Mapped interval: Difference between revisions
Cmloegcmluin (talk | contribs) Created page with "A '''mapped interval''' is an interval that has been mapped by a mapping matrix for a regular temperament. For example, if we begin with an unmapped, JI interval..." |
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A '''mapped interval''' is an interval that has been mapped by a [[mapping]] matrix for a [[regular temperament]]. | A '''mapped interval''' is an [[interval]] that has been mapped by a [[mapping]] matrix for a [[regular temperament]]. | ||
For example, if we begin with an unmapped, [[JI]] interval <math>\frac{10}{9}</math> with [[prime-count vector]] <math>\textbf{i} =</math> {{ket|1 -2 1}}, the mapped interval ~<math>\frac{10}{9}</math> under [[meantone temperament]] {{rket|{{bra|1 1 0}} {{bra|0 1 4}}}} would have [[generator-count vector]] <math>\textbf{y} =</math> {{rket|{{bra|1 1 0}} {{bra|0 1 4}}}}{{ket|1 -2 1}} = {{rket|-3 2}}. | For example, if we begin with an unmapped, [[JI]] interval <math>\frac{10}{9}</math> with [[prime-count vector]] <math>\textbf{i} =</math> {{ket|1 -2 1}}, the mapped interval ~<math>\frac{10}{9}</math> under [[meantone temperament]] {{rket|{{bra|1 1 0}} {{bra|0 1 4}}}} would have [[generator-count vector]] <math>\textbf{y} =</math> {{rket|{{bra|1 1 0}} {{bra|0 1 4}}}}{{ket|1 -2 1}} = {{rket|-3 2}}. | ||