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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.)
| | #REDIRECT [[Temperament merging]] |
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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".
| | [[Category:Symbols]] |
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| 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}}}}.
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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]].
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| Note that while a given cross-breeding uniquely defines a temperament, a given temperament has multiple cross-breedings.
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| The pipe symbol '''|''' has been proposed as the operator for the opposite operation, [[meet]].
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| [[Category:Temperament]]
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| [[Category:Regular temperament theory]]
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| [[Category:Theory]]
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| [[Category:Terms]]
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| [[Category:Val]]
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| [[Category:Method]] | |