Cross-set scale: Difference between revisions

Revision as of 22:44, 31 July 2023 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits →Theory ← Older edit		Revision as of 22:44, 31 July 2023 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits No edit summary Newer edit →
Line 1:		Line 1:
	A '''cross-set scale''' (or simply '''cross-set''') is a [[scale]] produced by taking every ordered pair in the [[Wikipedia:Cartesian product\|Cartesian product]] of two scales, or of a scale with itself, and stacking ~~all~~ elements in each ordered pair. Cross-set scales may also be generalized to more than two initial scales.		A '''cross-set scale''' (or simply '''cross-set''') is a [[scale]] produced by taking every ordered pair in the [[Wikipedia:Cartesian product\|Cartesian product]] of two scales, or of a scale with itself, and stacking both elements in each ordered pair. Cross-set scales may also be generalized to more than two initial scales.

	If the second scale is the inverse of the first scale (e.g. ''a'' becomes 1/''a''), the result is a reciprocal cross-set (scale). If additionally the first scale is a sequence of odd harmonics starting from 1, the result is a [[tonality diamond]].		If the second scale is the inverse of the first scale (e.g. ''a'' becomes 1/''a''), the result is a reciprocal cross-set (scale). If additionally the first scale is a sequence of odd harmonics starting from 1, the result is a [[tonality diamond]].