Composing Powerstart: Difference between revisions

Line 71:

If that's still not accurate enough for you, and you insist on using an EDO, you have 41-EDO and 46-EDO, both of which handle the 13-limit very well, especially the latter. 41-EDO has very accurate 3/2's, even more so than 12-EDO, and is a "schismatic" temperament, which says that instead of 5/4 being four 3/2's minus a few octaves, it's now eight 4/3's minus a few octaves. In other words, spelled the usual way, C-E s no longer 5/4, but C-Fb is.

In contrast, 46-EDO has slightly sharp fifths, a bit less sharp than 17-EDO and well within tolerable range. It's also an excellent tuning for "sensi" temperament, which envisions a stack of 9/7's such that two of them makes 5/3, a continuation of this stack hits a number of 7-limit ratios very accurately, and in 46-EDO the 11-limit is supported as well. The sensi-9 scale is 5 5 7 5 5 7 5 7 (and its modes), and you should feel free to use this as a diatonic scale while modulating around and chromatically altering things by 2 steps out of 46 (this is the difference between the large and small step, or 7-5=2).

In contrast, 46-EDO has slightly sharp fifths, a bit less sharp than 17-EDO and well within tolerable range. It's also an excellent tuning for "sensi" temperament, which envisions a stack of 9/7's such that two of them makes 5/3, a continuation of this stack hits a number of 7-limit ratios very accurately, and in 46-EDO the 11-limit is [[support|supported]] as well. The sensi-9 scale is 5 5 7 5 5 7 5 7 (and its modes), and you should feel free to use this as a diatonic scale while modulating around and chromatically altering things by 2 steps out of 46 (this is the difference between the large and small step, or 7-5=2).

Once you get to 53-EDO, the 5-limit is so accurate that it's barely distinguishable from JI. If you want almost perfect 5-limit harmony in an EDO, 53-EDO is hard to beat. It also performs extremely well in the 13-limit. 53-EDO, along with 22-EDO and 31-EDO, also supports a very interesting temperament called "orwell," which can be envisioned as a chain of 7/6's, such that two of them makes a pretty decent 11/8, three of them makes a pretty decent 8/5, and seven of them makes a pretty decent 3/1. A good scale to mess around with is 3 2 3 2 3 2 3 2 2 in 22-EDO, or 4 3 4 3 4 3 4 3 3 in 31-EDO. I sort of hear this stack-of-7/6's temperament as being an evil twin to the more lighthearted stack-of-9/7's which is sensi temperament above.

@@ Line 71: / Line 71: @@
 If that's still not accurate enough for you, and you insist on using an EDO, you have 41-EDO and 46-EDO, both of which handle the 13-limit very well, especially the latter. 41-EDO has very accurate 3/2's, even more so than 12-EDO, and is a "schismatic" temperament, which says that instead of 5/4 being four 3/2's minus a few octaves, it's now eight 4/3's minus a few octaves. In other words, spelled the usual way, C-E s no longer 5/4, but C-Fb is.
-In contrast, 46-EDO has slightly sharp fifths, a bit less sharp than 17-EDO and well within tolerable range. It's also an excellent tuning for "sensi" temperament, which envisions a stack of 9/7's such that two of them makes 5/3, a continuation of this stack hits a number of 7-limit ratios very accurately, and in 46-EDO the 11-limit is supported as well. The sensi-9 scale is 5 5 7 5 5 7 5 7 (and its modes), and you should feel free to use this as a diatonic scale while modulating around and chromatically altering things by 2 steps out of 46 (this is the difference between the large and small step, or 7-5=2).
+In contrast, 46-EDO has slightly sharp fifths, a bit less sharp than 17-EDO and well within tolerable range. It's also an excellent tuning for "sensi" temperament, which envisions a stack of 9/7's such that two of them makes 5/3, a continuation of this stack hits a number of 7-limit ratios very accurately, and in 46-EDO the 11-limit is [[support|supported]] as well. The sensi-9 scale is 5 5 7 5 5 7 5 7 (and its modes), and you should feel free to use this as a diatonic scale while modulating around and chromatically altering things by 2 steps out of 46 (this is the difference between the large and small step, or 7-5=2).
 Once you get to 53-EDO, the 5-limit is so accurate that it's barely distinguishable from JI. If you want almost perfect 5-limit harmony in an EDO, 53-EDO is hard to beat. It also performs extremely well in the 13-limit. 53-EDO, along with 22-EDO and 31-EDO, also supports a very interesting temperament called "orwell," which can be envisioned as a chain of 7/6's, such that two of them makes a pretty decent 11/8, three of them makes a pretty decent 8/5, and seven of them makes a pretty decent 3/1. A good scale to mess around with is 3 2 3 2 3 2 3 2 2 in 22-EDO, or 4 3 4 3 4 3 4 3 3 in 31-EDO. I sort of hear this stack-of-7/6's temperament as being an evil twin to the more lighthearted stack-of-9/7's which is sensi temperament above.