Exotemperament: Difference between revisions
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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¢). Depending on both who you ask and the specific tunings, timbres and chords used, others such as [[mint temperaments|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. | 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¢). Depending on both who you ask and the specific tunings, timbres and chords used, others such as [[mint temperaments|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, 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. | 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. | ||
The opposite of an exotemperament is a [[microtemperament]]. | The opposite of an exotemperament is a [[microtemperament]]. | ||
Revision as of 01:31, 25 September 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.
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, structuring, or thinking about 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. 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.
The opposite of an exotemperament is a microtemperament.