home | tumblrblog | musics | electronics | ask | about | more
Recently I’ve been interested in tunings that divide the octave into equal parts other than twelve. I mean, twelve seems like a pretty arbitrary number, right? It’s just one of those things that no one seems to question, but when you do, people get pretty upset or freak out for some reason.
I wanted to know why this was the case, so for my music perception class, I wrote a paper on it. It didn’t turn out quite like I had hoped as there are no definitive conclusions or groundbreaking revelations, but it serves as an excellent introduction into the topic of equal temperaments.
I had a link to the paper but idk, I can find it if you reach out to me and let me know you want it.
Music
Of course, I have been writing some music that use this concept. Some of it is below.
https://w.soundcloud.com/player/?url=http%3A%2F%2Fapi.soundcloud.com%2Fplaylists%2F613768
And! Some of the scores were available at one time, but not anymore, unless you really want them and let me know. Most of them are either in the draft or sketch state and aren’t written for anything in particular, except perhaps a microtonal keyboard instrument. But they should still be good for study.
Methods
So how exactly does one notate music in these temperaments? It seems that many who delve into the world of microtones develops their own way of notating things. What I have attempted to do is make the “face-value” notation clearly speak something that is recognizable to the Western musician. To me, this means relying on our standard notation system, for better or for worse.
If you’ve checked out my scores, you might have some idea of how I’ve attempted to do this. Basically, our modern notation system only accounts for 12 distinct pitches due to equal enharmonics. To the average Western musician, a B# and a C are the same pitch, with the only reason there is a difference being due to either convenience of notation or harmonic implication (among some other reasons). But in a non-12-TET system, these enharmonics can represent two distinct pitches. For a complete (and unique) explanation of how this can apply (especially for a Just-Intonation system), check out this presentation, specifically when it begins talking about accidentals (scroll down to the 13 Tones section).
Our traditional enharmonic system is practical up to around 19-TET or so, with maybe a few more ETs being feasible after that. Below 12-TET, the matter is as simple as throwing away the pitches that deviate farthest from 12-TET. Here’s a musical example of chromatic scales in 12-TET, 10-TET, and 19-TET:
I have written for such moderately large ETs as 31-TET, and for those I’ve found it most practical to decided on a pattern of intervals from the large ET that approximates a chromatic 12-TET scale, with some adjustments. For many moderately large ETs, the pattern can be simply expressed by a series of small (s) and large (L) intervals that are similar in size to semi-tones. For 31-TET, I use sLLsLsLLsLss. Then, in the score I notate which pitch on the staff correlates to which pitch class in 31-TET that I use and which note the interval pattern starts.
To clarify this nonsense, think about it this way. If I have a C-major scale in 31-TET, I need a certain set of intervals to make it sound “good” or “normal”. This set of intervals has to move around relative to what key I am in, because they might not be the same. So, I notate which “key” I am in by stating which note on the page starts that interval pattern, and exact which pitch class in 31-TET that is. Clear as mud? Hopefully checking out my score (nope sorry not anymore) of a 31-TET piece help clarify things.
I don’t have too many notation examples of this yet because I am still working an easy way to play them back, but since I’m a lazy guy, it will be a bit.