Detempering: Difference between revisions
Cmloegcmluin (talk | contribs) disambiguate wording, clarify relationship with transversal scales, and remove potential mistaken usage of "transversal" |
JI shouldn't be assumed to be the result. "Detempered scale" -> "detempered system". Re-add "detemperament" |
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In [[regular temperament theory]], '''detempering''' is the process of taking a tempered | 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 pitch, then the detempering is called a [[transversal]], 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. | ||
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. | |||
The term ''deregularization'' can be used as a [[JI-agnostic]] alternative to ''detempering''. In this sense, [[diasem]] (LMLSLMLSL) is a deregularization of [[semiquartal]] (LSLSLSLSL) which "detempers" the S step of semiquartal into two steps sizes M and S. | The term ''deregularization'' can be used as a [[JI-agnostic]] alternative to ''detempering''. In this sense, [[diasem]] (LMLSLMLSL) is a deregularization of [[semiquartal]] (LSLSLSLSL) which "detempers" the S step of semiquartal into two steps sizes M and S. | ||
Revision as of 07:16, 20 January 2023
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. 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 pitch, then the detempering is called a transversal, 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.
The term deregularization can be used as a JI-agnostic alternative to detempering. In this sense, diasem (LMLSLMLSL) is a deregularization of semiquartal (LSLSLSLSL) which "detempers" the S step of semiquartal into two steps sizes M and S.
It is a distinct concept from a 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.