User:Cmloegcmluin/EPD

An EPD, or equal pitch division, is a kind of arithmetic and monotonic tuning.

n-EDp: n equal (pitch) divisions of interval p (e.g. 12-EDO) (equivalent to rank-1 temperament of p/n)

The most common example of this type of tuning is 12-EDO, standard tuning, which takes the interval of the octave, and equally divides its pitch into 12 parts. For long, we could call this 12-EPDO, for 12 equal pitch divisions of the octave (whenever pitch is the chosen kind of quality, we can assume it, and skip pointing it out; that's why 12-EDO is the better name).

example: 4-EDO = rank-1 temperament w/ generator 300¢ = APS⁴√2 ≈ APS1.189

quantity	1	2	3	4	5	6	7	8	9
frequency	1.00	1.19	1.41	1.68	2.00	2.38	2.83	3.36	4.00
pitch	0.00	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00
length	1.00	0.84	0.71	0.59	0.50	0.42	0.35	0.30	0.25