& - Revision history

Fredg999 category edits: Categories

2022-03-14T00:12:02Z

Cmloegcmluin: redirect to complete article

2022-01-03T03:44:58Z

redirect to complete article

← Older revision		Revision as of 03:44, 3 January 2022
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	~~The '''&''' (ampersand) operator is commonly used<ref>For example, on~~ [~~http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to~~ [~~[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".~~		#REDIRECT [[Temperament merging]]

	For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{ket\|{{map\|12 19 28}} {{map\|19 30 44}}}}, or in other words, to concatenate (and reduce) mappings. This results in the mapping for [[meantone]] temperament; it may not be immediately apparent after just the concatenation step, but [[Normal lists\|reducing]] that mapping matrix can give something more familiar like {{ket\|{{map\|1 1 0}} {{map\|0 1 4}}}}.

	~~More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].~~

	~~Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.~~

	~~The pipe symbol '''\|''' is used as the operator for the opposite operation, [[meet]].~~

	~~[[Category:Regular temperament theory]]~~
	~~[[Category:Terms]]~~
	~~[[Category:Val]]~~
	~~[[Category:Method~~]]

Cmloegcmluin: consolidate categories, and remove temporary parenthetical now that the meet and join questions are resolved

2021-12-25T13:33:52Z

consolidate categories, and remove temporary parenthetical now that the meet and join questions are resolved

← Older revision		Revision as of 13:33, 25 December 2021
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	(Many statements on this page have been recently thrown into question by recent developments re: meet and join. It will be updated ASAP to conform to the conclusions we arrive at, and probably eventually merged in to a general audience version of the Meet and join page, in part because concerns were recently raised about the format of the page title.)

	The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".		The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".

	For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{ket\|{{map\|12 19 28}} {{map\|19 30 44}}}}. This is the mapping for [[meantone]] temperament; it may not be immediately apparent, but [[Normal lists\|reducing]] that mapping matrix can give something more familiar like {{ket\|{{map\|1 1 0}} {{map\|0 1 4}}}}.		For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{ket\|{{map\|12 19 28}} {{map\|19 30 44}}}}, or in other words, to concatenate (and reduce) mappings. This results in the mapping for [[meantone]] temperament; it may not be immediately apparent after just the concatenation step, but [[Normal lists\|reducing]] that mapping matrix can give something more familiar like {{ket\|{{map\|1 1 0}} {{map\|0 1 4}}}}.

	More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].		More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].
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	Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.		Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.

	The pipe symbol '''\|''' ~~has been proposed~~ as the operator for the opposite operation, [[meet]].		The pipe symbol '''\|''' is used as the operator for the opposite operation, [[meet]].

	~~[[Category:Temperament]]~~
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Theory]]~~
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Val]]		[[Category:Val]]
	[[Category:Method]]		[[Category:Method]]

Cmloegcmluin at 17:28, 20 December 2021

2021-12-20T17:28:51Z

← Older revision		Revision as of 17:28, 20 December 2021
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			(Many statements on this page have been recently thrown into question by recent developments re: meet and join. It will be updated ASAP to conform to the conclusions we arrive at, and probably eventually merged in to a general audience version of the Meet and join page, in part because concerns were recently raised about the format of the page title.)

	The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".		The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".

Cmloegcmluin: add categories

2021-12-10T17:13:33Z

add categories

← Older revision		Revision as of 17:13, 10 December 2021
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	The pipe symbol '''\|''' has been proposed as the operator for the opposite operation, [[meet]].		The pipe symbol '''\|''' has been proposed as the operator for the opposite operation, [[meet]].

			[[Category:Temperament]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
			[[Category:Theory]]
			[[Category:Terms]]
	[[Category:Val]]		[[Category:Val]]
	[[Category:Method]]		[[Category:Method]]

Cmloegcmluin: note re: pipe for meet

2021-10-11T21:38:01Z

note re: pipe for meet

← Older revision		Revision as of 21:38, 11 October 2021
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	Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.		Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.

			The pipe symbol '''\|''' has been proposed as the operator for the opposite operation, [[meet]].

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Val]]		[[Category:Val]]
	[[Category:Method]]		[[Category:Method]]

Cmloegcmluin: fix bad vector and map templates

2021-10-11T21:35:16Z

fix bad vector and map templates

← Older revision		Revision as of 21:35, 11 October 2021
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	The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".		The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".

	For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{~~vector~~\|{{map\|12 19 28}} {{map\|19 30 44}}}}. This is the mapping for [[meantone]] temperament; it may not be immediately apparent, but [[Normal lists\|reducing]] that mapping matrix can give something more familiar like {{~~vector~~\|{{map\|1 1 0}} {{map\|0 1 4}}}}.		For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{ket\|{{map\|12 19 28}} {{map\|19 30 44}}}}. This is the mapping for [[meantone]] temperament; it may not be immediately apparent, but [[Normal lists\|reducing]] that mapping matrix can give something more familiar like {{ket\|{{map\|1 1 0}} {{map\|0 1 4}}}}.

	More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].		More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].

FloraC: +note the non-uniqueness of this notation

2021-07-07T10:47:22Z

+note the non-uniqueness of this notation

← Older revision		Revision as of 10:47, 7 July 2021
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	More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].		More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].

			Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Val]]		[[Category:Val]]
	[[Category:Method]]		[[Category:Method]]

FloraC: +categories

2021-07-01T07:22:16Z

+categories

← Older revision		Revision as of 07:22, 1 July 2021
Line 4:		Line 4:

	More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].		More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].

			[[Category:Regular temperament theory]]
			[[Category:Val]]
			[[Category:Method]]

FloraC: Improve linking style and correct meantone mapping

2021-07-01T07:21:03Z

Improve linking style and correct meantone mapping

← Older revision		Revision as of 07:21, 1 July 2021
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	The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular ~~temperaments~~]]. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed~~\|breeds~~]]".		The '''&''' (ampersand) operator is commonly used<ref>For example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool].</ref> to [[join]] [[equal temperaments]] into higher-[[rank]] [[regular temperament]]s. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "[[breed]]s".

	For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{vector\|{{map\|12 19 28}} {{map\|19 30 44}}}}. This is the mapping for [[meantone]] temperament; it may not be immediately apparent, but [[~~Normal_lists~~\|reducing]] that mapping matrix can give something more familiar like {{vector\|{{map\|1 1 0}} {{map\|0 1 -4}}}}.		For example, 12&19 means to join the [[map]] for [[12-ET]] with the map for [[19-ET]]. In the [[5-limit]], that looks like {{map\|12 19 28}}&{{map\|19 30 44}} = {{vector\|{{map\|12 19 28}} {{map\|19 30 44}}}}. This is the mapping for [[meantone]] temperament; it may not be immediately apparent, but [[Normal lists\|reducing]] that mapping matrix can give something more familiar like {{vector\|{{map\|1 1 0}} {{map\|0 1 4}}}}.

	More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].		More than two maps may be combined like this at a time, such as 22&34d&37 to give [[ares]]. The 'd' of 34d reveals that these representations of ET maps are in [[wart notation]].

← Older revision		Revision as of 00:12, 14 March 2022
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	#REDIRECT [[Temperament merging]]		#REDIRECT [[Temperament merging]]

			[[Category:Symbols]]