Exotemperament: Difference between revisions
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! Tag: Undo |
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¢). | 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. | ||