Pathology of enfactoring: Difference between revisions

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There's a couple good ways to interpret this situation:

# We've turned on a teleportation field for every point outside this swath, so that it moves by these (-3,2) intervals until it finds its way inside the swath.

# We've rolled up space, so that the line from 1/1 to 9/~~8 ₋ the~~ width of our ~~swath ₋ is~~ like the circumference of a tube. In this case, since we're only working with 3-limit JI, "space" was only ever 2D, so we can just think of it as paper that we've rolled up, so the pair of dotted lines visualized here are touching along their entire lengths (and if you wanted to imagine further copies of these dotted lines at every (-3,2) interval farther out in either direction, and the paper is infinitely thin, just stack all the dotted lines on top of each other forever).

# We've rolled up space, so that the line from 1/1 to 9/8 — the width of our swath — is like the circumference of a tube. In this case, since we're only working with 3-limit JI, "space" was only ever 2D, so we can just think of it as paper that we've rolled up, so the pair of dotted lines visualized here are touching along their entire lengths (and if you wanted to imagine further copies of these dotted lines at every (-3,2) interval farther out in either direction, and the paper is infinitely thin, just stack all the dotted lines on top of each other forever).

Either way, then we just superimpose the new tempered lattice on top. It's drawn in blue.

@@ Line 13: / Line 13: @@
 There's a couple good ways to interpret this situation:
 # We've turned on a teleportation field for every point outside this swath, so that it moves by these (-3,2) intervals until it finds its way inside the swath.
-# We've rolled up space, so that the line from 1/1 to 9/8 ₋ the width of our swath ₋ is like the circumference of a tube. In this case, since we're only working with 3-limit JI, "space" was only ever 2D, so we can just think of it as paper that we've rolled up, so the pair of dotted lines visualized here are touching along their entire lengths (and if you wanted to imagine further copies of these dotted lines at every (-3,2) interval farther out in either direction, and the paper is infinitely thin, just stack all the dotted lines on top of each other forever).
+# We've rolled up space, so that the line from 1/1 to 9/8 — the width of our swath — is like the circumference of a tube. In this case, since we're only working with 3-limit JI, "space" was only ever 2D, so we can just think of it as paper that we've rolled up, so the pair of dotted lines visualized here are touching along their entire lengths (and if you wanted to imagine further copies of these dotted lines at every (-3,2) interval farther out in either direction, and the paper is infinitely thin, just stack all the dotted lines on top of each other forever).
 Either way, then we just superimpose the new tempered lattice on top. It's drawn in blue.