Detempering: Difference between revisions

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In [[regular temperament theory]], '''detempering''' is the process of taking a tempered [[tuning system]] and replacing each of its pitches with one or more pitches from its [[preimage]], that is, the just or tempered pitches that the pitch represents. It is the opposite of [[tempering out|tempering]]. Specifically, a '''detempered system''' (aka '''detemperament''' or '''detempering''') has each pitch of a tempered system (according to a fixed regular temperament) replaced with some set of interpretations of the pitch under the temperament mapping. If exactly one JI interpretation is used for each degree of a scale, then the detempered scale is called a [[transversal]], an '''epimorphic scale''' or ''one-to-one detempering''. Ideally the resultant ~~JI pitch system~~ will have a compact lattice. A higher rank temperament is also called a detempering of a lower-rank temperament if the lower-rank temperament results from tempering out one or more commas in the higher-rank temperament. For example, meantone is a detempering of 12edo.

In [[regular temperament theory]], '''detempering''' is the process of taking a tempered [[tuning system]] and replacing each of its pitches with one or more pitches from its [[preimage]], that is, the just or tempered pitches that the pitch represents. It is the opposite of [[tempering out|tempering]]. Specifically, a '''detempered system''' (aka '''detemperament''' or '''detempering''') has each pitch of a tempered system (according to a fixed regular temperament) replaced with some set of interpretations of the pitch under the temperament mapping. If exactly one interpretation is used for each degree of a scale, then the detempered scale is called a [[transversal]], an '''epimorphic scale''' or ''one-to-one detempering''. Ideally the resultant detempered scale will have a compact lattice. A higher rank temperament is also called a detempering of a lower-rank temperament if the lower-rank temperament results from tempering out one or more commas in the higher-rank temperament. For example, meantone is a detempering of 12edo.

Detempering is one way among many to create a [[neji]], or a JI scale approximating a given scale.

Revision as of 08:54, 7 April 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,636 edits m →Epimorphic scales ← Older edit		Revision as of 08:56, 7 April 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,636 edits mNo edit summary Newer edit →
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	In [[regular temperament theory]], '''detempering''' is the process of taking a tempered [[tuning system]] and replacing each of its pitches with one or more pitches from its [[preimage]], that is, the just or tempered pitches that the pitch represents. It is the opposite of [[tempering out\|tempering]]. Specifically, a '''detempered system''' (aka '''detemperament''' or '''detempering''') has each pitch of a tempered system (according to a fixed regular temperament) replaced with some set of interpretations of the pitch under the temperament mapping. If exactly one JI interpretation is used for each degree of a scale, then the detempered scale is called a [[transversal]], an '''epimorphic scale''' or ''one-to-one detempering''. Ideally the resultant ~~JI pitch system~~ will have a compact lattice. A higher rank temperament is also called a detempering of a lower-rank temperament if the lower-rank temperament results from tempering out one or more commas in the higher-rank temperament. For example, meantone is a detempering of 12edo.		In [[regular temperament theory]], '''detempering''' is the process of taking a tempered [[tuning system]] and replacing each of its pitches with one or more pitches from its [[preimage]], that is, the just or tempered pitches that the pitch represents. It is the opposite of [[tempering out\|tempering]]. Specifically, a '''detempered system''' (aka '''detemperament''' or '''detempering''') has each pitch of a tempered system (according to a fixed regular temperament) replaced with some set of interpretations of the pitch under the temperament mapping. If exactly one interpretation is used for each degree of a scale, then the detempered scale is called a [[transversal]], an '''epimorphic scale''' or ''one-to-one detempering''. Ideally the resultant detempered scale will have a compact lattice. A higher rank temperament is also called a detempering of a lower-rank temperament if the lower-rank temperament results from tempering out one or more commas in the higher-rank temperament. For example, meantone is a detempering of 12edo.

	Detempering is one way among many to create a [[neji]], or a JI scale approximating a given scale.		Detempering is one way among many to create a [[neji]], or a JI scale approximating a given scale.