Comma basis: Difference between revisions
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== With respect to the mapping == | == With respect to the mapping == | ||
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 more about finding the nullspace, see [[Dave Keenan %26 Douglas Blumeyer%27s guide to RTT | 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 more about finding the nullspace, see [[Dave Keenan %26 Douglas Blumeyer%27s guide to RTT/Exploring temperaments#Nullspace|here]]. | ||
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. | ||