Interval of equivalence: Difference between revisions
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{{interwiki | {{interwiki | ||
| | | en = Equave | ||
| | | de = Äquave | ||
|es = | | es = | ||
|ja = | | ja = | ||
}} | }} | ||
{{Wikipedia|Pseudo-octave}} | {{Wikipedia|Pseudo-octave}} | ||
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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]]. | ||
== 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 (although the kinds of "tempering" are treated completely differently musically, both define an equivalence class of intervals) | |||
== See also == | == See also == | ||
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* [[Stretched tuning]] | * [[Stretched tuning]] | ||
* [[Equave limit]] | * [[Equave limit]] | ||
== Notes == | == Notes == | ||