&

(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 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.

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