&: Difference between revisions

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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".

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]].

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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:Theory]]~~

[[Category:Terms]]

[[Category:Val]]

[[Category:Method]]

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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".
-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]].
@@ Line 9: / Line 7: @@
 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:Theory]]
 [[Category:Terms]]
 [[Category:Val]]
 [[Category:Method]]