MOS scale: Difference between revisions

Line 47:

== Properties ==

=== Basic properties ===

* For every MOS scale with an arbitrary period (which is usually the [[octave]]), if ''x''-[[edo]] is the [[collapsed]] tuning (where the small step vanishes) and ''y''-[[edo]] is the [[equalized]] tuning (where the large (L) step and small (s) step are the same size), then by definition it is an ''x''L (''y''-''x'')s MOS scale, and the [[basic]] tuning where L = 2s is thus (''x''+''y'')-[[edo]]. Because this is true regardless of the period (as long as the period can be expressed in both ''x''-[[edo]] and ''y''-[[edo]]), this is also true if the period is 1\''p'', that is, 1 step of ''p''-[[edo]], which implies that ''x'' and ''y'' are divisible by ''p''.

* More generally, whenever ''px''-[[edo]] and ''py''-[[edo]] are used to define two [[val]]s (usually but not necessarily through taking the [[patent val]]s) on top of also being used to define the ''px''L ''py''s MOS scale (where ''p'' is the number of periods per octave), then the ''px'' & ''py'' temperament corresponds to that MOS scale, and adding ''x'' and/or ''y'' corresponds to tuning closer to ''x''-[[edo]] and/or ''y''-[[edo]] respectively.

* Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are ({{nowrap|''a'' + ''b''}})L ''a''s (generated by generators of soft-of-basic ''a''L ''b''s) and ''a''L ({{nowrap|''a'' + ''b''}})s (generated by generators of hard-of-basic ''a''L'' b''s).

* Every MOS scale (with a specified [[equave]] ''E''), excluding ''a''L ''a''s⟨''E''⟩, has a ''parent MOS''. If {{nowrap|''a'' > ''b''}}, the parent of ''a''L ''b''s is ''b''L ({{nowrap|''a'' − ''b''}})s; if {{nowrap|''a'' < ''b''}}, the parent of ''a''L ''b''s is ''a''L ({{nowrap|''b'' − ''a''}})s.

@@ Line 47: / Line 47: @@
 == Properties ==
 === Basic properties ===
+* For every MOS scale with an arbitrary period (which is usually the [[octave]]), if ''x''-[[edo]] is the [[collapsed]] tuning (where the small step vanishes) and ''y''-[[edo]] is the [[equalized]] tuning (where the large (L) step and small (s) step are the same size), then by definition it is an ''x''L (''y''-''x'')s MOS scale, and the [[basic]] tuning where L = 2s is thus (''x''+''y'')-[[edo]]. Because this is true regardless of the period (as long as the period can be expressed in both ''x''-[[edo]] and ''y''-[[edo]]), this is also true if the period is 1\''p'', that is, 1 step of ''p''-[[edo]], which implies that ''x'' and ''y'' are divisible by ''p''.
+* More generally, whenever ''px''-[[edo]] and ''py''-[[edo]] are used to define two [[val]]s (usually but not necessarily through taking the [[patent val]]s) on top of also being used to define the ''px''L ''py''s MOS scale (where ''p'' is the number of periods per octave), then the ''px'' & ''py'' temperament corresponds to that MOS scale, and adding ''x'' and/or ''y'' corresponds to tuning closer to ''x''-[[edo]] and/or ''y''-[[edo]] respectively.
 * Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are ({{nowrap|''a'' + ''b''}})L ''a''s (generated by generators of soft-of-basic ''a''L ''b''s) and ''a''L ({{nowrap|''a'' + ''b''}})s (generated by generators of hard-of-basic ''a''L'' b''s).
 * Every MOS scale (with a specified [[equave]] ''E''), excluding ''a''L ''a''s⟨''E''⟩, has a ''parent MOS''. If {{nowrap|''a'' &gt; ''b''}}, the parent of ''a''L ''b''s is ''b''L ({{nowrap|''a'' &minus; ''b''}})s; if {{nowrap|''a'' &lt; ''b''}}, the parent of ''a''L ''b''s is ''a''L ({{nowrap|''b'' &minus; ''a''}})s.