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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}} = {{ | 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]]. | ||
Revision as of 21:35, 11 October 2021
The & (ampersand) operator is commonly used[1] to join equal temperaments into higher-rank regular temperaments. This is sometimes called "cross-breeding", because the maps for these ETs are sometimes called "breeds".
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 ⟨12 19 28]&⟨19 30 44] = [⟨12 19 28] ⟨19 30 44]⟩. This is the mapping for meantone temperament; it may not be immediately apparent, but reducing that mapping matrix can give something more familiar like [⟨1 1 0] ⟨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.
- ↑ For example, on Graham Breed's temperament finding tool.