Projection: Difference between revisions

Line 1,268:

The typical use case for a projection matrix is to re-embed a temperament lattice back into the original JI space from which it was tempered. But it is also possible to project to a completely different JI space after tempering, even a higher-dimensional one than the original space, or a lower-dimensional one than the tempered lattice. As long as you know how to translate vectors in the destination space into size, it's fair game. In fact, there's nothing stopping you from taking vectors in that space and projecting again, and again, and again. Though the present author fails to see if there are any meaningful musical purposes for this much temperamental distortion.

== Comma bases should always have integer entries ==

While projections, generator embeddings, and unchanged-interval bases may have non-integer entries, comma bases should not. Rather than temper out a comma with rational entries, clear its denominators. And a comma with irrational entries is departing from a scenario where RTT has much practical value.

==Applications==

@@ Line 1,268: / Line 1,268: @@
 The typical use case for a projection matrix is to re-embed a temperament lattice back into the original JI space from which it was tempered. But it is also possible to project to a completely different JI space after tempering, even a higher-dimensional one than the original space, or a lower-dimensional one than the tempered lattice. As long as you know how to translate vectors in the destination space into size, it's fair game. In fact, there's nothing stopping you from taking vectors in that space and projecting again, and again, and again. Though the present author fails to see if there are any meaningful musical purposes for this much temperamental distortion.
+== Comma bases should always have integer entries ==
+While projections, generator embeddings, and unchanged-interval bases may have non-integer entries, comma bases should not. Rather than temper out a comma with rational entries, clear its denominators. And a comma with irrational entries is departing from a scenario where RTT has much practical value.
 ==Applications==