Exotemperament - Revision history

FloraC: + how to listen

2025-12-31T08:43:07Z

+ how to listen

← Older revision		Revision as of 08:43, 31 December 2025
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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.		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.		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.

FloraC: "Degenerate" cases do exist but "bixby" and "archon" aren't proper examples

2025-12-31T08:30:06Z

"Degenerate" cases do exist but "bixby" and "archon" aren't proper examples

← Older revision		Revision as of 08:30, 31 December 2025
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	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.

	In the most extreme case, an exotemperament may temper a prime altogether, resulting in the total deletion of a prime from the system~~, as is the case with [[bixby]] and [[archon]]~~. 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.		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.

	The opposite of an exotemperament is a [[microtemperament]].		The opposite of an exotemperament is a [[microtemperament]].

Eufalesio: Degeneracy

2025-12-31T01:55:30Z

Degeneracy

← Older revision		Revision as of 01:55, 31 December 2025
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	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.

			In the most extreme case, an exotemperament may temper a prime altogether, resulting in the total deletion of a prime from the system, as is the case with [[bixby]] and [[archon]]. 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.

	The opposite of an exotemperament is a [[microtemperament]].		The opposite of an exotemperament is a [[microtemperament]].

2^67-1 at 01:31, 25 September 2025

2025-09-25T01:31:37Z

← Older revision		Revision as of 01:31, 25 September 2025
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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]].

VectorGraphics at 02:51, 16 June 2025

2025-06-16T02:51:56Z

← Older revision		Revision as of 02:51, 16 June 2025
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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.		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]].

FloraC: Cleanup

2025-01-17T17:01:30Z

Cleanup

← Older revision		Revision as of 17:01, 17 January 2025
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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 [[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¢), [[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, 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.

	The opposite of an exotemperament is a [[microtemperament]].		The opposite of an exotemperament is a [[microtemperament]].

Godtone: 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))

2025-01-09T00:21:45Z

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))

← Older revision		Revision as of 00:21, 9 January 2025
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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.

Godtone: 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!

2025-01-03T01:15:42Z

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!

← Older revision		Revision as of 01:15, 3 January 2025
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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. ~~Examples~~ of exotemperaments are [[father]] (tempers out [[16/15]], ≈111.7¢), [[trienstonic clan\|trienstonian]] (tempers out [[28/27]], ≈63¢), and [[dicot]] (tempers out [[25/24]], ≈70.7¢).		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.

	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.

FloraC: Mint is generally not considered an exotemp

2025-01-01T14:22:53Z

Mint is generally not considered an exotemp

← Older revision		Revision as of 14:22, 1 January 2025
Line 1:		Line 1:
	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. Examples of exotemperaments are [[father]] (tempers out [[16/15]], ≈111.7¢), [[trienstonic clan\|trienstonian]] (tempers out [[28/27]], ≈63¢), and [[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¢)~~. Others such as [[mint temperaments\|mint]] (tempers out [[36/35]], ≈48.8¢) 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.

ArrowHead294 at 14:17, 1 January 2025

2025-01-01T14:17:54Z

← Older revision		Revision as of 14:17, 1 January 2025
Line 1:		Line 1:
	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]] (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¢). Others such as [[mint temperaments\|mint]] (tempers out [[36/35]], ≈48.8¢) 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.