Diamond tradeoff

Revision as of 15:26, 27 May 2021 by Inthar (talk | contribs)

A tuning for a rank-r p-limit regular temperament is diamond pure, or diamond nice, if it fits the following definition: we may define the diamond pure tuning range by finding the convex hull in tuning space of the set of all tunings with r eigenmonzos chosen as follows: one eigenmonzo 2 (pure octaves tunings) and the rest of the eigenmonzos any set of r - 1 members of the p-odd limit tonality diamond, whenever such a tuning is defined.

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 "nice" tuning range.

Diamond pure tunings are always guaranteed to occur, but diamond monotone tunings are not.

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