Douglas Blumeyer's RTT How-To: Difference between revisions

Line 838:

If the familiar usage of vectors has been as prime count lists, we can now generalize that definition to things like this {{monzo|1 1}}: generator count lists. Since interval vectors are often called monzos, you’ll often see these called tempered monzos or [[Tmonzos_and_Tvals|tmonzos]] for short. There’s very little difference. We can use these vectors as coordinates in a lattice just the same as before. The main difference is that the nodes we visit on this lattice aren’t pure JI; they’re a tempered lattice.

We haven’t specified the size of either of these generators, but that’s not important here. These mappings are just like a set of requirements for any pair of generators that might implement this temperament. This is as good a time as any to emphasize the fact that temperaments are abstract; they are not ready-to-go tunings, but more like instructions for a tuning to follow. This can sometimes feel frustrating or hard to understand, but ultimately it’s a ~~bit~~ part of the power of temperament theory.

We haven’t specified the size of either of these generators, but that’s not important here. These mappings are just like a set of requirements for any pair of generators that might implement this temperament. This is as good a time as any to emphasize the fact that temperaments are abstract; they are not ready-to-go tunings, but more like instructions for a tuning to follow. This can sometimes feel frustrating or hard to understand, but ultimately it’s a big part of the power of temperament theory.

The critical thing here is that if {{monzo|-4 4 -1}} is mapped to 0 steps by {{val|5 8 12}} individually and to 0 steps by {{val|7 11 16}} individually, then in total it comes out to 0 steps in the temperament, and thus is tempered out, or has vector {{monzo|0 0}}.

@@ Line 838: / Line 838: @@
 If the familiar usage of vectors has been as prime count lists, we can now generalize that definition to things like this {{monzo|1 1}}: generator count lists. Since interval vectors are often called monzos, you’ll often see these called tempered monzos or [[Tmonzos_and_Tvals|tmonzos]] for short. There’s very little difference. We can use these vectors as coordinates in a lattice just the same as before. The main difference is that the nodes we visit on this lattice aren’t pure JI; they’re a tempered lattice.
-We haven’t specified the size of either of these generators, but that’s not important here. These mappings are just like a set of requirements for any pair of generators that might implement this temperament. This is as good a time as any to emphasize the fact that temperaments are abstract; they are not ready-to-go tunings, but more like instructions for a tuning to follow. This can sometimes feel frustrating or hard to understand, but ultimately it’s a bit part of the power of temperament theory.
+We haven’t specified the size of either of these generators, but that’s not important here. These mappings are just like a set of requirements for any pair of generators that might implement this temperament. This is as good a time as any to emphasize the fact that temperaments are abstract; they are not ready-to-go tunings, but more like instructions for a tuning to follow. This can sometimes feel frustrating or hard to understand, but ultimately it’s a big part of the power of temperament theory.
 The critical thing here is that if {{monzo|-4 4 -1}} is mapped to 0 steps by {{val|5 8 12}} individually and to 0 steps by {{val|7 11 16}} individually, then in total it comes out to 0 steps in the temperament, and thus is tempered out, or has vector {{monzo|0 0}}.