POTE tuning: Difference between revisions

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'''Destretched tunings''' are tuning [[optimization]] techniques with the [[tuning map]] scaled until a certain interval is just, that is, its stretch introduced in the optimization is removed. ''~~'DTE tuning''' ('''destretched~~ Tenney–Euclidean tuning''') is the most typical instance and will be the focus of this article. Otherwise normed tunings can be defined and computed analogously.

'''Destretched tunings''' are tuning [[optimization]] techniques with the [[tuning map]] scaled until a certain interval is just, that is, its stretch introduced in the optimization is removed. ''Destretched Tenney–Euclidean tuning''{{idiosyncratic}} is the most typical instance and will be the focus of this article. Otherwise normed tunings can be defined and computed analogously.

The most significant form of ~~DTE tuning~~ is pure-octave destretched, which is assumed unless specified otherwise. This has been called the '''POTE tuning''' ('''pure-octave Tenney–Euclidean tuning'''), although there are other ways to enforce a pure octave (→ [[Constrained tuning]]). POTE can be computed from [[TE tuning]] with all primes scaled until 2/1 is just.

The most significant form of these tunings is pure-octave destretched, which is assumed unless specified otherwise. This has been called the '''POTE tuning''' ('''pure-octave Tenney–Euclidean tuning'''), although there are other ways to enforce a pure octave (→ [[Constrained tuning]]). POTE can be computed from [[TE tuning]] with all primes scaled until 2/1 is just.

== Motivation ==

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-'''Destretched tunings''' are tuning [[optimization]] techniques with the [[tuning map]] scaled until a certain interval is just, that is, its stretch introduced in the optimization is removed. '''DTE tuning''' ('''destretched Tenney–Euclidean tuning''') is the most typical instance and will be the focus of this article. Otherwise normed tunings can be defined and computed analogously.
+'''Destretched tunings''' are tuning [[optimization]] techniques with the [[tuning map]] scaled until a certain interval is just, that is, its stretch introduced in the optimization is removed. ''Destretched Tenney–Euclidean tuning''{{idiosyncratic}} is the most typical instance and will be the focus of this article. Otherwise normed tunings can be defined and computed analogously.
-The most significant form of DTE tuning is pure-octave destretched, which is assumed unless specified otherwise. This has been called the '''POTE tuning''' ('''pure-octave Tenney–Euclidean tuning'''), although there are other ways to enforce a pure octave (→ [[Constrained tuning]]). POTE can be computed from [[TE tuning]] with all primes scaled until 2/1 is just.
+The most significant form of these tunings is pure-octave destretched, which is assumed unless specified otherwise. This has been called the '''POTE tuning''' ('''pure-octave Tenney–Euclidean tuning'''), although there are other ways to enforce a pure octave (→ [[Constrained tuning]]). POTE can be computed from [[TE tuning]] with all primes scaled until 2/1 is just.
 == Motivation ==