Exotemperament

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Revision as of 01:15, 3 January 2025 by Godtone (talk | contribs) (it said "could also be considered" not "has to also be considered", and there is nothing that even concords like both 7/6 and 6/5. mint is obviously an exotemp if 49/48 is contentious. it's literally tempering out an entire quarter-tone that exists directly between multiple target intervals!)
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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¢), trienstonian (tempers out 28/27, ≈63¢), and dicot (tempers out 25/24, ≈70.7¢). Others such as 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 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.

See also