Douglas Blumeyer's RTT How-To: Difference between revisions
Cmloegcmluin (talk | contribs) m →the other side of duality: Steve Martin's suggestion for "column of rows" |
Cmloegcmluin (talk | contribs) →the other side of duality: Steve Martin noticed that I never actually explain what the heck I meant by sides of duality |
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=== the other side of duality === | === the other side of duality === | ||
So we can now convert back and forth between a mapping and a comma basis. We could imagine drawing a diagram with a line of duality down the center, with a temperament's mapping on the left, and its comma basis on the right. Either side ultimately gives the same information, but sometimes you want to come at it in terms of the maps, and sometimes in terms of the commas. | |||
So far we've looked at how to intersect comma vectors to form a comma basis. Next, let's look at the other side of duality, and see how to form a mapping out of unioning maps. In many ways, the approaches are similar; the line of duality is a lot like a mirror in that way. | |||
When we union two maps, we put them together into a matrix, just like how we put two vectors together into a matrix. But again, where vectors are vertical columns, maps are horizontal rows. So when we combine {{val|5 8 12}} and {{val|7 11 16}}, we get a matrix that looks like | When we union two maps, we put them together into a matrix, just like how we put two vectors together into a matrix. But again, where vectors are vertical columns, maps are horizontal rows. So when we combine {{val|5 8 12}} and {{val|7 11 16}}, we get a matrix that looks like | ||