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Encyclopedia of Microtonal Music Theory

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EDO 11-odd-limit error

[Joe Monzo]

On this page I present a detailed examination of the amount of error of the representations of all ratios of odd-factors from 3 to 11 (an arbitrarily selected stopping point, commensurate with Partch's 11-odd-limit tonality diamond), for several various EDOs.

Different EDOs approximate JI intervals in different ways. In these graphs, errors are given as a percentage of one degree or "step" of that EDO. Thus, the maximum error on the graph is 50%, which would indicate that the prime-factor lies midway between two neighboring EDO degrees.

Error values tend to cluster into groups -- this clustering is plainly visible on the graphs, and I have also divided the lists accordingly, putting a blank row between clusters.

MouseOver the cardinality names of the various EDOs to see a graph of them showing the error from the closest EDO approximation to 11-odd-limit just intonation.

10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
768
. . . . . . . . .

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