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.

The term ''detempering'' is often also used in an RTT-agnostic way to refer to a scale with more step sizes which, when some set of step sizes are identified, "temper" 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.

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.

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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.
+The term ''detempering'' is often also used in an RTT-agnostic way to refer to a scale with more step sizes which, when some set of step sizes are identified, "temper" 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.
 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.