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| * In [[Bohlen–Pierce]], the equave may be taken as [[3/1]]. | | * In [[Bohlen–Pierce]], the equave may be taken as [[3/1]]. |
| * In [[edf]]s, the equave may be taken as [[3/2]] or less commonly [[9/4]]. | | * In [[edf]]s, the equave may be taken as [[3/2]] or less commonly [[9/4]]. |
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| == Mathematical interpretation ==
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| 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)
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| == See also == | | == See also == |