Exotemperament: Difference between revisions

Godtone (talk | contribs)
m 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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Godtone (talk | contribs)
m 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.
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 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.
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/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.