Interval of equivalence: Difference between revisions
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== Mathematical interpretation == | == Mathematical interpretation == | ||
If intervals and notes an equave apart are considered to be wholly equivalent to one another, and are collapsed down to a single representative interval (as is usually the case when constructing lattices), this is mathematically identical to [[tempering out]] the equave, as it is an interval separating notes that are treated as the same thing. This gives us a tool to formalize the notion of equivalence in the language of regular temperament theory - for example, octave-equivalent meantone is a rank-1 temperament that tempers out 81/80, but also "tempers out" 2/1 | If intervals and notes an equave apart are considered to be wholly equivalent to one another, and are collapsed down to a single representative interval (as is usually the case when constructing lattices), this is mathematically identical to [[tempering out]] the equave, as it is an interval separating notes that are treated as the same thing. This gives us a tool to formalize the notion of equivalence in the language of regular temperament theory - for example, octave-equivalent meantone is a rank-1 temperament that tempers out 81/80, but also "tempers out" 2/1 (although the kinds of "tempering" are treated completely differently musically, both define an equivalence class of intervals) | ||
== Notes == | == Notes == | ||