Exotemperament

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Revision as of 00:21, 9 January 2025 by Godtone (talk | contribs) (make more neutral and representative (i failed to account for that 36/35 can spread its damage over more primes, making it strangely seem more reasonable than 49/48 which should be noted for its contentiousness (depending on who you ask)))
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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¢). Depending on both who you ask and the specific tunings, timbres and chords used, others such as mint (tempers out (6/5)/(7/6) = 36/35, ≈48.8¢) and semaphore (tempers out (7/6)/(8/7) = 49/48, ≈35.7¢) 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