Support: Difference between revisions

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The word "supports" is also used in a more informal and generic sense, both in and outside of regular temperament theory: a pitch structure '''A''' supports another pitch structure '''B''' when '''A''' ''can be used for'' '''B'''. For example, a temperament or tuning may be said to support a scale or a chord, or a temperament may be said to support a tuning of another temperament, or scale may be said to support a chord or harmony within a certain [[prime limit|prime-]] or [[odd-limit]] or [[interval basis|interval subspace]], etc.

Most typically, this sense of "support" is reserved for such cases where not only is '''B''' merely possible or ''valid'' with '''A''', but '''A''' is actually ''good'' for '''B'''. ~~Due to the fact that the~~ technical RTT sense of "supports" defined above is strictly mathematical and makes no such stipulation of aesthetic goodness, it ~~may occasionally conflict with~~ this informal definition and surprise some readers.

Most typically, this sense of "support" is reserved for such cases where not only is '''B''' merely possible or ''valid'' with '''A''', but '''A''' is actually ''good'' for '''B'''. The technical RTT sense of "supports" defined above is strictly mathematical and makes no such stipulation of aesthetic goodness, however. According to it, the [[wart notation|2c]] [[map]] for [[2edo|2-ET]] supports [[meantone]] despite tuning the fifth to 600c, well outside the [[diamond tuning ranges]] for meantone. Furthermore, since [[0edo|0-ET]] tempers out every comma, it therefore supports ''every temperament'', though clearly it does not do so in any musically useful sense. Due to this key difference between the technical RTT definition and the informal general definition, occasionally usages may conflict and surprise some readers.

== Footnotes ==

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 The word "supports" is also used in a more informal and generic sense, both in and outside of regular temperament theory: a pitch structure '''A''' supports another pitch structure '''B''' when '''A''' ''can be used for'' '''B'''. For example, a temperament or tuning may be said to support a scale or a chord, or a temperament may be said to support a tuning of another temperament, or scale may be said to support a chord or harmony within a certain [[prime limit|prime-]] or [[odd-limit]] or [[interval basis|interval subspace]], etc.
-Most typically, this sense of "support" is reserved for such cases where not only is '''B''' merely possible or ''valid'' with '''A''', but '''A''' is actually ''good'' for '''B'''. Due to the fact that the technical RTT sense of "supports" defined above is strictly mathematical and makes no such stipulation of aesthetic goodness, it may occasionally conflict with this informal definition and surprise some readers.
+Most typically, this sense of "support" is reserved for such cases where not only is '''B''' merely possible or ''valid'' with '''A''', but '''A''' is actually ''good'' for '''B'''. The technical RTT sense of "supports" defined above is strictly mathematical and makes no such stipulation of aesthetic goodness, however. According to it, the [[wart notation|2c]] [[map]] for [[2edo|2-ET]] supports [[meantone]] despite tuning the fifth to 600c, well outside the [[diamond tuning ranges]] for meantone. Furthermore, since [[0edo|0-ET]] tempers out every comma, it therefore supports ''every temperament'', though clearly it does not do so in any musically useful sense. Due to this key difference between the technical RTT definition and the informal general definition, occasionally usages may conflict and surprise some readers.
 == Footnotes ==