Exotemperament: Difference between revisions
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An '''exotemperament''' or '''macrotemperament''' is a very inaccurate [[regular temperament]], or in other words, one which [[tempers out]] an interval that is very large and low-[[complexity]] or otherwise equates wildly different intervals. | An '''exotemperament''' or '''macrotemperament''' is a very inaccurate [[regular temperament]], or in other words, one which [[tempers out]] an interval that is very large and low-[[complexity]] or otherwise equates wildly different intervals. Examples of exotemperaments are [[father]] (tempers out [[16/15]], ≈111.7¢), [[trienstonic clan|trienstonian]] (tempers out [[28/27]], ≈63¢), and [[dicot]] (tempers out [[25/24]], ≈70.7¢). | ||
The main useful property of exotemperaments is their role as "archetypes" for different ways of organizing/thinking about/structuring [[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. | The main useful property of exotemperaments is their role as "archetypes" for different ways of organizing/thinking about/structuring [[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. | ||
Revision as of 14:22, 1 January 2025
An exotemperament or macrotemperament is a very inaccurate regular temperament, or in other words, one which tempers out an interval that is very large and low-complexity or otherwise equates wildly different intervals. Examples of exotemperaments are father (tempers out 16/15, ≈111.7¢), trienstonian (tempers out 28/27, ≈63¢), and dicot (tempers out 25/24, ≈70.7¢).
The main useful property of exotemperaments is their role as "archetypes" for different ways of organizing/thinking about/structuring JI and temperaments alike, that is, as mappings. 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.
The opposite of an exotemperament is a microtemperament.