Monday, December 26, 2011

for three

An idea for a piece:
Three notes - tone + semitone between them - played by three instruments.
Use whole number ratios to generate precise tunings (see below) but render these in cents, so that performers, using digital tuners, can tune their individual notes (seated as far apart as necessary to get a 'clean' reading on the tuner).
The tunings are based on segments of a justly-tuned twelve-tone scale.
The basis of this scale is that (identified by La Monte Young in his Selected Writings (Heiner Friedrich, 1969. 37-8)) of a diatonic major scale:
In this scale, do:re:mi are in the expected 8:9:10 ratio; both do:so, and fa:do are in a 2:3 ratio; fa:so:la repeat the 8:9:10 ratios of do:re:mi; and te:do repeats the 15:16 ratio of mi:fa.
There are plenty of pleasant symmetries and repetitions here to satisfy (at least my) aesthetic desires.
In order to generate the other notes of the fabric, I took utonal relationships based on do, fa and so to create mi flat (5:6 above do), la flat (5:6 above fa) and te flat (5:6 above so). This creates possibilities for just chords based on la flat and on mi flat (both 4:5:6). By the same logic, I calculated re flat from a ratio of 4:5 with fa (just chord re flat:fa:la flat - 4:5:6). This only left me with a so flat/fa sharp to calculate, and I did this by replicating the ratio between la flat and te (64:75), which also gives a 15:16 ratio between fa sharp and so (as you would expect, given that te:do is also 15:16).
Final ratios of all twelve tones are (in integer ratios):
480 : 512 : 540 : 576 : 600 : 640 : 675 : 720 : 768 : 800 : 864 : 900 : 960

Whoopee. Good for me.
Why do I want to turn this into a piece?
I like the idea that these three notes can appear in different rhythmic configurations (like in late Feldman, a persistent and fruitful inspiration) and also in different tonal (here, I mean tonal as in proportional) configurations. When studying temperament, the characters of individual keys in temperaments such as well temperament are emphasised, and the idea of presenting a sample of a tuning like this in close-up, so that you're almost sitting in these two proportions for a period of time, is (for me at least) rather an attractive endeavour.

The instrumentation (and octave displacement) is variable (although all instruments must be at the same octave displacement). I haven't decided how dynamics are going to work, but I suspect they will either be equally balanced and as quiet as possible (whilst maintaining stability of tone), or there will be different dynamic configurations as well (within a pppp, ppp, pp, p band).

The title is currently for three.
If anyone is interested, do drop me a line. I am 100% more likely to finish it if someone wants to play it.

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