Mapped interval: Difference between revisions

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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]] (or "[[monzo]]") <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]] (or "[[tmonzo]]") <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]] (or "[[monzo]]") <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]] (or "[[tmonzo]]") <math>\textbf{y} =</math> {{rket|{{bra|1 1 0}} {{bra|0 1 4}}}}{{ket|1 -2 1}} = {{rket|-1 2}}.

Note that we've notated the mapped interval with a tilde, <span style="background-color: yellow">~</span><math>\frac{10}{9}</math>, to indicate that its size is now approximate.

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 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]] (or "[[monzo]]") <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]] (or "[[tmonzo]]") <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]] (or "[[monzo]]") <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]] (or "[[tmonzo]]") <math>\textbf{y} =</math> {{rket|{{bra|1 1 0}} {{bra|0 1 4}}}}{{ket|1 -2 1}} = {{rket|-1 2}}.
 Note that we've notated the mapped interval with a tilde, <span style="background-color: yellow">~</span><math>\frac{10}{9}</math>, to indicate that its size is now approximate.