Scala analysis: edo-28
28 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 42.857 cents 42.857143 2: 85.714 cents 85.714286 3: 128.571 cents 128.571429 4: 171.429 cents 171.428571 5: 214.286 cents 214.285714 6: 257.143 cents 257.142857 7: 300.000 cents 300.000000 8: 342.857 cents 342.857143 9: 385.714 cents 385.714286 10: 428.571 cents 428.571429 11: 471.429 cents 471.428571 12: 514.286 cents 514.285714 13: 557.143 cents 557.142857 14: 600.000 cents 600.000000 15: 642.857 cents 642.857143 16: 685.714 cents 685.714286 17: 728.571 cents 728.571429 18: 771.429 cents 771.428571 19: 814.286 cents 814.285714 20: 857.143 cents 857.142857 21: 900.000 cents 900.000000 22: 942.857 cents 942.857143 23: 985.714 cents 985.714286 24: 1028.571 cents 1028.571429 25: 1071.429 cents 1071.428571 26: 1114.286 cents 1114.285714 27: 1157.143 cents 1157.142857 28: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 42.8571 cents 42.8571 1: 42.8571 cents 42.8571 2: 42.8571 cents 42.8571 3: 42.8571 cents 42.8571 4: 42.8571 cents 42.8571 5: 42.8571 cents 42.8571 6: 42.8571 cents 42.8571 7: 42.8571 cents 42.8571 8: 42.8571 cents 42.8571 9: 42.8571 cents 42.8571 10: 42.8571 cents 42.8571 11: 42.8571 cents 42.8571 12: 42.8571 cents 42.8571 13: 42.8571 cents 42.8571 14: 42.8571 cents 42.8571 15: 42.8571 cents 42.8571 16: 42.8571 cents 42.8571 17: 42.8571 cents 42.8571 18: 42.8571 cents 42.8571 19: 42.8571 cents 42.8571 20: 42.8571 cents 42.8571 21: 42.8571 cents 42.8571 22: 42.8571 cents 42.8571 23: 42.8571 cents 42.8571 24: 42.8571 cents 42.8571 25: 42.8571 cents 42.8571 26: 42.8571 cents 42.8571 27: 42.8571 cents 42.8571 28: 42.8571 cents 42.8571
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 28 42.85714 cents 2: 28 85.71429 cents 3: 28 128.57143 cents 4: 28 171.42857 cents 5: 28 214.28571 cents 6: 28 257.14286 cents 7: 28 300.00000 cents 8: 28 342.85714 cents 9: 28 385.71429 cents 10: 28 428.57143 cents 11: 28 471.42857 cents 12: 28 514.28571 cents 13: 28 557.14286 cents 14: 28 600.00000 cents 15: 28 642.85714 cents 16: 28 685.71429 cents 17: 28 728.57143 cents 18: 28 771.42857 cents 19: 28 814.28571 cents 20: 28 857.14286 cents 21: 28 900.00000 cents 22: 28 942.85714 cents 23: 28 985.71429 cents 24: 28 1028.57143 cents 25: 28 1071.42857 cents 26: 28 1114.28571 cents 27: 28 1157.14286 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 0.0 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 42.9 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 85.7 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 128.6 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 171.4 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 214.3 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 257.1 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 300.0 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 342.9 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 385.7 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 428.6 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 471.4 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 514.3 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 557.1 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 600.0 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 642.9 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 685.7 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 728.6 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 771.4 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 814.3 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 857.1 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 900.0 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 942.9 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 985.7 : 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 1028.6: 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 1071.4: 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 1114.3: 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 1157.1: 42.9 85.7 128.6 171.4 214.3 257.1 300.0 342.9 385.7 428.6 471.4 514.3 557.1 600.0 642.9 685.7 728.6 771.4 814.3 857.1 900.0 942.9 985.7 1028.6 1071.4 1114.3 1157.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.8571 .. 42.8571 cents 1/1, 0.0000 cents 42.85714 cents 2: 85.7143 .. 85.7143 cents 1/1, 0.0000 cents 42.85714 cents 3: 128.5714 .. 128.5714 cents 1/1, 0.0000 cents 42.85714 cents 4: 171.4286 .. 171.4286 cents 1/1, 0.0000 cents 42.85714 cents 5: 214.2857 .. 214.2857 cents 1/1, 0.0000 cents 42.85714 cents 6: 257.1429 .. 257.1429 cents 1/1, 0.0000 cents 42.85714 cents 7: 300.0000 .. 300.0000 cents 1/1, 0.0000 cents 42.85714 cents 8: 342.8571 .. 342.8571 cents 1/1, 0.0000 cents 42.85714 cents 9: 385.7143 .. 385.7143 cents 1/1, 0.0000 cents 42.85714 cents 10: 428.5714 .. 428.5714 cents 1/1, 0.0000 cents 42.85714 cents 11: 471.4286 .. 471.4286 cents 1/1, 0.0000 cents 42.85714 cents 12: 514.2857 .. 514.2857 cents 1/1, 0.0000 cents 42.85714 cents 13: 557.1429 .. 557.1429 cents 1/1, 0.0000 cents 42.85714 cents 14: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 42.85714 cents 15: 642.8571 .. 642.8571 cents 1/1, 0.0000 cents 42.85714 cents 16: 685.7143 .. 685.7143 cents 1/1, 0.0000 cents 42.85714 cents 17: 728.5714 .. 728.5714 cents 1/1, 0.0000 cents 42.85714 cents 18: 771.4286 .. 771.4286 cents 1/1, 0.0000 cents 42.85714 cents 19: 814.2857 .. 814.2857 cents 1/1, 0.0000 cents 42.85714 cents 20: 857.1429 .. 857.1429 cents 1/1, 0.0000 cents 42.85714 cents 21: 900.0000 .. 900.0000 cents 1/1, 0.0000 cents 42.85714 cents 22: 942.8571 .. 942.8571 cents 1/1, 0.0000 cents 42.85714 cents 23: 985.7143 .. 985.7143 cents 1/1, 0.0000 cents 42.85714 cents 24: 1028.5714 .. 1028.5714 cents 1/1, 0.0000 cents 42.85714 cents 25: 1071.4286 .. 1071.4286 cents 1/1, 0.0000 cents 42.85714 cents 26: 1114.2857 .. 1114.2857 cents 1/1, 0.0000 cents 42.85714 cents 27: 1157.1429 .. 1157.1429 cents 1/1, 0.0000 cents 42.85714 cents
SHOW DATA
Number of notes : 28 -- Interval properties -- Smallest interval : 42.85714 cents, class 1 Average step (divided formal octave): 42.8571 cents Largest one step interval : 42.85714 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 42.85714 cents, amount: 28 Most common interval of one step : 42.85714 cents, amount: 28 Least squares average step : 42.85714 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 42.85714 cents Ratio Whole / Half tone : 1.000000 ( 1 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.035714 redundancy: 0.964286 Efficiency x scale size : 1.000000 Number of different interval sizes : 27 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 28, average 685.7143 cents Number of appreciable fifths : 0 Scale contains two identical disjunct "tetrachords" of 13 notes Best major thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
28: 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: 8.1204 cents 3 .. 6 match: 3 H SD: 7.5160 cents 4 .. 8 match: 4 H SD: 5.8595 cents 5 .. 10 match: 5 H SD: 5.1818 cents 6 .. 12 match: 6 H SD: 6.0072 cents 7 .. 14 match: 7 H SD: 4.1664 cents 8 .. 16 match: 8 H SD: 4.4204 cents 9 .. 18 match: 9 H SD: 3.5379 cents 10 .. 20 match: 10 H SD: 4.0370 cents 11 .. 22 match: 11 H SD: 3.5550 cents 12 .. 24 match: 12 H SD: 3.8991 cents 13 .. 26 match: 13 H SD: 3.2099 cents 14 .. 28 match: 14 H SD: 3.3403 cents 15 .. 30 match: 15 H SD: 3.5299 cents 16 .. 32 match: 16 H SD: 2.8115 cents 17 .. 34 match: 17 H SD: 3.3738 cents 18 .. 36 match: 18 H SD: 2.5975 cents 19 .. 38 match: 19 H SD: 2.5636 cents 20 .. 40 match: 20 H SD: 2.4874 cents 21 .. 42 match: 21 H SD: 2.3334 cents 22 .. 44 match: 22 H SD: 2.1942 cents 23 .. 46 match: 23 H SD: 2.4409 cents 24 .. 48 match: 23 SD: 2.8569 cents 25 .. 50 match: 24 S SD: 2.1778 cents 26 .. 52 match: 25 SD: 2.4414 cents 27 .. 54 match: 25 SD: 2.2993 cents 28 .. 56 match: 26 SD: 2.3089 cents 29 .. 58 match: 26 SD: 1.9557 cents 30 .. 60 match: 26 SD: 2.5478 cents 31 .. 62 match: 27 SD: 1.9285 cents 32 .. 64 match: 27 SD: 1.8398 cents 33 .. 66 match: 27 SD: 2.2057 cents 34 .. 68 match: 27 SD: 2.3938 cents 35 .. 70 match: 28 SD: 1.9681 cents 36 .. 72 match: 28 SD: 1.6458 cents 37 .. 74 match: 28 SD: 1.4418 cents 47 .. 94 match: 28 SD: 1.3961 cents 50 .. 100 match: 28 SD: 1.3803 cents 51 .. 102 match: 28 SD: 1.2900 cents 53 .. 106 match: 28 SD: 1.2622 cents 55 .. 110 match: 28 SD: 1.1455 cents 60 .. 120 match: 28 SD: 1.0756 cents 63 .. 126 match: 28 SD: 0.9822 cents 64 .. 128 match: 28 SD: 0.9653 cents 68 .. 136 match: 28 SD: 0.9106 cents 75 .. 150 match: 28 SD: 0.7912 cents 76 .. 152 match: 28 SD: 0.7437 cents 89 .. 178 match: 28 SD: 0.7433 cents 92 .. 184 match: 28 SD: 0.6863 cents 95 .. 190 match: 28 SD: 0.6545 cents 100 .. 200 match: 28 SD: 0.6218 cents 105 .. 210 match: 28 SD: 0.5505 cents 113 .. 226 match: 28 SD: 0.5070 cents 116 .. 232 match: 28 SD: 0.4787 cents 132 .. 264 match: 28 SD: 0.4498 cents 142 .. 284 match: 28 SD: 0.4093 cents 153 .. 306 match: 28 SD: 0.3754 cents 160 .. 320 match: 28 SD: 0.3453 cents 181 .. 362 match: 28 SD: 0.3394 cents 182 .. 364 match: 28 SD: 0.3379 cents 189 .. 378 match: 28 SD: 0.3376 cents 191 .. 382 match: 28 SD: 0.3329 cents 192 .. 384 match: 28 SD: 0.3215 cents 195 .. 390 match: 28 SD: 0.2890 cents 200 .. 400 match: 28 SD: 0.2827 cents 205 .. 410 match: 28 SD: 0.2793 cents 220 .. 440 match: 28 SD: 0.2706 cents 232 .. 464 match: 28 SD: 0.2436 cents 237 .. 474 match: 28 SD: 0.2260 cents 271 .. 542 match: 28 SD: 0.2140 cents 275 .. 550 match: 28 SD: 0.2140 cents 280 .. 560 match: 28 SD: 0.1979 cents 311 .. 622 match: 28 SD: 0.1939 cents 313 .. 626 match: 28 SD: 0.1865 cents 329 .. 658 match: 28 SD: 0.1828 cents 333 .. 666 match: 28 SD: 0.1804 cents 348 .. 696 match: 28 SD: 0.1604 cents 356 .. 712 match: 28 SD: 0.1494 cents 374 .. 748 match: 28 SD: 0.1489 cents 392 .. 784 match: 28 SD: 0.1452 cents 393 .. 786 match: 28 SD: 0.1358 cents 413 .. 826 match: 28 SD: 0.1311 cents 434 .. 868 match: 28 SD: 0.1236 cents 456 .. 912 match: 28 SD: 0.1222 cents 469 .. 938 match: 28 SD: 0.1220 cents 488 .. 976 match: 28 SD: 0.1193 cents 492 .. 984 match: 28 SD: 0.1177 cents 508 .. 1016 match: 28 SD: 0.1132 cents 518 .. 1036 match: 28 SD: 0.1098 cents 529 .. 1058 match: 28 SD: 0.0964 cents 556 .. 1112 match: 28 SD: 0.0894 cents 593 .. 1186 match: 28 SD: 0.0889 cents 598 .. 1196 match: 28 SD: 0.0824 cents