Cross-domain temperament merging: Difference between revisions

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So from these two opposing bulleted facts above, we can conclude that for any pair of domains where neither one is a subspace of the other, there would be no way for us to express ''either intervals or maps'' from one in the other. And that's why we could say that they're incomparable domains.

Notably, there is still a way to get intervals to a subspace, and maps to a superspace, but it's indirect. To do so, take the [[dual]] of your object, then change basis, then take the [[dual]] again. So for a mapping you would use the nullspace function to convert it to its corresponding comma basis, change domain basis, and then use the nullspace function to convert it back to its corresponding mapping on the other side.

Notably, there is still a way to get intervals to a subspace, and maps to a superspace, but it's indirect. To do so, [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_exploring_temperaments#Nullspace|take the dual]] of your object, then change basis, then take the dual again. So for a mapping you would use the nullspace function to convert it to its corresponding comma basis, change domain basis, and then use the nullspace function to convert it back to its corresponding mapping on the other side.

== General method to determine whether a domain is a subspace of another ==

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 So from these two opposing bulleted facts above, we can conclude that for any pair of domains where neither one is a subspace of the other, there would be no way for us to express ''either intervals or maps'' from one in the other. And that's why we could say that they're incomparable domains.
-Notably, there is still a way to get intervals to a subspace, and maps to a superspace, but it's indirect. To do so, take the [[dual]] of your object, then change basis, then take the [[dual]] again. So for a mapping you would use the nullspace function to convert it to its corresponding comma basis, change domain basis, and then use the nullspace function to convert it back to its corresponding mapping on the other side.
+Notably, there is still a way to get intervals to a subspace, and maps to a superspace, but it's indirect. To do so, [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_exploring_temperaments#Nullspace|take the dual]] of your object, then change basis, then take the dual again. So for a mapping you would use the nullspace function to convert it to its corresponding comma basis, change domain basis, and then use the nullspace function to convert it back to its corresponding mapping on the other side.
 == General method to determine whether a domain is a subspace of another ==