Convex scale: Difference between revisions
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is there maybe somebody who can explain this in plain English? |
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In a [[regular temperament]], a '''convex scale''' is a set of pitches that form a '''convex set''' in the interval lattice of the temperament. The "regular temperament" is often [[Just intonation|JI]], in which case the lattice is the familiar JI lattice, but convex scales exist for any regular temperament. | In a [[regular temperament]], a '''convex scale''' is a set of pitches that form a '''convex set''' in the interval lattice of the temperament. The "regular temperament" is often [[Just intonation|JI]], in which case the lattice is the familiar JI lattice, but convex scales exist for any regular temperament. | ||
{{todo|clarify|comment=Is there maybe somebody who can explain this in plain English?|increase applicability|inline=1}} | |||
A simple, easy-to-understand definition of a "convex set" in a lattice is the intersection of the lattice with any [http://en.wikipedia.org/wiki/Convex_set convex region] of continuous space. See below for a more formal definition. | A simple, easy-to-understand definition of a "convex set" in a lattice is the intersection of the lattice with any [http://en.wikipedia.org/wiki/Convex_set convex region] of continuous space. See below for a more formal definition. | ||