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

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But perhaps even more interesting than this continuous tuning space that appears in PTS between points is the continuous tuning space that does not appear in PTS because it exists within each point, that is, exactly out from and deeper into the page at each point. In tuning space, as we’ve just established, there are no maps in front of or behind each other that get collapsed to a single point. But there are still many things that get collapsed to a single point like this, but in tuning space they are different tunings ''(see Figure 2l)''. For example, {{val|1200 1900 2800}} is the way we’d write 12-ET in tuning space. But there are other tunings represented by this same point in PTS, such as {{val|1200.12 1900.19 2800.28}} (note that in order to remain at the same point, we’ve maintained the exact proportions of all the prime tunings). That tuning might not be of particular interest. I just used it as a simple example to illustrate the point. A more useful example would be {{val|1198.440 1897.531 2796.361}}, which by some algorithm is the optimal tuning for 12-ET (minimizes damage across primes or intervals); it may not be as obvious from looking at that one, but if you check the proportions of those terms with each other, you will find they are still exactly 12:19:28.

The key point here is that, as we mentioned before, the problems of tuning and tempering are largely separate. PTS projects all tunings of the same temperament to the same point. This way, issues of tuning are completely hidden and ignored on PTS, so we can focus instead on tempering.

=== regions ===

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 But perhaps even more interesting than this continuous tuning space that appears in PTS between points is the continuous tuning space that does not appear in PTS because it exists within each point, that is, exactly out from and deeper into the page at each point. In tuning space, as we’ve just established, there are no maps in front of or behind each other that get collapsed to a single point. But there are still many things that get collapsed to a single point like this, but in tuning space they are different tunings ''(see Figure 2l)''. For example, {{val|1200 1900 2800}} is the way we’d write 12-ET in tuning space. But there are other tunings represented by this same point in PTS, such as {{val|1200.12 1900.19 2800.28}} (note that in order to remain at the same point, we’ve maintained the exact proportions of all the prime tunings). That tuning might not be of particular interest. I just used it as a simple example to illustrate the point. A more useful example would be {{val|1198.440 1897.531 2796.361}}, which by some algorithm is the optimal tuning for 12-ET (minimizes damage across primes or intervals); it may not be as obvious from looking at that one, but if you check the proportions of those terms with each other, you will find they are still exactly 12:19:28.
+The key point here is that, as we mentioned before, the problems of tuning and tempering are largely separate. PTS projects all tunings of the same temperament to the same point. This way, issues of tuning are completely hidden and ignored on PTS, so we can focus instead on tempering.
 === regions ===