Comma basis: Difference between revisions
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The comma basis is considered the dual of the temperament's [[mapping]] matrix. Temperaments may be identified by either their mapping or comma basis. | The comma basis is considered the dual of the temperament's [[mapping]] matrix. Temperaments may be identified by either their mapping or comma basis. | ||
Functions for finding the nullspace of a matrix are readily available in many math libraries. All you need to do to get a comma basis for a mapping is to find the nullspace. To learn | Functions for finding the nullspace of a matrix are readily available in many math libraries. All you need to do to get a comma basis for a mapping is to find the nullspace. To learn about finding the nullspace by hand, see [[Dave Keenan & Douglas Blumeyer's guide to RTT/Exploring temperaments #Nullspace]]. | ||
To reverse the nullspace operation, that is, to find a mapping from a comma basis, you can also use the nullspace operation; the relationship between a matrix and its nullspace essentially works both ways. | To reverse the nullspace operation, that is, to find a mapping from a comma basis, you can also use the nullspace operation; the relationship between a matrix and its nullspace essentially works both ways. | ||