Douglas Blumeyer's RTT How-To: Difference between revisions
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7&12 is valid for meantone. So is 5&7, and 7&12. 12&19 and 19&7 are both fine too, and so are 5&17 and 17&12. Yes, these are all literally the same thing (though you may connote a meantone generator size on the meantone line somewhere between these two ETs). So how could we mess this one up, then? Well, here’s our first counterexamples: 5&19, 7&17, and 17&19. And what problem do all these share in common? The problem is that between 5 and 19 on the meantone line we find 12, and 12 is a smaller number than 19 (or, if you prefer, on PTS, it is printed as a larger numeral). It’s the same problem with 17&19, and with 7&17 the problem is that 12 is smaller than 17. It’s tricky, but you have to make sure that between the two ETs you union there’s not a smaller ET (which you should be unioning with instead). The reason why is out of scope to explain here, but we’ll get to it eventually. | 7&12 is valid for meantone. So is 5&7, and 7&12. 12&19 and 19&7 are both fine too, and so are 5&17 and 17&12. Yes, these are all literally the same thing (though you may connote a meantone generator size on the meantone line somewhere between these two ETs). So how could we mess this one up, then? Well, here’s our first counterexamples: 5&19, 7&17, and 17&19. And what problem do all these share in common? The problem is that between 5 and 19 on the meantone line we find 12, and 12 is a smaller number than 19 (or, if you prefer, on PTS, it is printed as a larger numeral). It’s the same problem with 17&19, and with 7&17 the problem is that 12 is smaller than 17. It’s tricky, but you have to make sure that between the two ETs you union there’s not a smaller ET (which you should be unioning with instead). The reason why is out of scope to explain here, but we’ll get to it eventually. | ||
I encourage you to spend some time playing around with [[Graham Breed]]'s [http://x31eq.com/temper/ online RTT tool]. For example, at http://x31eq.com/temper/net.html you can enter <code>12&19</code> in the "list of steps to the octave" field and <code>5</code> in the "limit" field and Submit, and you'll be taken to a results page for meantone. | |||
And the related constraint for rank-1 from two rank-2 is that you can’t choose two temperaments whose names are printed smaller on the page than another temperament between them. More on that later. | And the related constraint for rank-1 from two rank-2 is that you can’t choose two temperaments whose names are printed smaller on the page than another temperament between them. More on that later. | ||