Eigenmonzo: Difference between revisions

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== With respect to the projection matrix ==

The "eigen" part of the term "eigenmonzo" comes from the fact that these intervals are [[wikipedia: Eigenvalues and eigenvectors|eigenvectors]] of the tuning's [[projection matrix]] (not the [[~~Temperament_mapping_matrices~~|temperament's mapping matrix]]). Only eigenvectors of the projection matrix with [[wikipedia: Eigenvalues and eigenvectors|eigenvalue]] equal to 1 are considered eigenmonzos, while those with eigenvalue equal to 0 are the vanishing commas of the temperament; in other words, a vector that is a monzo and an eigenvector is not necessarily an eigenmonzo.

The "eigen" part of the term "eigenmonzo" comes from the fact that these intervals are [[wikipedia: Eigenvalues and eigenvectors|eigenvectors]] of the tuning's [[projection matrix]] (not the [[mapping|temperament's mapping matrix]]). Only eigenvectors of the projection matrix with [[wikipedia: Eigenvalues and eigenvectors|eigenvalue]] equal to 1 are considered eigenmonzos, while those with eigenvalue equal to 0 are the vanishing commas of the temperament; in other words, a vector that is a monzo and an eigenvector is not necessarily an eigenmonzo.

The "monzo" part of "eigenmonzo" should not be taken to imply that the interval is notated in monzo form, e.g. {{monzo| 2 -1 }}; for example, 4/3 may be called an eigenmonzo.

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 == With respect to the projection matrix ==
-The "eigen" part of the term "eigenmonzo" comes from the fact that these intervals are [[wikipedia: Eigenvalues and eigenvectors|eigenvectors]] of the tuning's [[projection matrix]] (not the [[Temperament_mapping_matrices|temperament's mapping matrix]]). Only eigenvectors of the projection matrix with [[wikipedia: Eigenvalues and eigenvectors|eigenvalue]] equal to 1 are considered eigenmonzos, while those with eigenvalue equal to 0 are the vanishing commas of the temperament; in other words, a vector that is a monzo and an eigenvector is not necessarily an eigenmonzo.
+The "eigen" part of the term "eigenmonzo" comes from the fact that these intervals are [[wikipedia: Eigenvalues and eigenvectors|eigenvectors]] of the tuning's [[projection matrix]] (not the [[mapping|temperament's mapping matrix]]). Only eigenvectors of the projection matrix with [[wikipedia: Eigenvalues and eigenvectors|eigenvalue]] equal to 1 are considered eigenmonzos, while those with eigenvalue equal to 0 are the vanishing commas of the temperament; in other words, a vector that is a monzo and an eigenvector is not necessarily an eigenmonzo.
 The "monzo" part of "eigenmonzo" should not be taken to imply that the interval is notated in monzo form, e.g. {{monzo| 2 -1 }}; for example, 4/3 may be called an eigenmonzo.