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.

Notable 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¢). Others such as [[mint temperaments|mint]] (tempers out [[36/35]], ≈48.8¢) could also be considered exotemperaments within their respective limits or subgroups.

Notable examples of exotemperaments are [[father]] (tempers out [[16/15]], ≈111.7¢), [[trienstonic clan|trienstonian]] (tempers out [[28/27]], ≈63¢), and [[dicot family|dicot]] (tempers out [[25/24]], ≈70.7¢). Others such as [[mint temperaments|mint]] (tempers out [[36/35]], ≈48.8¢) could also be considered exotemperaments within their respective limits or subgroups.

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.

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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.
-Notable 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¢). Others such as [[mint temperaments|mint]] (tempers out [[36/35]], ≈48.8¢) could also be considered exotemperaments within their respective limits or subgroups.
+Notable examples of exotemperaments are [[father]] (tempers out [[16/15]], ≈111.7¢), [[trienstonic clan|trienstonian]] (tempers out [[28/27]], ≈63¢), and [[dicot family|dicot]] (tempers out [[25/24]], ≈70.7¢). Others such as [[mint temperaments|mint]] (tempers out [[36/35]], ≈48.8¢) could also be considered exotemperaments within their respective limits or subgroups.
 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.