Scala analysis: edo-25
25 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48.000 cents 48.000000 2: 96.000 cents 96.000000 3: 144.000 cents 144.000000 4: 192.000 cents 192.000000 5: 240.000 cents 240.000000 6: 288.000 cents 288.000000 7: 336.000 cents 336.000000 8: 384.000 cents 384.000000 9: 432.000 cents 432.000000 10: 480.000 cents 480.000000 11: 528.000 cents 528.000000 12: 576.000 cents 576.000000 13: 624.000 cents 624.000000 14: 672.000 cents 672.000000 15: 720.000 cents 720.000000 16: 768.000 cents 768.000000 17: 816.000 cents 816.000000 18: 864.000 cents 864.000000 19: 912.000 cents 912.000000 20: 960.000 cents 960.000000 21: 1008.000 cents 1008.000000 22: 1056.000 cents 1056.000000 23: 1104.000 cents 1104.000000 24: 1152.000 cents 1152.000000 25: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 48.0000 cents 48.0000 1: 48.0000 cents 48.0000 2: 48.0000 cents 48.0000 3: 48.0000 cents 48.0000 4: 48.0000 cents 48.0000 5: 48.0000 cents 48.0000 6: 48.0000 cents 48.0000 7: 48.0000 cents 48.0000 8: 48.0000 cents 48.0000 9: 48.0000 cents 48.0000 10: 48.0000 cents 48.0000 11: 48.0000 cents 48.0000 12: 48.0000 cents 48.0000 13: 48.0000 cents 48.0000 14: 48.0000 cents 48.0000 15: 48.0000 cents 48.0000 16: 48.0000 cents 48.0000 17: 48.0000 cents 48.0000 18: 48.0000 cents 48.0000 19: 48.0000 cents 48.0000 20: 48.0000 cents 48.0000 21: 48.0000 cents 48.0000 22: 48.0000 cents 48.0000 23: 48.0000 cents 48.0000 24: 48.0000 cents 48.0000 25: 48.0000 cents 48.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 25 48.00000 cents 2: 25 96.00000 cents 3: 25 144.00000 cents 4: 25 192.00000 cents 5: 25 240.00000 cents 6: 25 288.00000 cents 7: 25 336.00000 cents 8: 25 384.00000 cents 9: 25 432.00000 cents 10: 25 480.00000 cents 11: 25 528.00000 cents 12: 25 576.00000 cents 13: 25 624.00000 cents 14: 25 672.00000 cents 15: 25 720.00000 cents 16: 25 768.00000 cents 17: 25 816.00000 cents 18: 25 864.00000 cents 19: 25 912.00000 cents 20: 25 960.00000 cents 21: 25 1008.00000 cents 22: 25 1056.00000 cents 23: 25 1104.00000 cents 24: 25 1152.00000 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 25 0.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 48.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 96.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 144.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 192.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 240.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 288.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 336.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 384.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 432.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 480.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 528.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 576.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 624.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 672.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 720.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 768.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 816.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 864.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 912.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 960.0 : 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 1008.0: 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 1056.0: 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 1104.0: 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 1152.0: 48.0 96.0 144.0 192.0 240.0 288.0 336.0 384.0 432.0 480.0 528.0 576.0 624.0 672.0 720.0 768.0 816.0 864.0 912.0 960.0 1008.0 1056.0 1104.0 1152.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.0000 .. 48.0000 cents 1/1, 0.0000 cents 48.00000 cents 2: 96.0000 .. 96.0000 cents 1/1, 0.0000 cents 48.00000 cents 3: 144.0000 .. 144.0000 cents 1/1, 0.0000 cents 48.00000 cents 4: 192.0000 .. 192.0000 cents 1/1, 0.0000 cents 48.00000 cents 5: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 48.00000 cents 6: 288.0000 .. 288.0000 cents 1/1, 0.0000 cents 48.00000 cents 7: 336.0000 .. 336.0000 cents 1/1, 0.0000 cents 48.00000 cents 8: 384.0000 .. 384.0000 cents 1/1, 0.0000 cents 48.00000 cents 9: 432.0000 .. 432.0000 cents 1/1, 0.0000 cents 48.00000 cents 10: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 48.00000 cents 11: 528.0000 .. 528.0000 cents 1/1, 0.0000 cents 48.00000 cents 12: 576.0000 .. 576.0000 cents 1/1, 0.0000 cents 48.00000 cents 13: 624.0000 .. 624.0000 cents 1/1, 0.0000 cents 48.00000 cents 14: 672.0000 .. 672.0000 cents 1/1, 0.0000 cents 48.00000 cents 15: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 48.00000 cents 16: 768.0000 .. 768.0000 cents 1/1, 0.0000 cents 48.00000 cents 17: 816.0000 .. 816.0000 cents 1/1, 0.0000 cents 48.00000 cents 18: 864.0000 .. 864.0000 cents 1/1, 0.0000 cents 48.00000 cents 19: 912.0000 .. 912.0000 cents 1/1, 0.0000 cents 48.00000 cents 20: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 48.00000 cents 21: 1008.0000 .. 1008.0000 cents 1/1, 0.0000 cents 48.00000 cents 22: 1056.0000 .. 1056.0000 cents 1/1, 0.0000 cents 48.00000 cents 23: 1104.0000 .. 1104.0000 cents 1/1, 0.0000 cents 48.00000 cents 24: 1152.0000 .. 1152.0000 cents 1/1, 0.0000 cents 48.00000 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 48.00000 cents, class 1 Average step (divided formal octave): 48.0000 cents Largest one step interval : 48.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 48.00000 cents, amount: 25 Most common interval of one step : 48.00000 cents, amount: 25 Least squares average step : 48.00000 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 48.00000 cents Ratio Whole / Half tone : infinite Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.040000 redundancy: 0.960000 Efficiency x scale size : 1.000000 Number of different interval sizes : 24 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 25, average 720.0000 cents Number of appreciable fifths : 0 Scale contains two identical disjunct "tetrachords" of 11 notes 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
25: 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: 9.0225 cents 3 .. 6 match: 3 H SD: 9.0683 cents 4 .. 8 match: 4 H SD: 5.0551 cents 5 .. 10 match: 5 H SD: 4.7088 cents 6 .. 12 match: 6 H SD: 6.5748 cents 7 .. 14 match: 7 H SD: 4.5911 cents 8 .. 16 match: 8 H SD: 5.4384 cents 9 .. 18 match: 9 H SD: 3.9778 cents 10 .. 20 match: 10 H SD: 4.3710 cents 11 .. 22 match: 11 H SD: 4.1527 cents 12 .. 24 match: 12 H SD: 4.5840 cents 13 .. 26 match: 13 H SD: 4.2261 cents 14 .. 28 match: 14 H SD: 3.3279 cents 15 .. 30 match: 15 H SD: 4.1136 cents 16 .. 32 match: 16 H SD: 3.2715 cents 17 .. 34 match: 17 H SD: 2.9946 cents 18 .. 36 match: 18 H SD: 2.8680 cents 19 .. 38 match: 19 H SD: 2.6778 cents 20 .. 40 match: 20 H SD: 2.6300 cents 21 .. 42 match: 21 H SD: 3.1049 cents 22 .. 44 match: 21 S SD: 3.1686 cents 23 .. 46 match: 22 S SD: 2.4018 cents 24 .. 48 match: 22 SD: 3.2879 cents 25 .. 50 match: 23 SD: 2.2012 cents 26 .. 52 match: 23 SD: 2.9065 cents 27 .. 54 match: 24 SD: 2.5066 cents 28 .. 56 match: 24 SD: 2.1435 cents 29 .. 58 match: 24 SD: 2.5997 cents 30 .. 60 match: 24 SD: 2.8716 cents 31 .. 62 match: 25 SD: 2.3714 cents 32 .. 64 match: 25 SD: 1.8708 cents 33 .. 66 match: 25 SD: 1.7576 cents 42 .. 84 match: 25 SD: 1.7282 cents 43 .. 86 match: 25 SD: 1.5342 cents 46 .. 92 match: 25 SD: 1.5064 cents 48 .. 96 match: 25 SD: 1.3520 cents 53 .. 106 match: 25 SD: 1.2709 cents 56 .. 112 match: 25 SD: 1.1235 cents 65 .. 130 match: 25 SD: 1.0705 cents 66 .. 132 match: 25 SD: 0.9426 cents 68 .. 136 match: 25 SD: 0.8337 cents 76 .. 152 match: 25 SD: 0.8331 cents 81 .. 162 match: 25 SD: 0.8086 cents 85 .. 170 match: 25 SD: 0.8011 cents 88 .. 176 match: 25 SD: 0.7295 cents 93 .. 186 match: 25 SD: 0.6313 cents 101 .. 202 match: 25 SD: 0.5601 cents 120 .. 240 match: 25 SD: 0.5128 cents 134 .. 268 match: 25 SD: 0.4956 cents 137 .. 274 match: 25 SD: 0.4813 cents 138 .. 276 match: 25 SD: 0.4568 cents 140 .. 280 match: 25 SD: 0.4460 cents 154 .. 308 match: 25 SD: 0.4012 cents 169 .. 338 match: 25 SD: 0.3867 cents 170 .. 340 match: 25 SD: 0.3817 cents 173 .. 346 match: 25 SD: 0.3239 cents 182 .. 364 match: 25 SD: 0.3213 cents 205 .. 410 match: 25 SD: 0.3105 cents 210 .. 420 match: 25 SD: 0.3051 cents 213 .. 426 match: 25 SD: 0.3012 cents 215 .. 430 match: 25 SD: 0.2655 cents 238 .. 476 match: 25 SD: 0.2651 cents 242 .. 484 match: 25 SD: 0.2591 cents 244 .. 488 match: 25 SD: 0.2287 cents 276 .. 552 match: 25 SD: 0.2274 cents 281 .. 562 match: 25 SD: 0.1789 cents 314 .. 628 match: 25 SD: 0.1517 cents 382 .. 764 match: 25 SD: 0.1215 cents 491 .. 982 match: 25 SD: 0.1133 cents 519 .. 1038 match: 25 SD: 0.1122 cents 532 .. 1064 match: 25 SD: 0.1079 cents 564 .. 1128 match: 25 SD: 0.0876 cents