Scala analysis: edo-31
31 equal divisions of the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.710 cents 38.709677 2: 77.419 cents 77.419355 3: 116.129 cents 116.129032 4: 154.839 cents 154.838710 5: 193.548 cents 193.548387 6: 232.258 cents 232.258065 7: 270.968 cents 270.967742 8: 309.677 cents 309.677419 9: 348.387 cents 348.387097 10: 387.097 cents 387.096774 11: 425.806 cents 425.806452 12: 464.516 cents 464.516129 13: 503.226 cents 503.225806 14: 541.935 cents 541.935484 15: 580.645 cents 580.645161 16: 619.355 cents 619.354839 17: 658.065 cents 658.064516 18: 696.774 cents 696.774194 19: 735.484 cents 735.483871 20: 774.194 cents 774.193548 21: 812.903 cents 812.903226 22: 851.613 cents 851.612903 23: 890.323 cents 890.322581 24: 929.032 cents 929.032258 25: 967.742 cents 967.741935 26: 1006.452 cents 1006.451613 27: 1045.161 cents 1045.161290 28: 1083.871 cents 1083.870968 29: 1122.581 cents 1122.580645 30: 1161.290 cents 1161.290323 31: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 38.7097 cents 38.7097 1: 38.7097 cents 38.7097 2: 38.7097 cents 38.7097 3: 38.7097 cents 38.7097 4: 38.7097 cents 38.7097 5: 38.7097 cents 38.7097 6: 38.7097 cents 38.7097 7: 38.7097 cents 38.7097 8: 38.7097 cents 38.7097 9: 38.7097 cents 38.7097 10: 38.7097 cents 38.7097 11: 38.7097 cents 38.7097 12: 38.7097 cents 38.7097 13: 38.7097 cents 38.7097 14: 38.7097 cents 38.7097 15: 38.7097 cents 38.7097 16: 38.7097 cents 38.7097 17: 38.7097 cents 38.7097 18: 38.7097 cents 38.7097 19: 38.7097 cents 38.7097 20: 38.7097 cents 38.7097 21: 38.7097 cents 38.7097 22: 38.7097 cents 38.7097 23: 38.7097 cents 38.7097 24: 38.7097 cents 38.7097 25: 38.7097 cents 38.7097 26: 38.7097 cents 38.7097 27: 38.7097 cents 38.7097 28: 38.7097 cents 38.7097 29: 38.7097 cents 38.7097 30: 38.7097 cents 38.7097 31: 38.7097 cents 38.7097
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 31 38.70968 cents 2: 31 77.41936 cents 3: 31 116.12903 cents 4: 31 154.83871 cents 5: 31 193.54839 cents 6: 31 232.25807 cents 7: 31 270.96774 cents 8: 31 309.67742 cents 9: 31 348.38710 cents 10: 31 387.09677 cents 11: 31 425.80645 cents 12: 31 464.51613 cents 13: 31 503.22581 cents 14: 31 541.93548 cents 15: 31 580.64516 cents 16: 31 619.35484 cents 17: 31 658.06452 cents 18: 31 696.77419 cents 19: 31 735.48387 cents 20: 31 774.19355 cents 21: 31 812.90323 cents 22: 31 851.61290 cents 23: 31 890.32258 cents 24: 31 929.03226 cents 25: 31 967.74194 cents 26: 31 1006.45161 cents 27: 31 1045.16129 cents 28: 31 1083.87097 cents 29: 31 1122.58065 cents 30: 31 1161.29032 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 31 0.0 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 38.7 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 77.4 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 116.1 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 154.8 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 193.5 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 232.3 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 271.0 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 309.7 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 348.4 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 387.1 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 425.8 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 464.5 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 503.2 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 541.9 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 580.6 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 619.4 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 658.1 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 696.8 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 735.5 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 774.2 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 812.9 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 851.6 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 890.3 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 929.0 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 967.7 : 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 1006.5: 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 1045.2: 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 1083.9: 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 1122.6: 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 1161.3: 38.7 77.4 116.1 154.8 193.5 232.3 271.0 309.7 348.4 387.1 425.8 464.5 503.2 541.9 580.6 619.4 658.1 696.8 735.5 774.2 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 38.7097 cents 1/1, 0.0000 cents 38.70968 cents 2: 77.4194 .. 77.4194 cents 1/1, 0.0000 cents 38.70968 cents 3: 116.1290 .. 116.1290 cents 1/1, 0.0000 cents 38.70968 cents 4: 154.8387 .. 154.8387 cents 1/1, 0.0000 cents 38.70968 cents 5: 193.5484 .. 193.5484 cents 1/1, 0.0000 cents 38.70968 cents 6: 232.2581 .. 232.2581 cents 1/1, 0.0000 cents 38.70968 cents 7: 270.9677 .. 270.9677 cents 1/1, 0.0000 cents 38.70968 cents 8: 309.6774 .. 309.6774 cents 1/1, 0.0000 cents 38.70968 cents 9: 348.3871 .. 348.3871 cents 1/1, 0.0000 cents 38.70968 cents 10: 387.0968 .. 387.0968 cents 1/1, 0.0000 cents 38.70968 cents 11: 425.8065 .. 425.8065 cents 1/1, 0.0000 cents 38.70968 cents 12: 464.5161 .. 464.5161 cents 1/1, 0.0000 cents 38.70968 cents 13: 503.2258 .. 503.2258 cents 1/1, 0.0000 cents 38.70968 cents 14: 541.9355 .. 541.9355 cents 1/1, 0.0000 cents 38.70968 cents 15: 580.6452 .. 580.6452 cents 1/1, 0.0000 cents 38.70968 cents 16: 619.3548 .. 619.3548 cents 1/1, 0.0000 cents 38.70968 cents 17: 658.0645 .. 658.0645 cents 1/1, 0.0000 cents 38.70968 cents 18: 696.7742 .. 696.7742 cents 1/1, 0.0000 cents 38.70968 cents 19: 735.4839 .. 735.4839 cents 1/1, 0.0000 cents 38.70968 cents 20: 774.1935 .. 774.1935 cents 1/1, 0.0000 cents 38.70968 cents 21: 812.9032 .. 812.9032 cents 1/1, 0.0000 cents 38.70968 cents 22: 851.6129 .. 851.6129 cents 1/1, 0.0000 cents 38.70968 cents 23: 890.3226 .. 890.3226 cents 1/1, 0.0000 cents 38.70968 cents 24: 929.0323 .. 929.0323 cents 1/1, 0.0000 cents 38.70968 cents 25: 967.7419 .. 967.7419 cents 1/1, 0.0000 cents 38.70968 cents 26: 1006.4516 .. 1006.4516 cents 1/1, 0.0000 cents 38.70968 cents 27: 1045.1613 .. 1045.1613 cents 1/1, 0.0000 cents 38.70968 cents 28: 1083.8710 .. 1083.8710 cents 1/1, 0.0000 cents 38.70968 cents 29: 1122.5806 .. 1122.5806 cents 1/1, 0.0000 cents 38.70968 cents 30: 1161.2903 .. 1161.2903 cents 1/1, 0.0000 cents 38.70968 cents
SHOW DATA
Number of notes : 31 -- Interval properties -- Smallest interval : 38.70968 cents, class 1 Average step (divided formal octave): 38.7097 cents Largest one step interval : 38.70968 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 38.70968 cents, amount: 31 Most common interval of one step : 38.70968 cents, amount: 31 Least squares average step : 38.70968 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 38.70968 cents Ratio Whole / Half tone : 1.666667 ( 5/3 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.032258 redundancy: 0.967742 Efficiency x scale size : 1.000000 Number of different interval sizes : 30 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 31, average 696.7742 cents Scale contains two identical disjunct "tetrachords" of 14 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
31: 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 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: 2.5904 cents 3 .. 6 match: 3 H SD: 2.6333 cents 4 .. 8 match: 4 H SD: 1.3377 cents 5 .. 10 match: 5 H SD: 2.5602 cents 6 .. 12 match: 6 H SD: 1.8536 cents 7 .. 14 match: 7 H SD: 2.5733 cents 8 .. 16 match: 8 H SD: 2.3922 cents 9 .. 18 match: 9 H SD: 3.4676 cents 10 .. 20 match: 10 H SD: 2.5252 cents 11 .. 22 match: 11 H SD: 3.2401 cents 12 .. 24 match: 12 H SD: 2.5986 cents 13 .. 26 match: 13 H SD: 3.6527 cents 14 .. 28 match: 14 H SD: 2.2195 cents 15 .. 30 match: 15 H SD: 2.5026 cents 16 .. 32 match: 16 H SD: 2.4278 cents 17 .. 34 match: 17 H SD: 3.0103 cents 18 .. 36 match: 18 H SD: 2.3908 cents 19 .. 38 match: 19 H SD: 2.8115 cents 20 .. 40 match: 20 H SD: 2.3049 cents 21 .. 42 match: 21 H SD: 2.2429 cents 22 .. 44 match: 22 H SD: 2.1628 cents 23 .. 46 match: 23 H SD: 2.0792 cents 24 .. 48 match: 24 H SD: 1.9595 cents 25 .. 50 match: 25 H SD: 1.9892 cents 26 .. 52 match: 25 SD: 2.5133 cents 27 .. 54 match: 26 S SD: 2.1136 cents 28 .. 56 match: 27 S SD: 1.8054 cents 29 .. 58 match: 27 SD: 2.3687 cents 30 .. 60 match: 28 SD: 1.6871 cents 31 .. 62 match: 28 SD: 2.2244 cents 32 .. 64 match: 29 SD: 1.6761 cents 33 .. 66 match: 29 SD: 1.8364 cents 34 .. 68 match: 29 SD: 2.1743 cents 35 .. 70 match: 30 SD: 1.5823 cents 36 .. 72 match: 30 SD: 1.5757 cents 37 .. 74 match: 30 SD: 1.8780 cents 38 .. 76 match: 30 SD: 2.0461 cents 39 .. 78 match: 31 SD: 1.6586 cents 40 .. 80 match: 31 SD: 1.4624 cents 41 .. 82 match: 31 SD: 1.2754 cents 51 .. 102 match: 31 SD: 1.2643 cents 52 .. 104 match: 31 SD: 1.2326 cents 53 .. 106 match: 31 SD: 1.2062 cents 55 .. 110 match: 31 SD: 1.1441 cents 57 .. 114 match: 31 SD: 1.1313 cents 58 .. 116 match: 31 SD: 1.0863 cents 60 .. 120 match: 31 SD: 0.9971 cents 65 .. 130 match: 31 SD: 0.9555 cents 68 .. 136 match: 31 SD: 0.8671 cents 71 .. 142 match: 31 SD: 0.8014 cents 75 .. 150 match: 31 SD: 0.7977 cents 76 .. 152 match: 31 SD: 0.7172 cents 83 .. 166 match: 31 SD: 0.6840 cents 85 .. 170 match: 31 SD: 0.6116 cents 100 .. 200 match: 31 SD: 0.5924 cents 104 .. 208 match: 31 SD: 0.5581 cents 107 .. 214 match: 31 SD: 0.5435 cents 117 .. 234 match: 31 SD: 0.4590 cents 127 .. 254 match: 31 SD: 0.4586 cents 128 .. 256 match: 31 SD: 0.4081 cents 147 .. 294 match: 31 SD: 0.3736 cents 160 .. 320 match: 31 SD: 0.3370 cents 172 .. 344 match: 31 SD: 0.3084 cents 175 .. 350 match: 31 SD: 0.2921 cents 204 .. 408 match: 31 SD: 0.2769 cents 214 .. 428 match: 31 SD: 0.2495 cents 244 .. 488 match: 31 SD: 0.2255 cents 255 .. 510 match: 31 SD: 0.2208 cents 259 .. 518 match: 31 SD: 0.2112 cents 264 .. 528 match: 31 SD: 0.2073 cents 270 .. 540 match: 31 SD: 0.1997 cents 279 .. 558 match: 31 SD: 0.1938 cents 299 .. 598 match: 31 SD: 0.1933 cents 302 .. 604 match: 31 SD: 0.1788 cents 312 .. 624 match: 31 SD: 0.1780 cents 331 .. 662 match: 31 SD: 0.1741 cents 332 .. 664 match: 31 SD: 0.1738 cents 342 .. 684 match: 31 SD: 0.1735 cents 344 .. 688 match: 31 SD: 0.1693 cents 348 .. 696 match: 31 SD: 0.1662 cents 354 .. 708 match: 31 SD: 0.1569 cents 355 .. 710 match: 31 SD: 0.1545 cents 387 .. 774 match: 31 SD: 0.1456 cents 391 .. 782 match: 31 SD: 0.1410 cents 430 .. 860 match: 31 SD: 0.1272 cents 439 .. 878 match: 31 SD: 0.1214 cents 459 .. 918 match: 31 SD: 0.1176 cents 474 .. 948 match: 31 SD: 0.1098 cents 480 .. 960 match: 31 SD: 0.1097 cents 525 .. 1050 match: 31 SD: 0.1007 cents 566 .. 1132 match: 31 SD: 0.0965 cents 591 .. 1182 match: 31 SD: 0.0937 cents