User:CompactStar/Ed11/5
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The equal division of 11/5 (ed11/5) is a tuning obtained by dividing the neutral ninth (11/5) into a certain number of equal steps.
Division of 11/5 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed11/5 have a perceptually important false octave, with various degrees of accuracy.
The structural utility of 11/5 is apparent by it being the high ninth of a just dominant 11th chord, being the best option for "no-twos-or-threes" harmony after the extremely wide harmonic 5 and the awkwardly narrow small septimal tritone, and being a relatively strong consonance by most metrics.
The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it might be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of 17/13 by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in catfish temperament, which can be viewed as an analog to meantone. It possesses mos scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
Ed11/5-edo correspondence
| Ed11/5 | Edo |
|---|---|
| 8ed11/5 | 7edo |
| 9ed11/5 | 8edo |
| 16ed11/5 | 14edo |
| 18ed11/5 | 16edo |
| 24ed11/5 | 21edo |
| 25ed11/5 | 22edo |
| 27ed11/5 | 24edo |
| 33ed11/5 | 29edo |
| 50ed11/5 | 44edo |
Individual pages for ed11/5's
| 0 | 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 | 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 |
| 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |
| 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 |