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

Revision as of 07:22, 1 July 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.