Detempering: Difference between revisions

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In [[regular temperament theory]], '''detempering''' is the process of taking a tempered pitch system and replacing each of its pitches with a nearby [[JI]] pitch (called a [[transversal]]). Specifically, a '''detempered scale''' or a '''detemperament''' has each pitch of a tempered scale (according to a fixed regular temperament) replaced with ~~one~~ JI ~~interpretation~~ of the pitch under the temperament map. Ideally the resultant JI pitch system will have low [[prime limit]] and a compact lattice.

In [[regular temperament theory]], '''detempering''' is the process of taking a tempered pitch system and replacing each of its pitches with a nearby [[JI]] pitch (called a [[transversal]]). Specifically, a '''detempered scale''' or a '''detemperament''' has each pitch of a tempered scale (according to a fixed regular temperament) replaced with some set of JI interpretations of the pitch under the temperament map. If exactly one JI interpretation is used for each pitch, then the detempering is called a '''one-to-one detempering''' Ideally the resultant JI pitch system will have low [[prime limit]] and a compact lattice.

It is a distinct concept from a [[Neji|quasi-equal rational tuning, or neji]], the main difference being that a neji replaces an equal temperament's pitches with pitches from a single harmonic series.

Revision as of 16:30, 20 July 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits m →Examples ← Older edit		Revision as of 05:22, 3 September 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits add term 1-1 detempering (due to ks26) Newer edit →
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	In [[regular temperament theory]], '''detempering''' is the process of taking a tempered pitch system and replacing each of its pitches with a nearby [[JI]] pitch (called a [[transversal]]). Specifically, a '''detempered scale''' or a '''detemperament''' has each pitch of a tempered scale (according to a fixed regular temperament) replaced with ~~one~~ JI ~~interpretation~~ of the pitch under the temperament map. Ideally the resultant JI pitch system will have low [[prime limit]] and a compact lattice.		In [[regular temperament theory]], '''detempering''' is the process of taking a tempered pitch system and replacing each of its pitches with a nearby [[JI]] pitch (called a [[transversal]]). Specifically, a '''detempered scale''' or a '''detemperament''' has each pitch of a tempered scale (according to a fixed regular temperament) replaced with some set of JI interpretations of the pitch under the temperament map. If exactly one JI interpretation is used for each pitch, then the detempering is called a '''one-to-one detempering''' Ideally the resultant JI pitch system will have low [[prime limit]] and a compact lattice.

	It is a distinct concept from a [[Neji\|quasi-equal rational tuning, or neji]], the main difference being that a neji replaces an equal temperament's pitches with pitches from a single harmonic series.		It is a distinct concept from a [[Neji\|quasi-equal rational tuning, or neji]], the main difference being that a neji replaces an equal temperament's pitches with pitches from a single harmonic series.