User:Cmloegcmluin/AS: Difference between revisions

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== 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.

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 ==

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=== Vs. 1D JI Lattice & equal multiplications ===

It 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-step_tuning#Equal_multiplications|~~equal multiplication]] of a rational interval p.

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-)~~ASp~~ and an [[APS|(n-)~~APSp~~ (arithmetic pitch sequence)]] is that the p for an AS must be rational.

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 ==

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[[Category:Equal-step tuning‏‎]]

[[Category:Equal divisions of the ~~octave‏‎~~ ]]

[[Category:Equal divisions of the octave]]

[[Category:Xenharmonic series]]

@@ Line 3: / Line 3: @@
 == 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.
+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 ==
@@ Line 9: / Line 13: @@
 === Vs. 1D JI Lattice & equal multiplications ===
-It 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-step_tuning#Equal_multiplications|equal multiplication]] of a rational interval p.
+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-)ASp and an [[APS|(n-)APSp (arithmetic pitch sequence)]] is that the p for an AS must be rational.
+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 ==
@@ Line 66: / Line 70: @@
 [[Category:Equal-step tuning‏‎]]
-[[Category:Equal divisions of the octave‏‎ ]]
+[[Category:Equal divisions of the octave]]
 [[Category:Xenharmonic series]]