User:Cmloegcmluin/APS: Difference between revisions

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== Specification ==

Its full specification is (''n''-)APS-''p'': (''n'' pitches of an) arithmetic pitch sequence adding by interval ''p''. The ''n'' is optional. If not provided, the sequence is open-ended.

Its full specification is (''n''-)APS-''p'': (''n'' pitches of an) arithmetic pitch sequence adding by 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.

== Formula ==

The pitch of ~~the~~ ''k''~~-th step~~ of an APS-''p'' is quite simply ''k''⋅''p'' for a pitch (log-frequency) quantity ''p''.

The pitch of ''k'' steps of APS-''p'' is quite simply ''k''⋅''p'' for a pitch (log-frequency) quantity ''p''.

== Relationship to other tunings ==

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=== Vs. EPD ===

If the ''n'' is not specified, an APS will be equivalent to an [[EPD|equal pitch division (EPD)]]. Specifically, ''n''-EPD-''p'' = APS(''p''/''n'') for a ~~log-frequency~~ quantity ''p''. For example, 12-EPD1200¢ = APS(1200¢/12) = APS100¢.

If the ''n'' is not specified, an APS will be equivalent to an [[EPD|equal pitch division (EPD)]]. Specifically, ''n''-EPD-''p'' = APS(''p''/''n'') for a pitch quantity ''p''. For example, 12-EPD1200¢ = APS(1200¢/12) = APS100¢.

=== Vs. AS ===

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 == Specification ==
-Its full specification is (''n''-)APS-''p'': (''n'' pitches of an) arithmetic pitch sequence adding by interval ''p''. The ''n'' is optional. If not provided, the sequence is open-ended.
+Its full specification is (''n''-)APS-''p'': (''n'' pitches of an) arithmetic pitch sequence adding by 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.
 == Formula ==
-The pitch of the ''k''-th step of an APS-''p'' is quite simply ''k''⋅''p'' for a pitch (log-frequency) quantity ''p''.
+The pitch of ''k'' steps of APS-''p'' is quite simply ''k''⋅''p'' for a pitch (log-frequency) quantity ''p''.
 == Relationship to other tunings ==
@@ Line 17: / Line 21: @@
 === Vs. EPD ===
-If the ''n'' is not specified, an APS will be equivalent to an [[EPD|equal pitch division (EPD)]]. Specifically, ''n''-EPD-''p'' = APS(''p''/''n'') for a log-frequency quantity ''p''. For example, 12-EPD1200¢ = APS(1200¢/12) = APS100¢.
+If the ''n'' is not specified, an APS will be equivalent to an [[EPD|equal pitch division (EPD)]]. Specifically, ''n''-EPD-''p'' = APS(''p''/''n'') for a pitch quantity ''p''. For example, 12-EPD1200¢ = APS(1200¢/12) = APS100¢.
 === Vs. AS ===