13 December 2014

72 equal temperament in old-school MIDI

I've been composing my music the same way I did when I started writing piano pieces in the mid-90s, using a cheap old scorewriter that allows pitch bends.

I started out using basic 12-tone tuning, then experimented with quarter tones (for non-piano instruments, of course), then spent years trying to figure out what tuning system I wanted to use (I was stuck on 53-equal for a while).

Then, after discovering miracle temperament, and the wonders of 72 equal temperament, and the glaring fact that 12 × 6 = 72, I decided to go with that. With a typical orchestral work, using 16 or more channels (I can load multiple instances of ARIA Engine for Garritan if I need more), I insert in-line pitch bends when needed. It's not perfect, since the pitch bends do affect release and reverb, but it gets the job done, and I can play it all back the way I want it recorded.

Also, ARIA uses Scala tuning files for tuning individual pitches, e.g. if you want all Es, Bs and F-sharps to be 50 cents flat, or you want quarter-comma meantone or Werckmeister well-temperament, and so on.

I haven't been entirely consistent on notation for 72 equal. If I want exact pitches specified, then I use a full system of regular accidentals, a de facto standard quarter tone notation, and arrows for morion (16.67 cent) adjustments:


Note: arrows alone can be used; these adjust pitch without canceling an existing natural, sharp or flat.

Also, I don't use the same notation as Maneri-Sims. I base mine on Tartini-Couper, and for a while, I called it Tartini-Couper-Bartók (TCB, which, of course, also stands for something else).

I also have a simplified system, which uses only the quarter tone symbols, and the regular accidentals with arrows for sixth tones (for example, the flat symbol with an arrow up is a third tone or 66.67 cents flat; a natural with an arrow up is 33.33 cents sharp). Most of the time, I just need to mark semitones, quarter tones and third tones.

For the harmonic series, with the fundamental on C, the seventh harmonic is a B two-thirds-tone flat, the eleventh is an F quarter-tone sharp, and the thirteenth is an A third-tone flat.

If the default pitch bend range of 2 semitones is used, microtuning would be 683 units for a twelfth-tone (1 morion), 1365 for a sixth-tone (2 moria) and 2048 for a quarter-tone (3 moria), and so on Naturally, I needed to have these numbers memorized.

Ultimately though, the main reason I'd rather composer in 72 tones per octave instead of 12, is the same reason you'd rather see an image in 16,777,216 colors instead of 256.

(Another reason I use 72: the ANS synthesizer, and Edward Artemiev.)

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