User:Cmloegcmluin/AS: Difference between revisions
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(Temporarily) clarify that this can be specified two ways. In the end it may entail distinct symbols for pitch relation and frequency ratio |
Cmloegcmluin (talk | contribs) →Examples: update row headers per agreement at https://en.xen.wiki/w/Talk:APS |
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| Line 35: | Line 35: | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(5⁰/4⁰) | |(5⁰/4⁰) | ||
|5¹/4¹ | |5¹/4¹ | ||
| Line 46: | Line 46: | ||
|5⁸/4⁸ | |5⁸/4⁸ | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
|0.32 | |0.32 | ||
| Line 57: | Line 57: | ||
|2.58 | |2.58 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(1/1) | |(1/1) | ||
|4/5 | |4/5 | ||
Revision as of 20:36, 19 October 2023
An AS, or ambitonal sequence, is a kind of arithmetic and harmonotonic tuning.
Specification
Its full specification is (n-)AS-p: (n pitches of an) ambitonal sequence adding by rational interval p.
Note:
- The n is optional. If not provided, the sequence is open-ended.
- The p can be dimensionless, in which case it refers to an interval by its frequency ratio. It can also take a unit proportional to octaves, in which case it refers to an interval by its pitch relation.
Relationship to other tunings
Vs. 1D JI Lattice & equal multiplications
AS-p 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-)AS-p and an (n-)APS-p (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, ratio) | (5⁰/4⁰) | 5¹/4¹ | 5²/4² | 5³/4³ | 5⁴/4⁴ | 5⁵/4⁵ | 5⁶/4⁶ | 5⁷/4⁷ | 5⁸/4⁸ |
| pitch (log₂f, octaves) | (0) | 0.32 | 0.64 | 0.97 | 1.29 | 1.61 | 1.93 | 2.25 | 2.58 |
| length (1/f, ratio) | (1/1) | 4/5 | 16/25 | 64/125 | 256/625 | 1024/3125 | 4096/15625 | 16384/78125 | 65536/390625 |