Rank and codimension: Difference between revisions
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The '''rank''' of a [[ | The '''rank''' of a [[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). | * [[edo]]s are rank-1 (1-dimensional) because their pitches can be described with one number (the number of edo steps). | ||
* [[MOS]]es 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]] 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. | * [[MOS]]es 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]] 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. | ||