A brief introduction to Regular Temperament Theory: Difference between revisions

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 When the generation of tunings is formulated in this way, the tools of linear algebra can be applied.
-The defining thing about a regular temperament is the the count of each generator required to approximate each prime number.<ref>Strictly speaking, it is the [[Canonical_form|canonical form]] of the rows of the mapping matrix that defines the temperament, because you can replace any set of generators with linear combinations of those generators, and change the mapping accordingly, to obtain the same temperament.</ref> This is called the temperament's [[Temperament_Mapping_Matrices_(M-maps)|mapping]], and can be represented as a matrix.
+The defining thing about a regular temperament is the the count of each generator required to approximate each prime number.<ref>Strictly speaking, it is the [[Canonical_form|canonical form]] of the mapping matrix that defines the temperament, because you can replace any set of generators with linear combinations of those generators, and change the mapping accordingly, to obtain the same temperament.</ref> This is called the temperament's [[Temperament_Mapping_Matrices_(M-maps)|mapping]], and can be represented as a matrix.
 We can then institute computer searches to find optimum mappings, with our desired balance of error versus complexity. Many such searches have been done and [[Tour_of_Regular_Temperaments|many resulting temperaments named and catalogued]].
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