UD
A UD, or utonal division, is a kind of arithmetic and harmonotonic tuning.
Its full specification is n-UDp: n utonal divisions of rational interval p. An n-UDO is equivalent to the nth undertone mode, or under-n scale.
The only difference between n-UDp and n-ELDp (equal length division) is that the p for UD is rational, while the p for ELD is irrational.
An n-EDL is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n).
| quantity | (0) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| frequency (f) | (8/8) | 8/7 | 8/6 | 8/5 | 8/4 |
| pitch (log₂f) | (0) | 0.19 | 0.42 | 0.68 | 1.00 |
| length (1/f) | (1/1) | 7/8 | 3/4 | 5/8 | 1/2 |