User:Cmloegcmluin/AS: Difference between revisions

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An '''AS''', or '''ambitonal sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Harmonotonic tunings|harmonotonic]] tuning.

Its full specification is (n-)ASp: (n pitches of an) ambitonal sequence adding by rational interval p. 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.

== Specification ==

The n is optional. If not provided, the sequence is open-ended.

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 [[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.

=== vs. APS ===

The only difference between an (n-)ASp and an [[APS|(n-)APSp (arithmetic pitch sequence)]] is that the p for an APS is irrational.

== Examples ==

{| class="wikitable"

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 An '''AS''', or '''ambitonal sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Harmonotonic tunings|harmonotonic]] tuning.
-Its full specification is (n-)ASp: (n pitches of an) ambitonal sequence adding by rational interval p. 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.
+== Specification ==
-The n is optional. If not provided, the sequence is open-ended.
+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 [[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.
+=== vs. APS ===
 The only difference between an (n-)ASp and an [[APS|(n-)APSp (arithmetic pitch sequence)]] is that the p for an APS is irrational.
+== Examples ==
 {| class="wikitable"