Rank and codimension: Difference between revisions

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	The '''rank''' of a [[Regular_Temperaments\|regular temperament]] is simply its dimension. For example, [[edo]]s are rank-1 because their pitches can be ~~arranged as equally-spaced points in a line~~, and MOSes and temperaments based on them are rank-2, because the two dimensions are the [[period]] and the [[generator]]. For instance, every interval of [[Meantone\|meantone]] can be obtained as a combination of a certain number of octaves (the period) up or down, plus a certain number of flattened meantone fifths (the generator) up or down.		The '''rank''' of a [[Regular_Temperaments\|regular temperament]] is simply its dimension. For example, [[edo]]s are rank-1 (1-dimensional) because their pitches can be described with one number (the number of edo steps), and MOSes and temperaments based on them are rank-2 (2-dimensional), because the two dimensions are the number of [[period]]s and the number of [[generator]]s. For instance, every interval of [[Meantone\|meantone]] can be obtained as a combination of a certain number of octaves (the period) up or down, plus a certain number of flattened meantone fifths (the generator) up or down.

	== Mathematical description ==		== Mathematical description ==