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An '''AS''', or '''ambitonal sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[ | {{Editable user page}} | ||
An '''AS''', or '''ambitonal sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Harmonotonic tunings|harmonotonic]] tuning. | |||
== Specification == | |||
(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. | |||
equal multiplications | == Relationship to other tunings == | ||
=== 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 === | |||
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 == | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 23: | Line 36: | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(5⁰/4⁰) | |(5⁰/4⁰) | ||
|5¹/4¹ | |5¹/4¹ | ||
| Line 34: | Line 47: | ||
|5⁸/4⁸ | |5⁸/4⁸ | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
|0.32 | |0.32 | ||
| Line 45: | Line 58: | ||
|2.58 | |2.58 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(1/1) | |(1/1) | ||
|4/5 | |4/5 | ||
| Line 56: | Line 69: | ||
|65536/390625 | |65536/390625 | ||
|} | |} | ||
== List of ASs == | |||
{{See also| APS #List of APSs }} | |||
; [[Superparticular]] | |||
* [[1ed8/7|AS8/7]] | |||
* [[1ed9/8|AS9/8]] | |||
* [[1ed10/9|AS10/9]] | |||
* [[1ed15/14|AS15/14]] | |||
* [[1ed16/15|AS16/15]] | |||
* [[1ed18/17|AS18/17]] | |||
* [[1ed21/20|AS21/20]] | |||
* [[1ed25/24|AS25/24]] | |||
* [[1ed26/25|AS26/25]] | |||
* [[1ed33/32|AS33/32]] | |||
* [[1ed81/80|AS81/80]] | |||
; Others | |||
* [[1ed13/10|AS13/10]] | |||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Equal divisions of the | [[Category:Equal divisions of the octave]] | ||
[[Category:Xenharmonic series]] | |||