User:Cmloegcmluin/AS: Difference between revisions
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Cmloegcmluin (talk | contribs) fix section capitalization |
Cmloegcmluin (talk | contribs) →Vs. APS: address Flora's recent concerns about rationality vs. irrationality in this system |
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=== Vs. APS === | === Vs. APS === | ||
The only difference between an (n-)ASp and an [[APS|(n-)APSp (arithmetic pitch sequence)]] is that the p for an | The only difference between an (n-)ASp and an [[APS|(n-)APSp (arithmetic pitch sequence)]] is that the p for an AS must be rational. | ||
== Examples == | == Examples == | ||
Revision as of 21:41, 28 March 2023
An AS, or ambitonal sequence, is a kind of arithmetic and harmonotonic tuning.
Specification
Its full specification is (n-)ASp: (n pitches of an) ambitonal sequence adding by rational interval p. The n is optional. If not provided, the sequence is open-ended.
Relationship to other tunings
Vs. 1D JI Lattice & equal multiplications
It is equivalent to a 1-dimensional JI lattice of p. These are sequences which are rational but ambiguous between otonality and utonality, such as a chain of the same JI pitch. It is also equivalent to an equal multiplication of a rational interval p.
Vs. APS
The only difference between an (n-)ASp and an (n-)APSp (arithmetic pitch sequence) is that the p for an AS must be rational.
Examples
| quantity | (0) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| frequency (f) | (5⁰/4⁰) | 5¹/4¹ | 5²/4² | 5³/4³ | 5⁴/4⁴ | 5⁵/4⁵ | 5⁶/4⁶ | 5⁷/4⁷ | 5⁸/4⁸ |
| pitch (log₂f) | (0) | 0.32 | 0.64 | 0.97 | 1.29 | 1.61 | 1.93 | 2.25 | 2.58 |
| length (1/f) | (1/1) | 4/5 | 16/25 | 64/125 | 256/625 | 1024/3125 | 4096/15625 | 16384/78125 | 65536/390625 |