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

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[[File:Shape_of_scale_of_movements_on_axes.png|thumb|left|200px|'''Figure 3e.''' the basic shape the scaled axes make between neighbor maps (maps with only 1 difference between their terms)]]

Our example ET will be 40. We'll start out at the map {{val|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (sometimes unfortunately called a "[[patent val]]", as referenced earlier).

Our example ET will be 40. We'll start out at the map {{val|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (sometimes unfortunately called a "[[patent val]]", which is related tot the generalized patent val concept referenced earlier).

From here, let’s move by a single step on the 5-axis by adding 1 to the 5-term of our map, from 93 to 94, therefore moving to the map {{val|40 63 94}}. This map is found directly to the left. This makes sense because the orientation of the 5-axis is horizontal, and the positive direction points out from the origin toward the left, so increases to the 5-term move us in that direction.

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We can imagine that if we hadn’t scaled the steps, as in our initial naive guess, we’d have ended up nowhere near the center of the diagram. How could we have, if the steps are all the same size, but we’re moving 28 of them to the left, but only 12 and 19 of them to the bottom left and top right? We’d clearly end up way, way further to the left, and also above the horizontal midline. And this is where pretty much any near-just ET would get plotted, because 3 being bigger than 2 would dominate its behavior, and 5 being larger still than 3 would dominate its behavior.

=== perspective ===

@@ Line 208: / Line 208: @@
 [[File:Shape_of_scale_of_movements_on_axes.png|thumb|left|200px|'''Figure 3e.''' the basic shape the scaled axes make between neighbor maps (maps with only 1 difference between their terms)]]
-Our example ET will be 40. We'll start out at the map {{val|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (sometimes unfortunately called a "[[patent val]]", as referenced earlier).
+Our example ET will be 40. We'll start out at the map {{val|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (sometimes unfortunately called a "[[patent val]]", which is related tot the generalized patent val concept referenced earlier).
 From here, let’s move by a single step on the 5-axis by adding 1 to the 5-term of our map, from 93 to 94, therefore moving to the map {{val|40 63 94}}. This map is found directly to the left. This makes sense because the orientation of the 5-axis is horizontal, and the positive direction points out from the origin toward the left, so increases to the 5-term move us in that direction.
@@ Line 245: / Line 245: @@
 We can imagine that if we hadn’t scaled the steps, as in our initial naive guess, we’d have ended up nowhere near the center of the diagram. How could we have, if the steps are all the same size, but we’re moving 28 of them to the left, but only 12 and 19 of them to the bottom left and top right? We’d clearly end up way, way further to the left, and also above the horizontal midline. And this is where pretty much any near-just ET would get plotted, because 3 being bigger than 2 would dominate its behavior, and 5 being larger still than 3 would dominate its behavior.
 === perspective ===