User:Cmloegcmluin/APS: Difference between revisions
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{| class="wikitable" | {| class="wikitable" | ||
|+example: | |+example: 4-EDO = rank-1 temperament w/ generator 300¢ = APS⁴√2 ≈ APS1.189 | ||
|- | |- | ||
! quantity | ! quantity | ||
| Line 20: | Line 20: | ||
|- | |- | ||
! frequency | ! frequency | ||
| | |1.00 | ||
| | |1.19 | ||
| | |1.41 | ||
| | |1.68 | ||
| | |2.00 | ||
| | |2.38 | ||
| | |2.83 | ||
| | |3.36 | ||
| | |4.00 | ||
|- | |- | ||
! pitch | ! pitch | ||
| | |0.00 | ||
| | |0.25 | ||
| | |0.50 | ||
| | |0.75 | ||
| | |1.00 | ||
| | |1.25 | ||
| | |1.50 | ||
| | |1.75 | ||
| | |2.00 | ||
|- | |- | ||
! length | ! length | ||
| | |1.00 | ||
| | |0.84 | ||
| | |0.71 | ||
| | |0.59 | ||
| | |0.50 | ||
| | |0.42 | ||
| | |0.35 | ||
| | |0.30 | ||
| | |0.25 | ||
|} | |} | ||
Revision as of 01:54, 22 March 2021
An APS, or arithmetic pitch sequence, is a kind of arithmetic and monotonic tuning.
(n-)APSp: (n pitches of an) arithmetic pitch sequence adding by p (equivalent to rank-1 temperament with generator p)
An AS is a specific (rational) type of APS.
| 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 |