Eigenmonzo basis: Difference between revisions
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== See also == | == See also == | ||
* [[ | * [[unchanged-interval basis]] | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 00:34, 20 February 2025
Given a regular temperament tuning T, an eigenmonzo (unchanged-interval) is a rational interval q such that T(q) = q; that is, T tunes q justly. The eigenmonzos of T define a just intonation subgroup, the eigenmonzo subgroup.
One sort of example is provided by any equal division of the octave, where 2 (the octave) is always an eigenmonzo and the group {2n} of powers of 2 is the eigenmonzo subgroup. The idea is most useful in connection to the minimax tunings of regular temperaments, where for a rank-r regular temperament, the eigenmonzo subgroup is a rank-r JI subgroup whose generators, together with generators for the commas of the subgroup, can be used to define the projection matrix of the minimax tuning and hence define the tuning.