Exotemperament: Difference between revisions

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The main useful property of exotemperaments is their role as "archetypes" for different ways of organizing, structuring, or thinking about [[JI]] and [[temperaments]] alike, that is, as [[mapping]]s. In this capacity, they are often useful as characterizing the musical logics underlying various [[JI]] scales, or more rarely, as the logics shared between temperaments with similar structure but different tuning, though they have also been explored by many people in their tempered versions out of curiosity. For example, [[dicot]] is the literal realization of the general tertian triadic structure of a fifth being constructed from two thirds, and [[father]] is the literal realization of the treatment of suspended harmony as tertian.

In the most extreme case, an exotemperament may temper a prime altogether, resulting in the total deletion of a prime from the system, as is the case with [[bixby]] and [[archon]]. While they mathematically fit the definition of a temperament, they are identical to [[JI subgroup]] restrictions; in other words, they are degenerate cases, not temperaments at all in the practical sense.

The opposite of an exotemperament is a [[microtemperament]].

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 The main useful property of exotemperaments is their role as "archetypes" for different ways of organizing, structuring, or thinking about [[JI]] and [[temperaments]] alike, that is, as [[mapping]]s. In this capacity, they are often useful as characterizing the musical logics underlying various [[JI]] scales, or more rarely, as the logics shared between temperaments with similar structure but different tuning, though they have also been explored by many people in their tempered versions out of curiosity. For example, [[dicot]] is the literal realization of the general tertian triadic structure of a fifth being constructed from two thirds, and [[father]] is the literal realization of the treatment of suspended harmony as tertian.
+In the most extreme case, an exotemperament may temper a prime altogether, resulting in the total deletion of a prime from the system, as is the case with [[bixby]] and [[archon]]. While they mathematically fit the definition of a temperament, they are identical to [[JI subgroup]] restrictions; in other words, they are degenerate cases, not temperaments at all in the practical sense.
 The opposite of an exotemperament is a [[microtemperament]].