Composing Powerstart: Difference between revisions

''Musicians and composers just getting into the area of microtuning might, in an initial survey of the available resources on tuning around the web, encounter a barrage of intimidating jargon and mathematical concepts. Fortunately, a composer or player need not worry about the math side of things! This article suggests a number of ways to jump right in and start putting the products of tuning theory to work.''

''Mike Battaglia wrote:''

''Mike Battaglia wrote:''

If you don't mind a bit less accuracy in representing harmonic ratios, the above temperament also exists in [[15edo|15-EDO]], except the diatonic-sized scale is now 3 2 2 2 2 2 2, the superdiatonic is 1 2 2 2 2 2 2 2, and the chromatic scale is all of 15-EDO. 15-EDO also has a really nice "symmetrical diatonic" scale, called the Blackwood-10 scale, which is 2 1 2 1 2 1 2 1 2 1. Play around with major and minor chords in this scale a bit, and transpose them up and down the shape of the scale, and you'll see why it's so magical - the circle of fifths is only five steps long."

If you don't care about harmonic ratios at all, but perhaps instead care about world music, then you might enjoy [[16edo|16-EDO]], which contains in it a wonderful extension of both gamelan music and Chopi timbila music; 5 2 2 5 2 is a great pelog and 3 3 3 4 3 works as slendro.

The 3 3 3 4 3 slendro can turn into the 3 3 3 1 3 3 "slendric-6" scale as well, though I prefer the 3 3 1 3 3 3 mode. This scale is nice because it sounds kind of like a "warped diatonic" scale. Chromatically altering things by 2 steps here, instead of 1 step, sounds really nice.

17-EDO is also notable for containing a very interesting diatonic scale, for which the fifths are slightly sharp from what we're used to (and rather pleasantly, I think). As a result, the "major thirds" in the diatonic scale end up being closer to 9/7 than 5/4, and the "minor thirds" end up being closer to 7/6 than 6/5. Major chords are thus a bit less "sweet" than usual, though I don't mind them much, whereas minor chords are now 6:7:9 and have a sort of "subminor" flavor to them. You can also think about ditching "thirds," and instead harmonizing this scale in terms of 4:6:7 chords, of which there are four instead of three. I really like this because it has a very calm, quiet, meditative sound to it. This is called "superpyth" temperament, short for "superpythagorean," because the fifths are a bit sharp of [http://en.wikipedia.org/wiki/Pythagorean_tuning Pythagorean] (instead of a bit flat as usual).

For people looking to mess with higher-limit stuff, 17-EDO is also really notable for giving decent 13-limit harmony, with the caveat that there's no good representation for 5/1 and other ratios containing 5.

A particularly well-known historical meantone tuning is 1/4-comma meantone, where the 3/2's are a bit flatter than we're used to, but the major thirds are exactly 5/4. What's particularly interesting is that this same tuning turns the augmented sixth, e.g. C-A#, into an almost exact 7/4 - so you can treat it as a 7-limit tuning.

You can do all sorts of amazing stuff with 19-EDO if you want, and make it sound almost exactly like ordinary 12-EDO music too, but then depart from it into some rather mind-blowing stuff if you want.

These people already tend to know a bit of math related to JI, so I'll assume you know what a prime limit is and what ratios are below, as well as having some compositional idea of the sounds you're after.

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.

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.

If you like the 72-EDO approach but like 17-EDO, you might try 68-EDO as a similar thing.

For people who don't care at all about EDOs, don't mind unequal chromatic scales and just want good harmony, there's a zillion options for you; Gene Smith will no doubt be able to add a lot to this, although I'm quite certain I've scared him off with this Margo-sized post here.

There are so many good unequal 11-limit temperaments that it's almost impossible for me to write about them all here; if this is really what you're after, post more about the things that you want specifically, and I'll answer specific questions.

There are two more groups of people I have yet to address:

I'd like to write something for those people, but I'm beat for now. I'm personally in both of these groups, so I've written something for everyone but me. Till next time..."