Interval of equivalence: Difference between revisions

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manual undo of earlier section about "tempering equave" which is not really how we use that term
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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 ==

Revision as of 20:59, 24 April 2025

English Wikipedia has an article on:

The equave (/ˈiːkwɪv/ EE-kwiv or /ˈiːkwəv/ EE-kwəv), also called interval of equivalence, equivalence interval, formal octave[1][note 1]or pseudo-octave[2][note 1], is the interval such that pitches separated by it are considered psychoacoustically or formally equivalent and are elements of the same pitch class.

If a periodic scale has an equave, the equave is typically the same as the period or a multiple thereof.

Etymology

The term equave was coined by Inthar. It is a portmanteau of equivalence and octave.

Examples

  • In octave-repeating scales, the equave is typically 2/1.
  • In Bohlen–Pierce, the equave may be taken as 3/1.
  • In edfs, the equave may be taken as 3/2 or less commonly 9/4.

See also

Notes

  1. 1.0 1.1 The terms formal octave and pseudo-octave are often used specifically to designate a stretched or compressed octave, but they may more generally designate any kind of equave.

References

  1. Op de Coul, E.F. Scala help.
  2. ASCL Specification. Ableton.