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

Line 84:

But a more interesting way to think about this result involves treating {{vector|-4 4 -1}} not as a single interval, but as the end result of moving by a combination of intervals. For example, moving up four fifths, 4 × {{vector|-1 1 0}} = {{vector|-4 4 0}}, and then moving down one pentave {{vector|0 0 -1}}, gets you right back where you started in 12-EDO. Or, in other words, moving by one pentave is the same thing as moving by four fifths ''(see Figure 2b)''. One can make compelling music that [[Keenan's comma pump page|exploits such harmonic mechanisms]].

From this perspective, the disappearance of 81/80 is not a shortcoming, but a fascinating feature of 12-EDO; we say that 12-EDO '''~~supports~~''' the meantone temperament. And 81/80 in 12-EDO is only the beginning of that journey. For many people, tempering commas is one of the biggest draws to RTT.

From this perspective, the disappearance of 81/80 is not a shortcoming, but a fascinating feature of 12-EDO; we say that 12-EDO '''[[support]]s''' the meantone temperament. And 81/80 in 12-EDO is only the beginning of that journey. For many people, tempering commas is one of the biggest draws to RTT.

But we’re still only talking about JI and EDOs. If you’re familiar with meantone as a historical temperament, you may be aware already that it is neither JI nor an EDO. Well, we’ve got a ways to go yet before we get there.

@@ Line 84: / Line 84: @@
 But a more interesting way to think about this result involves treating {{vector|-4 4 -1}} not as a single interval, but as the end result of moving by a combination of intervals. For example, moving up four fifths, 4 × {{vector|-1 1 0}} = {{vector|-4 4 0}}, and then moving down one pentave {{vector|0 0 -1}}, gets you right back where you started in 12-EDO. Or, in other words, moving by one pentave is the same thing as moving by four fifths ''(see Figure 2b)''. One can make compelling music that [[Keenan's comma pump page|exploits such harmonic mechanisms]].
-From this perspective, the disappearance of 81/80 is not a shortcoming, but a fascinating feature of 12-EDO; we say that 12-EDO '''supports''' the meantone temperament. And 81/80 in 12-EDO is only the beginning of that journey. For many people, tempering commas is one of the biggest draws to RTT.
+From this perspective, the disappearance of 81/80 is not a shortcoming, but a fascinating feature of 12-EDO; we say that 12-EDO '''[[support]]s''' the meantone temperament. And 81/80 in 12-EDO is only the beginning of that journey. For many people, tempering commas is one of the biggest draws to RTT.
 But we’re still only talking about JI and EDOs. If you’re familiar with meantone as a historical temperament, you may be aware already that it is neither JI nor an EDO. Well, we’ve got a ways to go yet before we get there.