.571429 19: 1085.714 cents 1085.714286 20: 1142.857 cents 1142.857143 21: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 57.1429 cents 57.1429 1: 57.1429 cents 57.1429 2: 57.1429 cents 57.1429 3: 57.1429 cents 57.1429 4: 57.1429 cents 57.1429 5: 57.1429 cents 57.1429 6: 57.1429 cents 57.1429 7: 57.1429 cents 57.1429 8: 57.1429 cents 57.1429 9: 57.1429 cents 57.1429 10: 57.1429 cents 57.1429 11: 57.1429 cents 57.1429 12: 57.1429 cents 57.1429 13: 57.1429 cents 57.1429 14: 57.1429 cents 57.1429 15: 57.1429 cents 57.1429 16: 57.1429 cents 57.1429 17: 57.1429 cents 57.1429 18: 57.1429 cents 57.1429 19: 57.1429 cents 57.1429 20: 57.1429 cents 57.1429 21: 57.1429 cents 57.1429
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 21 57.14286 cents 2: 21 114.28571 cents 3: 21 171.42857 cents 4: 21 228.57143 cents 5: 21 285.71429 cents 6: 21 342.85714 cents 7: 21 400.00000 cents 8: 21 457.14286 cents 9: 21 514.28571 cents 10: 21 571.42857 cents 11: 21 628.57143 cents 12: 21 685.71429 cents 13: 21 742.85714 cents 14: 21 800.00000 cents 15: 21 857.14286 cents 16: 21 914.28571 cents 17: 21 971.42857 cents 18: 21 1028.57143 cents 19: 21 1085.71429 cents 20: 21 1142.85714 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 0.0 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 57.1 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 114.3 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 171.4 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 228.6 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 285.7 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 342.9 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 400.0 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 457.1 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 514.3 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 571.4 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 628.6 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 685.7 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 742.9 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 800.0 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 857.1 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 914.3 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 971.4 : 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 1028.6: 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 1085.7: 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 1142.9: 57.1 114.3 171.4 228.6 285.7 342.9 400.0 457.1 514.3 571.4 628.6 685.7 742.9 800.0 857.1 914.3 971.4 1028.6 1085.7 1142.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.1429 .. 57.1429 cents 1/1, 0.0000 cents 57.14286 cents 2: 114.2857 .. 114.2857 cents 1/1, 0.0000 cents 57.14286 cents 3: 171.4286 .. 171.4286 cents 1/1, 0.0000 cents 57.14286 cents 4: 228.5714 .. 228.5714 cents 1/1, 0.0000 cents 57.14286 cents 5: 285.7143 .. 285.7143 cents 1/1, 0.0000 cents 57.14286 cents 6: 342.8571 .. 342.8571 cents 1/1, 0.0000 cents 57.14286 cents 7: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 57.14286 cents 8: 457.1429 .. 457.1429 cents 1/1, 0.0000 cents 57.14286 cents 9: 514.2857 .. 514.2857 cents 1/1, 0.0000 cents 57.14286 cents 10: 571.4286 .. 571.4286 cents 1/1, 0.0000 cents 57.14286 cents 11: 628.5714 .. 628.5714 cents 1/1, 0.0000 cents 57.14286 cents 12: 685.7143 .. 685.7143 cents 1/1, 0.0000 cents 57.14286 cents 13: 742.8571 .. 742.8571 cents 1/1, 0.0000 cents 57.14286 cents 14: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 57.14286 cents 15: 857.1429 .. 857.1429 cents 1/1, 0.0000 cents 57.14286 cents 16: 914.2857 .. 914.2857 cents 1/1, 0.0000 cents 57.14286 cents 17: 971.4286 .. 971.4286 cents 1/1, 0.0000 cents 57.14286 cents 18: 1028.5714 .. 1028.5714 cents 1/1, 0.0000 cents 57.14286 cents 19: 1085.7143 .. 1085.7143 cents 1/1, 0.0000 cents 57.14286 cents 20: 1142.8571 .. 1142.8571 cents 1/1, 0.0000 cents 57.14286 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 57.14286 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 57.14286 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 57.14286 cents, amount: 21 Most common interval of one step : 57.14286 cents, amount: 21 Least squares average step : 57.14286 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 57.14286 cents Ratio Whole / Half tone : 1.000000 ( 1 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.047619 redundancy: 0.952381 Efficiency x scale size : 1.000000 Number of different interval sizes : 20 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 21, average 685.7143 cents Number of appreciable fifths : 0 Scale contains two identical disjunct "tetrachords" of 10 notes Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
21: 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: 8.1204 cents 3 .. 6 match: 3 H SD: 10.5644 cents 4 .. 8 match: 4 H SD: 5.3494 cents 5 .. 10 match: 5 H SD: 6.8449 cents 6 .. 12 match: 6 H SD: 7.5564 cents 7 .. 14 match: 7 H SD: 5.4850 cents 8 .. 16 match: 8 H SD: 5.2337 cents 9 .. 18 match: 9 H SD: 5.6000 cents 10 .. 20 match: 10 H SD: 4.6405 cents 11 .. 22 match: 11 H SD: 5.0053 cents 12 .. 24 match: 12 H SD: 5.1280 cents 13 .. 26 match: 13 H SD: 4.5383 cents 14 .. 28 match: 14 H SD: 3.6908 cents 15 .. 30 match: 15 H SD: 3.8455 cents 16 .. 32 match: 16 H SD: 3.4183 cents 17 .. 34 match: 17 H SD: 3.2229 cents 18 .. 36 match: 18 H SD: 4.3281 cents 19 .. 38 match: 18 S SD: 3.8794 cents 20 .. 40 match: 19 SD: 3.2532 cents 21 .. 42 match: 19 SD: 3.6433 cents 22 .. 44 match: 20 SD: 3.3939 cents 23 .. 46 match: 20 SD: 2.7986 cents 24 .. 48 match: 20 SD: 3.5504 cents 25 .. 50 match: 20 SD: 3.7481 cents 26 .. 52 match: 21 SD: 2.7352 cents 27 .. 54 match: 21 SD: 2.3072 cents 28 .. 56 match: 21 SD: 2.3027 cents 33 .. 66 match: 21 SD: 2.2542 cents 36 .. 72 match: 21 SD: 2.2113 cents 37 .. 74 match: 21 SD: 2.0446 cents 39 .. 78 match: 21 SD: 1.9823 cents 41 .. 82 match: 21 SD: 1.7128 cents 46 .. 92 match: 21 SD: 1.5842 cents 49 .. 98 match: 21 SD: 1.3739 cents 55 .. 110 match: 21 SD: 1.3521 cents 56 .. 112 match: 21 SD: 1.1251 cents 69 .. 138 match: 21 SD: 0.9854 cents 73 .. 146 match: 21 SD: 0.9852 cents 76 .. 152 match: 21 SD: 0.9808 cents 77 .. 154 match: 21 SD: 0.9258 cents 78 .. 156 match: 21 SD: 0.8536 cents 84 .. 168 match: 21 SD: 0.7959 cents 86 .. 172 match: 21 SD: 0.7747 cents 89 .. 178 match: 21 SD: 0.7215 cents 92 .. 184 match: 21 SD: 0.7182 cents 105 .. 210 match: 21 SD: 0.6125 cents 115 .. 230 match: 21 SD: 0.5960 cents 116 .. 232 match: 21 SD: 0.5660 cents 119 .. 238 match: 21 SD: 0.5459 cents 123 .. 246 match: 21 SD: 0.5443 cents 128 .. 256 match: 21 SD: 0.4961 cents 142 .. 284 match: 21 SD: 0.4561 cents 150 .. 300 match: 21 SD: 0.4165 cents 173 .. 346 match: 21 SD: 0.3685 cents 201 .. 402 match: 21 SD: 0.3418 cents 205 .. 410 match: 21 SD: 0.3086 cents 228 .. 456 match: 21 SD: 0.2839 cents 233 .. 466 match: 21 SD: 0.2709 cents 261 .. 522 match: 21 SD: 0.2266 cents 278 .. 556 match: 21 SD: 0.2204 cents 297 .. 594 match: 21 SD: 0.2085 cents 319 .. 638 match: 21 SD: 0.2062 cents 324 .. 648 match: 21 SD: 0.2025 cents 327 .. 654 match: 21 SD: 0.1951 cents 334 .. 668 match: 21 SD: 0.1934 cents 335 .. 670 match: 21 SD: 0.1882 cents 356 .. 712 match: 21 SD: 0.1749 cents 368 .. 736 match: 21 SD: 0.1705 cents 381 .. 762 match: 21 SD: 0.1656 cents 384 .. 768 match: 21 SD: 0.1319 cents 424 .. 848 match: 21 SD: 0.1287 cents 453 .. 906 match: 21 SD: 0.1266 cents 480 .. 960 match: 21 SD: 0.1214 cents 509 .. 1018 match: 21 SD: 0.1166 cents 539 .. 1078 match: 21 SD: 0.1041 cents