Tiny Everything

A couple of months ago I learned one or two pieces in Book 4 of Bela Bartok’s Mikrokosmos. And recently one of the people on the Xenharmonic Alliance II group on Facebook posted a link to a really nice piece for solo piano (digital, of course) in 17-note equal temperament.

Inspired by that piece, I figured I’d try my hand at a Mikrokosmos-style piece — short, melodic, and harmonically modern, in 17et. It only took a few hours to whip something up:

I enjoyed the process so much that a few days later I tried again:

In case you’re curious: No, these weren’t played in real time. There’s a lot of hand-editing of note lengths and velocities, quantizing, trying different harmonies by dragging the notes up and down, and manually adjusting the tempo here and there.

If I do more of these, I’m going to have to call the series “Tiny Everything,” so the first piece needs its own name. How about “Antic”? The second piece, with those heavy minor chords in the lower register, seems to be called “Gloom.”

I’m still foodling with the question of how best to notate a 17-note scale on a conventional five-line staff. Or even whether to bother. If you look at the Wikipedia article on 17et, you’ll find Easley Blackwood’s method. Easley obviously put a lot of thought into questions of this sort, but I find it odd that his chromatic scale zigzags. The first three notes, for instance, are C, D-flat, and then C-sharp. Also, with his method the interval of a neutral third (which divides the perfect fifth evenly) is spelled either as an augmented second or as a diminished fourth, never as a third.

If I were to try notating this tuning, one possibility would be to use about ten “white keys,” lettered A through K (omitting I, because it would be confusing to read). This notation system has peculiar properties of its own; if you modulate up a fifth from the all-white-keys scale, you’ll find that the key signature has two flats, not one sharp. But we’ll leave that brain-twister for another day.

Because the topic of notating microtonal music has come up in the Facebook Xenharmonic Alliance group, I figured I’d try a more conventional approach using seven “white keys” and ten black ones. The most straightforward way to do this (not the way Blackwood did it) seemed to be to separate the white keys by black keys in a 2-1-1-2-1-2-1 pattern. Or, to look at it another way, the pattern of white keys is 3-2-2-3-2-3-2 (almost as smooth as the 2-2-1-2-2-2-1 we’re used to).

If you write it out this way, 17 is not a meantone tuning. That is, D is not halfway between C and E. The E is, in fact, the neutral third, exactly halfway between C and G. And because it’s not a meantone scale, you have to choose whether the A will be a third above F or a fifth above D. I chose to spell the lower pitch as A, which makes the C, F, and G white-key triads identical but means the D-A fifth is diminished.

As it turns out, “Antic” is in the key of F. And in 17et as I’ve chosen to spell it, the key of F has two flats — B-flat and D-flat. The key signatures proceed not in a circle of fifths but in a circle of neutral thirds: C has no sharps or flats, E has one sharp (F#), G has two sharps, B has three, and so on. The key of A has one flat (Db), the key of F has two, the key of Db has three, and so on.

For reference, the full chromatic scale is C-C#-Db-D, Eb-E, E#-F, F#-Gb-G, G#-A, A#-Bb-B, Cb-C. The enharmonic equivalents are D#/Eb, E#/Fb, G#/Ab, and B#/Cb.

Here’s the opening phrase of “Antic” notated using this system:

Tiny Everything

If you had an actual 17-note keyboard, I don’t think this would be especially hard to read. There are many ways to notate microtonal music, of course — and which system you prefer doesn’t really matter, because no more than about three people will ever acquire your printed score, much less try to make sense of it.

A few years ago, a proposal was made for a system of accidentals called Sagittal notation; you can read about it here. On page 3, this document makes reference to an earlier system called Stein/Zimmerman notation. The good news is, the extra Stein/Zimmerman accidentals are all included in Sibelius (the well-known notation program). With a bit of mixing and matching, you can easily indicate about a hundred notes per octave on a standard staff using the Stein/Zimmerman accidentals alongside the familiar ones. If you need more than a hundred notes per octave, you can import graphic symbols into your score, but my advice would be to take a long walk in the fresh air instead.

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2 Responses to Tiny Everything

  1. dranorter says:

    Both these pieces are just delightful. “short, melodic, and harmonically modern” is a great set of goals.

  2. Pingback: Easley We Roll Along | Jim Aikin's Oblong Blob

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