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

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So: we now know which point is {{val|12 19 28}}, and we know a couple of 17’s, 40’s and a 41. But can we answer in the general case? Given an arbitrary map, like {{val|7 11 16}}, can we find it on the diagram? Well, you may look to the first term, 7, which tells you it’s [[7edo|7-ET]]. There’s only one big 7 on this diagram, so it’s probably that. (You’re right). But that one’s easy. The 7 is huge.

What if I gave you {{val|43 68 100}}. Where’s [[43edo|43-ET]]? I’ll bet you’re still complaining: the map expresses the ~~mistunings~~ of 2, 3, and 5 in terms of their shared generator, but doesn’t tell us directly which primes are sharp, and which primes are flat, so how could we know in which region to look for this ET?

What if I gave you {{val|43 68 100}}. Where’s [[43edo|43-ET]]? I’ll bet you’re still complaining: the map expresses the detunings of 2, 3, and 5 in terms of their shared generator, but doesn’t tell us directly which primes are sharp, and which primes are flat, so how could we know in which region to look for this ET?

The answer to that is, unfortunately: that’s just how it is. It can be a bit of a hunt sometimes. But the chances are, in the real world, if you’re looking for a map or thinking about it, then you probably already have at least some other information about it to help you find it, whether it’s memorized in your head, or you’re reading it off the results page for an automatic temperament search tool.

Probably you have the information about the primes’ ~~mistunings~~; maybe you get lucky and a 43 jumps out at you but it’s not the one you’re looking for, but you can use what you know about the perspectival scaling and axis directions and log-of-prime scaling to find other 43’s relative to it.

Probably you have the information about the primes’ detunings; maybe you get lucky and a 43 jumps out at you but it’s not the one you’re looking for, but you can use what you know about the perspectival scaling and axis directions and log-of-prime scaling to find other 43’s relative to it.

Or maybe you know which commas {{val|43 68 100}} tempers out, so you can find it along the line for that comma’s temperament.

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 So: we now know which point is {{val|12 19 28}}, and we know a couple of 17’s, 40’s and a 41. But can we answer in the general case? Given an arbitrary map, like {{val|7 11 16}}, can we find it on the diagram? Well, you may look to the first term, 7, which tells you it’s [[7edo|7-ET]]. There’s only one big 7 on this diagram, so it’s probably that. (You’re right). But that one’s easy. The 7 is huge.
-What if I gave you {{val|43 68 100}}. Where’s [[43edo|43-ET]]? I’ll bet you’re still complaining: the map expresses the mistunings of 2, 3, and 5 in terms of their shared generator, but doesn’t tell us directly which primes are sharp, and which primes are flat, so how could we know in which region to look for this ET?
+What if I gave you {{val|43 68 100}}. Where’s [[43edo|43-ET]]? I’ll bet you’re still complaining: the map expresses the detunings of 2, 3, and 5 in terms of their shared generator, but doesn’t tell us directly which primes are sharp, and which primes are flat, so how could we know in which region to look for this ET?
 The answer to that is, unfortunately: that’s just how it is. It can be a bit of a hunt sometimes. But the chances are, in the real world, if you’re looking for a map or thinking about it, then you probably already have at least some other information about it to help you find it, whether it’s memorized in your head, or you’re reading it off the results page for an automatic temperament search tool.
-Probably you have the information about the primes’ mistunings; maybe you get lucky and a 43 jumps out at you but it’s not the one you’re looking for, but you can use what you know about the perspectival scaling and axis directions and log-of-prime scaling to find other 43’s relative to it.
+Probably you have the information about the primes’ detunings; maybe you get lucky and a 43 jumps out at you but it’s not the one you’re looking for, but you can use what you know about the perspectival scaling and axis directions and log-of-prime scaling to find other 43’s relative to it.
 Or maybe you know which commas {{val|43 68 100}} tempers out, so you can find it along the line for that comma’s temperament.