Rank-3 scale: Difference between revisions

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MOS scales consist of ''strict MOS'', which are the MOS scales as originally defined by Erv Wilson, and ''multi-MOS'' scales.

Strict MOS scales are the MOS scales that possess [[~~Scale~~ properties ~~simplified~~#Properties|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.

Strict MOS scales are the MOS scales that possess [[Glossary of scale properties#Properties|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.

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 MOS scales consist of ''strict MOS'', which are the MOS scales as originally defined by Erv Wilson, and ''multi-MOS'' scales.
-Strict MOS scales are the MOS scales that possess [[Scale properties simplified#Properties|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.
+Strict MOS scales are the MOS scales that possess [[Glossary of scale properties#Properties|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.