Diamond monotone

A tuning for a rank-r p-limit regular temperament is diamond monotone, or diamond valid, if it satisfies the following condition: the p-odd limit tonality diamond, when sorted by increasing size, is mapped to a tempered version which is also monotone increasing (i.e. nondecreasing).

In the original work by Andrew Milne, Bill Sethares and James Plamondon — and to some extent on the wiki and in the regular temperament community — this tuning range was referred to simply as the "valid" tuning range.

For examples and other information, see the topic page Tuning ranges of regular temperaments.