Mathematical theory of regular temperaments: Difference between revisions
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{{main| Normal lists #Normal val list }} | {{main| Normal lists #Normal val list }} | ||
Given a list of vals, we may [[ | Given a list of vals, we may [[Mathematical theory of saturation|saturate]] it and reduce it using the [[Normal lists|Hermite normal form]] to a normal val list, which canonically represents the abstract temperament. Applying the vals successively (an operation we may regard as a matrix multiplication if we like) to a rational interval gives an element in an abelian group representing the notes of the temperament. For example, the normal val list for 7-limit miracle is [{{val| 1 1 3 3 }}, {{val| 0 6 -7 -2 }}] and applying this to the monzo for either 16/15 or 15/14 leads to [0 1]. | ||
=== Frobenius projection matrix === | === Frobenius projection matrix === | ||