Rank 3 scale: Difference between revisions

Line 2:

== Rank-2 scales ==

MOS scales are the MV2 (~~Max Variety~~ 2) scales. MOS scales are DE ([[distributionally even]]), along with rank-1 scales, i.e., [[ET]]<nowiki/>s, which are MV1.

MOS scales are the MV2 ([[maximum variety]] 2) scales. MOS scales are DE ([[distributionally even]]), along with rank-1 scales, i.e., [[ET]]<nowiki/>s, which are MV1.

MOS scales can be generated by stacking a single generator modulo a period. Not all generated scales are MOS.

Line 14:

''Multi-MOS'' scales are MOS scales that are multiple periods of a WF scale. The interval class represented by any multiple of a period of a WF scale comes in only a single size, hence multi-MOS scales do not possess Myhill’s property.

MOS scales are ''[[Constant structure|constant structures]]'', meaning that it's generic interval classes are distinct, meaning that each specific interval is always subtended by the same number of steps. This is also known as the ''~~[[Scale properties simplified|~~partitioning property]]''. ''[[MODMOS scales]]'' are also constant structures - which may be arrived at by raising or lower an interval or intervals of a MOS scale by a chroma. Constant structures exist in any rank. ETs are the rank-1 constant structures.

MOS scales are ''[[Constant structure|constant structures]]'', meaning that it's generic interval classes are distinct, meaning that each specific interval is always subtended by the same number of steps. This is also known as the ''partitioning property''. ''[[MODMOS scales]]'' are also constant structures - which may be arrived at by raising or lower an interval or intervals of a MOS scale by a chroma. Constant structures exist in any rank. ETs are the rank-1 constant structures.

== Rank-3 scales ==

@@ Line 2: / Line 2: @@
 == Rank-2 scales ==
-MOS scales are the MV2 (Max Variety 2) scales. MOS scales are DE ([[distributionally even]]), along with rank-1 scales, i.e., [[ET]]<nowiki/>s, which are MV1.
+MOS scales are the MV2 ([[maximum variety]] 2) scales. MOS scales are DE ([[distributionally even]]), along with rank-1 scales, i.e., [[ET]]<nowiki/>s, which are MV1.
 MOS scales can be generated by stacking a single generator modulo a period. Not all generated scales are MOS.
@@ Line 14: / Line 14: @@
 ''Multi-MOS'' scales are MOS scales that are multiple periods of a WF scale. The interval class represented by any multiple of a period of a WF scale comes in only a single size, hence multi-MOS scales do not possess Myhill’s property.
-MOS scales are ''[[Constant structure|constant structures]]'', meaning that it's generic interval classes are distinct, meaning that each specific interval is always subtended by the same number of steps. This is also known as the ''[[Scale properties simplified|partitioning property]]''. ''[[MODMOS scales]]'' are also constant structures - which may be arrived at by raising or lower an interval or intervals of a MOS scale by a chroma. Constant structures exist in any rank. ETs are the rank-1 constant structures.
+MOS scales are ''[[Constant structure|constant structures]]'', meaning that it's generic interval classes are distinct, meaning that each specific interval is always subtended by the same number of steps. This is also known as the ''partitioning property''. ''[[MODMOS scales]]'' are also constant structures - which may be arrived at by raising or lower an interval or intervals of a MOS scale by a chroma. Constant structures exist in any rank. ETs are the rank-1 constant structures.
 == Rank-3 scales ==