AS

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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 APS is irrational.

Examples

example: AS5/4 = 1D JI lattice of 5/4 = 5/4 chain
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