Rank-3 scale: Difference between revisions
mNo edit summary |
→Rank-2 scales: Added reference to Erv's original MOS definition |
||
| Line 15: | Line 15: | ||
MOS scales and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s. | MOS scales and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s. | ||
MOS scales consist of ''strict MOS'' and ''Multi-MOS'' scales. | 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 ''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 ''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. | ||
| Line 21: | Line 21: | ||
''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. | ''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. | ||
Rank 3 scales are introduced from here, as generalizations of MOS scales. | Rank-3 scales are introduced from here, as generalizations of MOS scales. | ||
==[[User:Inthar/MV3|MV3 scales]]== | ==[[User:Inthar/MV3|MV3 scales]]== | ||
Maximum variety 3, or MV3 scales are a generalization of MOS scales (the scales of MV2) into rank-3. | Maximum variety 3, or MV3 scales are a generalization of MOS scales (the scales of MV2) into rank-3. | ||