Cross-domain temperament merging: Difference between revisions

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Elsewhere, these types of matrices have been called [[subgroup basis matrices]], but that terminology will not be used here, for the same reasons as are described in the last section of this article (here: [[Domain basis#Terminology: domain basis vs. subgroup]]).

As discussed earlier, only certain domain basis changes are possible: (here: [[Cross-domain temperament merging#Application: determining whether it is possible to change the domain]]). To quickly recap here, it is only possible to change between domains where one is a subspace of the other. So when we say a given basis change matrix works like a two-way bridge, there's a more specific way to say what we mean: a basis change matrix allows us to change either ''from the subspace to the superspace'', or ''from the superspace to the subspace''. Which direction we go just depends on which side we enter the bridge from: the right side or the left side.

As discussed earlier, only certain domain basis changes are possible (here: [[Cross-domain temperament merging#Application: determining whether it is possible to change the domain]]). To quickly recap here, it is only possible to change between domains where one is a subspace of the other. So when we say a given basis change matrix works like a two-way bridge, there's a more specific way to say what we mean: a basis change matrix allows us to change either ''from the subspace to the superspace'', or ''from the superspace to the subspace''. Which direction we go just depends on which side we enter the bridge from: the right side or the left side.

== Constructing a basis change matrix ==

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 Elsewhere, these types of matrices have been called [[subgroup basis matrices]], but that terminology will not be used here, for the same reasons as are described in the last section of this article (here: [[Domain basis#Terminology: domain basis vs. subgroup]]).
-As discussed earlier, only certain domain basis changes are possible: (here: [[Cross-domain temperament merging#Application: determining whether it is possible to change the domain]]). To quickly recap here, it is only possible to change between domains where one is a subspace of the other. So when we say a given basis change matrix works like a two-way bridge, there's a more specific way to say what we mean: a basis change matrix allows us to change either ''from the subspace to the superspace'', or ''from the superspace to the subspace''. Which direction we go just depends on which side we enter the bridge from: the right side or the left side.
+As discussed earlier, only certain domain basis changes are possible (here: [[Cross-domain temperament merging#Application: determining whether it is possible to change the domain]]). To quickly recap here, it is only possible to change between domains where one is a subspace of the other. So when we say a given basis change matrix works like a two-way bridge, there's a more specific way to say what we mean: a basis change matrix allows us to change either ''from the subspace to the superspace'', or ''from the superspace to the subspace''. Which direction we go just depends on which side we enter the bridge from: the right side or the left side.
 == Constructing a basis change matrix ==