Exotemperament: Difference between revisions

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An '''exotemperament''' or '''macrotemperament''' is a very inaccurate [[regular temperament]], or in other words, one which [[tempering out|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¢). 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{{c}}), [[trienstonic clan|trienstonian]] (tempers out [[28/27]], ≈63.0{{c}}), and [[dicot family|dicot]] (tempers out [[25/24]], ≈70.7{{c}}). 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{{c}}) and [[semaphore]] (tempers out ([[7/6]])/([[8/7]]) = [[49/48]], ≈35.7{{c}}) 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.

To get one's head around music in exotemperaments, one needs to be less critical about what they hear and turn their attention to rough melodic and impressionistic categories instead.

Another 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.

In the most extreme case, an exotemperament may temper out a [[prime harmonic]] altogether, resulting in the total deletion of a prime from the system. While they mathematically fit the definition of a temperament, they are identical to [[JI subgroup]] restrictions; in other words, they are degenerate cases, not temperaments at all in the practical sense.

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 An '''exotemperament''' or '''macrotemperament''' is a very inaccurate [[regular temperament]], or in other words, one which [[tempering out|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¢). 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{{c}}), [[trienstonic clan|trienstonian]] (tempers out [[28/27]], ≈63.0{{c}}), and [[dicot family|dicot]] (tempers out [[25/24]], ≈70.7{{c}}). 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{{c}}) and [[semaphore]] (tempers out ([[7/6]])/([[8/7]]) = [[49/48]], ≈35.7{{c}}) 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.
+To get one's head around music in exotemperaments, one needs to be less critical about what they hear and turn their attention to rough melodic and impressionistic categories instead.
+Another 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.
 In the most extreme case, an exotemperament may temper out a [[prime harmonic]] altogether, resulting in the total deletion of a prime from the system. While they mathematically fit the definition of a temperament, they are identical to [[JI subgroup]] restrictions; in other words, they are degenerate cases, not temperaments at all in the practical sense.