Rank 3 scale: Difference between revisions

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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 can be generated by stacking a single generator modulo a period ~~(not~~ all generated scales are MOS).

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

MOS scales are [[Scale properties simplified|symmetric]] (not all symmetric scales are MOS) and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s.

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MOS scales consist of ''strict MOS'' and ''Multi-MOS'' scales.

Strict MOS scales are the MOS scales that possess ''Myhill’s property'', in which all generic intervals come in 2 sizes, and are also known as ''well-formed (WF)'' scales. The two sizes of each interval class in a WF or strict MOS scale differ by the ''chroma'' – the difference between the large and small steps of the scale. We will refer to these scales as WF scales for the remainder of this page.

Strict MOS scales are the MOS scales that possess ''Myhill’s property'', in which all generic intervals come in 2 sizes, and are also known as ''well-formed (WF)'' scales. The two sizes of each interval class in a WF or strict MOS scale differ by the ''chroma'' – the difference between the large and small steps of the scale. We will refer to these scales as WF scales for the remainder of this page. WF scales are defined (Carey & Clampitt, 1989) as generated scales for which the generator is of invariant generic interval size.

''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.

@@ Line 4: / Line 4: @@
 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 can be generated by stacking a single generator modulo a period (not all generated scales are MOS).
+MOS scales can be generated by stacking a single generator modulo a period. Not all generated scales are MOS.
 MOS scales are [[Scale properties simplified|symmetric]] (not all symmetric scales are MOS) and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s.
@@ Line 10: / Line 10: @@
 MOS scales consist of ''strict MOS'' and ''Multi-MOS'' scales.
-Strict MOS scales are the MOS scales that possess ''Myhill’s property'', in which all generic intervals come in 2 sizes, and are also known as ''well-formed (WF)'' scales. The two sizes of each interval class in a WF or strict MOS scale differ by the ''chroma'' – the difference between the large and small steps of the scale. We will refer to these scales as WF scales for the remainder of this page.
+Strict MOS scales are the MOS scales that possess ''Myhill’s property'', in which all generic intervals come in 2 sizes, and are also known as ''well-formed (WF)'' scales. The two sizes of each interval class in a WF or strict MOS scale differ by the ''chroma'' – the difference between the large and small steps of the scale. We will refer to these scales as WF scales for the remainder of this page. WF scales are defined (Carey & Clampitt, 1989) as generated scales for which the generator is of invariant generic interval size.
 ''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.