User:Cmloegcmluin/AS: Difference between revisions
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m Added to category "xenharmonic series" |
(Temporarily) clarify that this can be specified two ways. In the end it may entail distinct symbols for pitch relation and frequency ratio |
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== Specification == | == Specification == | ||
Its full specification is (n-) | 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 [[octave]]s, in which case it refers to an interval by its pitch relation. | |||
== Relationship to other tunings == | == Relationship to other tunings == | ||
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=== Vs. 1D JI Lattice & equal multiplications === | === Vs. 1D JI Lattice & equal multiplications === | ||
AS-''p'' is equivalent to a 1-dimensional [[Harmonic lattice diagram|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 === | === Vs. APS === | ||
The only difference between an (n-) | The only difference between an (''n''-)AS-''p'' and an [[APS|(''n''-)APS-''p'' (arithmetic pitch sequence)]] is that the ''p'' for an AS must be rational. | ||
== Examples == | == Examples == | ||
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[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Equal divisions of the | [[Category:Equal divisions of the octave]] | ||
[[Category:Xenharmonic series]] | [[Category:Xenharmonic series]] | ||
Revision as of 15:55, 18 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) | (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 |