Scala analysis: edo-30
30 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.000 cents 40.000000 2: 80.000 cents 80.000000 3: 120.000 cents 120.000000 4: 160.000 cents 160.000000 5: 200.000 cents 200.000000 6: 240.000 cents 240.000000 7: 280.000 cents 280.000000 8: 320.000 cents 320.000000 9: 360.000 cents 360.000000 10: 400.000 cents 400.000000 11: 440.000 cents 440.000000 12: 480.000 cents 480.000000 13: 520.000 cents 520.000000 14: 560.000 cents 560.000000 15: 600.000 cents 600.000000 16: 640.000 cents 640.000000 17: 680.000 cents 680.000000 18: 720.000 cents 720.000000 19: 760.000 cents 760.000000 20: 800.000 cents 800.000000 21: 840.000 cents 840.000000 22: 880.000 cents 880.000000 23: 920.000 cents 920.000000 24: 960.000 cents 960.000000 25: 1000.000 cents 1000.000000 26: 1040.000 cents 1040.000000 27: 1080.000 cents 1080.000000 28: 1120.000 cents 1120.000000 29: 1160.000 cents 1160.000000 30: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 40.0000 cents 40.0000 1: 40.0000 cents 40.0000 2: 40.0000 cents 40.0000 3: 40.0000 cents 40.0000 4: 40.0000 cents 40.0000 5: 40.0000 cents 40.0000 6: 40.0000 cents 40.0000 7: 40.0000 cents 40.0000 8: 40.0000 cents 40.0000 9: 40.0000 cents 40.0000 10: 40.0000 cents 40.0000 11: 40.0000 cents 40.0000 12: 40.0000 cents 40.0000 13: 40.0000 cents 40.0000 14: 40.0000 cents 40.0000 15: 40.0000 cents 40.0000 16: 40.0000 cents 40.0000 17: 40.0000 cents 40.0000 18: 40.0000 cents 40.0000 19: 40.0000 cents 40.0000 20: 40.0000 cents 40.0000 21: 40.0000 cents 40.0000 22: 40.0000 cents 40.0000 23: 40.0000 cents 40.0000 24: 40.0000 cents 40.0000 25: 40.0000 cents 40.0000 26: 40.0000 cents 40.0000 27: 40.0000 cents 40.0000 28: 40.0000 cents 40.0000 29: 40.0000 cents 40.0000 30: 40.0000 cents 40.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 30 40.00000 cents 2: 30 80.00000 cents 3: 30 120.00000 cents 4: 30 160.00000 cents 5: 30 200.00000 cents 6: 30 240.00000 cents 7: 30 280.00000 cents 8: 30 320.00000 cents 9: 30 360.00000 cents 10: 30 400.00000 cents 11: 30 440.00000 cents 12: 30 480.00000 cents 13: 30 520.00000 cents 14: 30 560.00000 cents 15: 30 600.00000 cents 16: 30 640.00000 cents 17: 30 680.00000 cents 18: 30 720.00000 cents 19: 30 760.00000 cents 20: 30 800.00000 cents 21: 30 840.00000 cents 22: 30 880.00000 cents 23: 30 920.00000 cents 24: 30 960.00000 cents 25: 30 1000.00000 cents 26: 30 1040.00000 cents 27: 30 1080.00000 cents 28: 30 1120.00000 cents 29: 30 1160.00000 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 26 27 28 29 30 0.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 40.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 80.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 120.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 160.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 200.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 240.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 280.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 320.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 360.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 400.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 440.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 480.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 520.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 560.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 600.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 640.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 680.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 720.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 760.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 800.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 840.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 880.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 920.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 960.0 : 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 1000.0: 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 1040.0: 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 1080.0: 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 1120.0: 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 1160.0: 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 400.0 440.0 480.0 520.0 560.0 600.0 640.0 680.0 720.0 760.0 800.0 840.0 880.0 920.0 960.0 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.0000 .. 40.0000 cents 1/1, 0.0000 cents 40.00000 cents 2: 80.0000 .. 80.0000 cents 1/1, 0.0000 cents 40.00000 cents 3: 120.0000 .. 120.0000 cents 1/1, 0.0000 cents 40.00000 cents 4: 160.0000 .. 160.0000 cents 1/1, 0.0000 cents 40.00000 cents 5: 200.0000 .. 200.0000 cents 1/1, 0.0000 cents 40.00000 cents 6: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 40.00000 cents 7: 280.0000 .. 280.0000 cents 1/1, 0.0000 cents 40.00000 cents 8: 320.0000 .. 320.0000 cents 1/1, 0.0000 cents 40.00000 cents 9: 360.0000 .. 360.0000 cents 1/1, 0.0000 cents 40.00000 cents 10: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 40.00000 cents 11: 440.0000 .. 440.0000 cents 1/1, 0.0000 cents 40.00000 cents 12: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 40.00000 cents 13: 520.0000 .. 520.0000 cents 1/1, 0.0000 cents 40.00000 cents 14: 560.0000 .. 560.0000 cents 1/1, 0.0000 cents 40.00000 cents 15: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 40.00000 cents 16: 640.0000 .. 640.0000 cents 1/1, 0.0000 cents 40.00000 cents 17: 680.0000 .. 680.0000 cents 1/1, 0.0000 cents 40.00000 cents 18: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 40.00000 cents 19: 760.0000 .. 760.0000 cents 1/1, 0.0000 cents 40.00000 cents 20: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 40.00000 cents 21: 840.0000 .. 840.0000 cents 1/1, 0.0000 cents 40.00000 cents 22: 880.0000 .. 880.0000 cents 1/1, 0.0000 cents 40.00000 cents 23: 920.0000 .. 920.0000 cents 1/1, 0.0000 cents 40.00000 cents 24: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 40.00000 cents 25: 1000.0000 .. 1000.0000 cents 1/1, 0.0000 cents 40.00000 cents 26: 1040.0000 .. 1040.0000 cents 1/1, 0.0000 cents 40.00000 cents 27: 1080.0000 .. 1080.0000 cents 1/1, 0.0000 cents 40.00000 cents 28: 1120.0000 .. 1120.0000 cents 1/1, 0.0000 cents 40.00000 cents 29: 1160.0000 .. 1160.0000 cents 1/1, 0.0000 cents 40.00000 cents
SHOW DATA
Number of notes : 30 -- Interval properties -- Smallest interval : 40.00000 cents, class 1 Average step (divided formal octave): 40.0000 cents Largest one step interval : 40.00000 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 40.00000 cents, amount: 30 Most common interval of one step : 40.00000 cents, amount: 30 Least squares average step : 40.00000 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 40.00000 cents Ratio Whole / Half tone : infinite Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.033333 redundancy: 0.966667 Efficiency x scale size : 1.000000 Number of different interval sizes : 29 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 30, average 720.0000 cents Number of appreciable fifths : 0 Scale contains two identical disjunct "tetrachords" of 13 notes Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
30: 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 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: 6.1880 cents 4 .. 8 match: 4 H SD: 6.0768 cents 5 .. 10 match: 5 H SD: 5.7333 cents 6 .. 12 match: 6 H SD: 5.0834 cents 7 .. 14 match: 7 H SD: 4.4162 cents 8 .. 16 match: 8 H SD: 3.4236 cents 9 .. 18 match: 9 H SD: 3.8857 cents 10 .. 20 match: 10 H SD: 3.8128 cents 11 .. 22 match: 11 H SD: 3.2227 cents 12 .. 24 match: 12 H SD: 3.3428 cents 13 .. 26 match: 13 H SD: 3.1668 cents 14 .. 28 match: 14 H SD: 3.4258 cents 15 .. 30 match: 15 H SD: 3.4611 cents 16 .. 32 match: 16 H SD: 2.9298 cents 17 .. 34 match: 17 H SD: 2.5157 cents 18 .. 36 match: 18 H SD: 3.0188 cents 19 .. 38 match: 19 H SD: 2.4902 cents 20 .. 40 match: 20 H SD: 2.3260 cents 21 .. 42 match: 21 H SD: 2.3626 cents 22 .. 44 match: 22 H SD: 2.2772 cents 23 .. 46 match: 23 H SD: 2.1150 cents 24 .. 48 match: 24 H SD: 2.0259 cents 25 .. 50 match: 25 H SD: 2.5103 cents 26 .. 52 match: 25 SD: 2.3451 cents 27 .. 54 match: 26 S SD: 1.8565 cents 28 .. 56 match: 26 SD: 2.5435 cents 29 .. 58 match: 27 SD: 1.8316 cents 30 .. 60 match: 27 SD: 2.3976 cents 31 .. 62 match: 28 SD: 1.6866 cents 32 .. 64 match: 28 SD: 2.0684 cents 33 .. 66 match: 29 SD: 2.1162 cents 34 .. 68 match: 29 SD: 1.6050 cents 35 .. 70 match: 29 SD: 1.7583 cents 36 .. 72 match: 29 SD: 2.0620 cents 37 .. 74 match: 29 SD: 2.0881 cents 38 .. 76 match: 30 SD: 1.6233 cents 39 .. 78 match: 30 SD: 1.4549 cents 40 .. 80 match: 30 SD: 1.3735 cents 41 .. 82 match: 30 SD: 1.3467 cents 46 .. 92 match: 30 SD: 1.3387 cents 50 .. 100 match: 30 SD: 1.3315 cents 51 .. 102 match: 30 SD: 1.2172 cents 56 .. 112 match: 30 SD: 1.1175 cents 58 .. 116 match: 30 SD: 1.0362 cents 60 .. 120 match: 30 SD: 1.0293 cents 65 .. 130 match: 30 SD: 0.9468 cents 68 .. 136 match: 30 SD: 0.9075 cents 69 .. 138 match: 30 SD: 0.8447 cents 73 .. 146 match: 30 SD: 0.7800 cents 80 .. 160 match: 30 SD: 0.7258 cents 81 .. 162 match: 30 SD: 0.7242 cents 82 .. 164 match: 30 SD: 0.6973 cents 83 .. 166 match: 30 SD: 0.6834 cents 85 .. 170 match: 30 SD: 0.6627 cents 89 .. 178 match: 30 SD: 0.6612 cents 97 .. 194 match: 30 SD: 0.6287 cents 100 .. 200 match: 30 SD: 0.5989 cents 107 .. 214 match: 30 SD: 0.5687 cents 112 .. 224 match: 30 SD: 0.5295 cents 113 .. 226 match: 30 SD: 0.5262 cents 114 .. 228 match: 30 SD: 0.5028 cents 123 .. 246 match: 30 SD: 0.4582 cents 125 .. 250 match: 30 SD: 0.4523 cents 128 .. 256 match: 30 SD: 0.4414 cents 142 .. 284 match: 30 SD: 0.4196 cents 143 .. 286 match: 30 SD: 0.4066 cents 147 .. 294 match: 30 SD: 0.4018 cents 154 .. 308 match: 30 SD: 0.3544 cents 165 .. 330 match: 30 SD: 0.3282 cents 181 .. 362 match: 30 SD: 0.3224 cents 194 .. 388 match: 30 SD: 0.2931 cents 207 .. 414 match: 30 SD: 0.2851 cents 208 .. 416 match: 30 SD: 0.2785 cents 210 .. 420 match: 30 SD: 0.2733 cents 228 .. 456 match: 30 SD: 0.2510 cents 248 .. 496 match: 30 SD: 0.2495 cents 250 .. 500 match: 30 SD: 0.2461 cents 251 .. 502 match: 30 SD: 0.2179 cents 269 .. 538 match: 30 SD: 0.2153 cents 277 .. 554 match: 30 SD: 0.2099 cents 290 .. 580 match: 30 SD: 0.2070 cents 291 .. 582 match: 30 SD: 0.1878 cents 301 .. 602 match: 30 SD: 0.1838 cents 311 .. 622 match: 30 SD: 0.1836 cents 320 .. 640 match: 30 SD: 0.1784 cents 335 .. 670 match: 30 SD: 0.1464 cents 376 .. 752 match: 30 SD: 0.1356 cents 403 .. 806 match: 30 SD: 0.1323 cents 432 .. 864 match: 30 SD: 0.1082 cents 463 .. 926 match: 30 SD: 0.0940 cents 545 .. 1090 match: 30 SD: 0.0935 cents 557 .. 1114 match: 30 SD: 0.0889 cents 597 .. 1194 match: 30 SD: 0.0817 cents