Scala analysis: edo-29
29 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 41.379 cents 41.379310 2: 82.759 cents 82.758621 3: 124.138 cents 124.137931 4: 165.517 cents 165.517241 5: 206.897 cents 206.896552 6: 248.276 cents 248.275862 7: 289.655 cents 289.655172 8: 331.034 cents 331.034483 9: 372.414 cents 372.413793 10: 413.793 cents 413.793103 11: 455.172 cents 455.172414 12: 496.552 cents 496.551724 13: 537.931 cents 537.931034 14: 579.310 cents 579.310345 15: 620.690 cents 620.689655 16: 662.069 cents 662.068966 17: 703.448 cents 703.448276 18: 744.828 cents 744.827586 19: 786.207 cents 786.206897 20: 827.586 cents 827.586207 21: 868.966 cents 868.965517 22: 910.345 cents 910.344828 23: 951.724 cents 951.724138 24: 993.103 cents 993.103448 25: 1034.483 cents 1034.482759 26: 1075.862 cents 1075.862069 27: 1117.241 cents 1117.241379 28: 1158.621 cents 1158.620690 29: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 41.3793 cents 41.3793 1: 41.3793 cents 41.3793 2: 41.3793 cents 41.3793 3: 41.3793 cents 41.3793 4: 41.3793 cents 41.3793 5: 41.3793 cents 41.3793 6: 41.3793 cents 41.3793 7: 41.3793 cents 41.3793 8: 41.3793 cents 41.3793 9: 41.3793 cents 41.3793 10: 41.3793 cents 41.3793 11: 41.3793 cents 41.3793 12: 41.3793 cents 41.3793 13: 41.3793 cents 41.3793 14: 41.3793 cents 41.3793 15: 41.3793 cents 41.3793 16: 41.3793 cents 41.3793 17: 41.3793 cents 41.3793 18: 41.3793 cents 41.3793 19: 41.3793 cents 41.3793 20: 41.3793 cents 41.3793 21: 41.3793 cents 41.3793 22: 41.3793 cents 41.3793 23: 41.3793 cents 41.3793 24: 41.3793 cents 41.3793 25: 41.3793 cents 41.3793 26: 41.3793 cents 41.3793 27: 41.3793 cents 41.3793 28: 41.3793 cents 41.3793 29: 41.3793 cents 41.3793
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 29 41.37931 cents 2: 29 82.75862 cents 3: 29 124.13793 cents 4: 29 165.51724 cents 5: 29 206.89655 cents 6: 29 248.27586 cents 7: 29 289.65517 cents 8: 29 331.03448 cents 9: 29 372.41379 cents 10: 29 413.79310 cents 11: 29 455.17241 cents 12: 29 496.55172 cents 13: 29 537.93103 cents 14: 29 579.31034 cents 15: 29 620.68965 cents 16: 29 662.06897 cents 17: 29 703.44828 cents 18: 29 744.82759 cents 19: 29 786.20690 cents 20: 29 827.58621 cents 21: 29 868.96552 cents 22: 29 910.34483 cents 23: 29 951.72414 cents 24: 29 993.10345 cents 25: 29 1034.48276 cents 26: 29 1075.86207 cents 27: 29 1117.24138 cents 28: 29 1158.62069 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 28 29 0.0 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 41.4 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 82.8 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 124.1 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 165.5 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 206.9 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 248.3 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 289.7 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 331.0 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 372.4 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 413.8 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 455.2 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 496.6 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 537.9 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 579.3 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 620.7 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 662.1 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 703.4 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 744.8 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 786.2 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 827.6 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 869.0 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 910.3 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 951.7 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 993.1 : 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 1034.5: 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 1075.9: 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 1117.2: 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 1158.6: 41.4 82.8 124.1 165.5 206.9 248.3 289.7 331.0 372.4 413.8 455.2 496.6 537.9 579.3 620.7 662.1 703.4 744.8 786.2 827.6 869.0 910.3 951.7 993.1 1034.5 1075.9 1117.2 1158.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.3793 .. 41.3793 cents 1/1, 0.0000 cents 41.37931 cents 2: 82.7586 .. 82.7586 cents 1/1, 0.0000 cents 41.37931 cents 3: 124.1379 .. 124.1379 cents 1/1, 0.0000 cents 41.37931 cents 4: 165.5172 .. 165.5172 cents 1/1, 0.0000 cents 41.37931 cents 5: 206.8966 .. 206.8966 cents 1/1, 0.0000 cents 41.37931 cents 6: 248.2759 .. 248.2759 cents 1/1, 0.0000 cents 41.37931 cents 7: 289.6552 .. 289.6552 cents 1/1, 0.0000 cents 41.37931 cents 8: 331.0345 .. 331.0345 cents 1/1, 0.0000 cents 41.37931 cents 9: 372.4138 .. 372.4138 cents 1/1, 0.0000 cents 41.37931 cents 10: 413.7931 .. 413.7931 cents 1/1, 0.0000 cents 41.37931 cents 11: 455.1724 .. 455.1724 cents 1/1, 0.0000 cents 41.37931 cents 12: 496.5517 .. 496.5517 cents 1/1, 0.0000 cents 41.37931 cents 13: 537.9310 .. 537.9310 cents 1/1, 0.0000 cents 41.37931 cents 14: 579.3103 .. 579.3103 cents 1/1, 0.0000 cents 41.37931 cents 15: 620.6897 .. 620.6897 cents 1/1, 0.0000 cents 41.37931 cents 16: 662.0690 .. 662.0690 cents 1/1, 0.0000 cents 41.37931 cents 17: 703.4483 .. 703.4483 cents 1/1, 0.0000 cents 41.37931 cents 18: 744.8276 .. 744.8276 cents 1/1, 0.0000 cents 41.37931 cents 19: 786.2069 .. 786.2069 cents 1/1, 0.0000 cents 41.37931 cents 20: 827.5862 .. 827.5862 cents 1/1, 0.0000 cents 41.37931 cents 21: 868.9655 .. 868.9655 cents 1/1, 0.0000 cents 41.37931 cents 22: 910.3448 .. 910.3448 cents 1/1, 0.0000 cents 41.37931 cents 23: 951.7241 .. 951.7241 cents 1/1, 0.0000 cents 41.37931 cents 24: 993.1034 .. 993.1034 cents 1/1, 0.0000 cents 41.37931 cents 25: 1034.4828 .. 1034.4828 cents 1/1, 0.0000 cents 41.37931 cents 26: 1075.8621 .. 1075.8621 cents 1/1, 0.0000 cents 41.37931 cents 27: 1117.2414 .. 1117.2414 cents 1/1, 0.0000 cents 41.37931 cents 28: 1158.6207 .. 1158.6207 cents 1/1, 0.0000 cents 41.37931 cents
SHOW DATA
Number of notes : 29 -- Interval properties -- Smallest interval : 41.37931 cents, class 1 Average step (divided formal octave): 41.3793 cents Largest one step interval : 41.37931 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 41.37931 cents, amount: 29 Most common interval of one step : 41.37931 cents, amount: 29 Least squares average step : 41.37931 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 41.37931 cents Ratio Whole / Half tone : 2.500000 ( 5/2 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.034483 redundancy: 0.965517 Efficiency x scale size : 1.000000 Number of different interval sizes : 28 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 29, average 703.4483 cents Scale contains two identical disjunct "tetrachords" of 13 notes Best fifths form a closed circle Best major thirds 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
29: 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 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: 0.7466 cents 3 .. 6 match: 3 H SD: 5.1552 cents 4 .. 8 match: 4 H SD: 5.5222 cents 5 .. 10 match: 5 H SD: 5.3873 cents 6 .. 12 match: 6 H SD: 4.7393 cents 7 .. 14 match: 7 H SD: 4.7016 cents 8 .. 16 match: 8 H SD: 3.9478 cents 9 .. 18 match: 9 H SD: 4.6093 cents 10 .. 20 match: 10 H SD: 2.8885 cents 11 .. 22 match: 11 H SD: 2.5666 cents 12 .. 24 match: 12 H SD: 3.7132 cents 13 .. 26 match: 13 H SD: 2.4523 cents 14 .. 28 match: 14 H SD: 3.0437 cents 15 .. 30 match: 15 H SD: 2.6512 cents 16 .. 32 match: 16 H SD: 2.8922 cents 17 .. 34 match: 17 H SD: 2.8507 cents 18 .. 36 match: 18 H SD: 2.9410 cents 19 .. 38 match: 19 H SD: 2.4763 cents 20 .. 40 match: 20 H SD: 2.4365 cents 21 .. 42 match: 21 H SD: 2.4393 cents 22 .. 44 match: 22 H SD: 2.1935 cents 23 .. 46 match: 23 H SD: 2.1146 cents 24 .. 48 match: 24 H SD: 2.4561 cents 25 .. 50 match: 24 SD: 2.6010 cents 26 .. 52 match: 25 S SD: 1.9800 cents 27 .. 54 match: 26 SD: 2.5746 cents 28 .. 56 match: 26 SD: 2.0413 cents 29 .. 58 match: 27 SD: 2.4682 cents 30 .. 60 match: 27 SD: 1.7780 cents 31 .. 62 match: 27 SD: 2.3113 cents 32 .. 64 match: 28 SD: 2.0006 cents 33 .. 66 match: 28 SD: 1.6900 cents 34 .. 68 match: 28 SD: 1.9667 cents 35 .. 70 match: 28 SD: 2.2329 cents 36 .. 72 match: 29 SD: 2.0427 cents 37 .. 74 match: 29 SD: 1.6165 cents 38 .. 76 match: 29 SD: 1.4257 cents 46 .. 92 match: 29 SD: 1.4232 cents 49 .. 98 match: 29 SD: 1.2804 cents 52 .. 104 match: 29 SD: 1.2680 cents 54 .. 108 match: 29 SD: 1.2053 cents 56 .. 112 match: 29 SD: 1.1499 cents 58 .. 116 match: 29 SD: 1.1146 cents 60 .. 120 match: 29 SD: 1.0853 cents 63 .. 126 match: 29 SD: 0.9911 cents 66 .. 132 match: 29 SD: 0.8935 cents 71 .. 142 match: 29 SD: 0.8287 cents 77 .. 154 match: 29 SD: 0.8064 cents 78 .. 156 match: 29 SD: 0.7051 cents 93 .. 186 match: 29 SD: 0.6521 cents 103 .. 206 match: 29 SD: 0.6317 cents 104 .. 208 match: 29 SD: 0.5844 cents 108 .. 216 match: 29 SD: 0.5732 cents 109 .. 218 match: 29 SD: 0.5328 cents 118 .. 236 match: 29 SD: 0.5229 cents 120 .. 240 match: 29 SD: 0.4699 cents 123 .. 246 match: 29 SD: 0.4697 cents 129 .. 258 match: 29 SD: 0.4687 cents 137 .. 274 match: 29 SD: 0.4347 cents 142 .. 284 match: 29 SD: 0.4271 cents 149 .. 298 match: 29 SD: 0.4094 cents 150 .. 300 match: 29 SD: 0.4027 cents 159 .. 318 match: 29 SD: 0.3967 cents 160 .. 320 match: 29 SD: 0.3426 cents 181 .. 362 match: 29 SD: 0.3113 cents 199 .. 398 match: 29 SD: 0.2906 cents 204 .. 408 match: 29 SD: 0.2647 cents 241 .. 482 match: 29 SD: 0.2463 cents 246 .. 492 match: 29 SD: 0.2338 cents 247 .. 494 match: 29 SD: 0.2070 cents 259 .. 518 match: 29 SD: 0.2031 cents 279 .. 558 match: 29 SD: 0.1986 cents 285 .. 570 match: 29 SD: 0.1868 cents 292 .. 584 match: 29 SD: 0.1803 cents 299 .. 598 match: 29 SD: 0.1795 cents 322 .. 644 match: 29 SD: 0.1696 cents 329 .. 658 match: 29 SD: 0.1683 cents 362 .. 724 match: 29 SD: 0.1498 cents 367 .. 734 match: 29 SD: 0.1456 cents 403 .. 806 match: 29 SD: 0.1429 cents 408 .. 816 match: 29 SD: 0.1386 cents 428 .. 856 match: 29 SD: 0.1349 cents 445 .. 890 match: 29 SD: 0.1275 cents 449 .. 898 match: 29 SD: 0.1231 cents 488 .. 976 match: 29 SD: 0.1148 cents 489 .. 978 match: 29 SD: 0.1091 cents 526 .. 1052 match: 29 SD: 0.1012 cents 538 .. 1076 match: 29 SD: 0.0989 cents 566 .. 1132 match: 29 SD: 0.0960 cents 578 .. 1156 match: 29 SD: 0.0930 cents 592 .. 1184 match: 29 SD: 0.0922 cents