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 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.

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 a compact lattice.

The term ''detempering'' is often also used in an RTT-agnostic way to refer to a scale which, when some subset of its step sizes are equated, "tempers" to a given simpler scale structure (with fewer step sizes). In this sense, [[diasem]] (LMLSLMLSL) is a detempering of [[semiquartal]] (LSLSLSLSL) which "detempers" the S step of semiquartal into two steps sizes M and S.

Revision as of 05:28, 3 September 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits mNo edit summary ← Older edit		Revision as of 05:34, 3 September 2021 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits m prime limit is given by the choice of temperament interpretation 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 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.		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 a compact lattice.

	The term ''detempering'' is often also used in an RTT-agnostic way to refer to a scale which, when some subset of its step sizes are equated, "tempers" to a given simpler scale structure (with fewer step sizes). In this sense, [[diasem]] (LMLSLMLSL) is a detempering of [[semiquartal]] (LSLSLSLSL) which "detempers" the S step of semiquartal into two steps sizes M and S.		The term ''detempering'' is often also used in an RTT-agnostic way to refer to a scale which, when some subset of its step sizes are equated, "tempers" to a given simpler scale structure (with fewer step sizes). In this sense, [[diasem]] (LMLSLMLSL) is a detempering of [[semiquartal]] (LSLSLSLSL) which "detempers" the S step of semiquartal into two steps sizes M and S.