User:Moremajorthanmajor/Ed9/4
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The equal division of 9/4 (ed9/4) is a tuning obtained by dividing the Pythagorean ninth (9/4) in a certain number of equal steps.
Properties
Relation to edfs
An ed9/4 can be generated by taking every other tone of an edf, so even-numbered ed9/4's are integer edfs.
This is the primary use for ed9/4s — to get the same benefits of a particular edf, without having to juggle such a large number of notes per period. This is a similar principle to using an ed4 in place of a very large edo.
Perhaps a composer wanting to explore Nedf but daunted by the number of notes, could instead simply use Ned9/4. Otherwise, they could also compose for two instruments, both tuned to Ned9/4, but each tuned one step of Nedf apart, making the piece overall in Nedf, but each individual instrument Ned9/4. This is a similar strategy to how some composers have approached 24edo — using two 12edo instruments tuned a 24edo-step apart.
Relation to common practice
9/4 or another major ninth is a standard replacement for the root in jazz piano voicings. Perhaps, then, a composer could approach the period of ed9/4 not as an equivalence, but as a skeleton for chords to be built out of.
Equivalence
Few would argue that 9/4 itself could be heard as an equivalence. Some might argue that some degree of 3/2 equivalence may be possible in a scale which has no 2/1, 3/1, or 4/1, though this is quite controversial. If that is the case, then perhaps in a similar scale that also has no 3/2, 9/4 may have some form of faint equivalence as it might sound like two periods of 3/2.
Individual pages for ed9/4's
| 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 |
| 21 | 23 | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 |
| 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | 57 | 59 |
| 61 | 63 | 65 | 67 | 69 | 71 | 73 | 75 | 77 | 79 |
| 81 | 83 | 85 | 87 | 89 | 91 | 93 | 95 | 97 | 99 |
See also
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Todo: review , cleanup, improve layout |