# 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

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 |