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limited approximations, for 6 micro-tonally tuned pianos and orchestra (2010)

Akiko Okabe, Pi-Hsien Chen, Christoph Grund, Florian Hoelscher, Julia Vogelsänger & Sven Thomas Kiebler, piano

SWR-Sinfonieorchester Baden-Baden und Freiburg
Sylvain Cambreling

The twelfth-tone interval is so small that it is no longer heard as an interval, but rather as the shading of a single note. A single tone played by a romantic orchestra has a wider frequency. The aural effect of a scale in twelfth-tone intervals is thus similar to a glissando. The effect of a cluster of twelfth-tones depends on the register: higher up, it is sharp, abrasive, biting, lower down it is soft, melting, rich. Of course it is also possible to build raw, dissonant chords with twelve-tone intervals -- much more differentiated (also in the degree of acuteness) than with the traditional 12 tones per octave. But it is also possible to build much more "consonant" chords than in the traditional twelve-note scale: a close approximation of the twelve-tone scale can be produced in the overtone scale, accurate up to a twelfth of a tone.

The intonation of the pianos is precisely measurable at all times -- where it would be extremely time-consuming to construct overtone chords with the orchestra alone (including overtone chords based on tonics outside the traditional twelve-tone system), the six precisely tuned pianos can produce these chords in an instant -- admittedly, only in the limited approximation of the 72 twelfth-tones per octave. The score gives the following instruction on the intonation of the overtone scale:

"The twelfth-tone tuning of the pianos provides a good approximation of the intervals of the overtone scale, but diverges from it markedly in some respects. Ideally, the instruments of the orchestra would take the example of the tuning of the piano only at the tonic and the octaves, and correct all other intervals by ear towards the "correct" tuning (particularly the fifths and augmented ninths, the major thirds and the minor sixths), with the twelfth-tone scale of the pianos merely serving as an orientation point."

limited approximations does not tell a story. As with all my compositions, there is also no formal development or traditional formal structure. Contrasting elements alternate with one another -- moments of smoothness and friction. "Pseudo-glissandi" in the pianos arrive unexpectedly at overtone chords. Apparently stable constellations of intervals begin to falter as the twelfth-tones merge.

The spectral, telescoping chords of the pianos are taken up by the orchestra, over and over again. In my early works I had to limit myself to a few basic tones, out of respect for what was practically realisable: in vain makes do with only the 12 tones of the traditionally tuned scale. Natures mortes uses only six different overtone chords, of which four are based on tones found in the traditionally tuned system. In limited approximations, thanks to the pianos, the whole world of sound is open to me. A microtonal countermovement is composed into the final third of the piece: from the fifth C'-G' to the neutral second between the E sharp raised by a twelfth-tone and the F lowered by a sixth-tone. Thus 10 different intervals arise, each of which becomes the centre of an overtone chord. This section last more than 100 bars. Or: an overtone chord, starting fortissimo, rings out, is picked up in the orchestra, swells again to a crescendo, which masks the start of a new overtone chord in the pianos, only the reverberation can be heard, it rings out, is taken up by the orchestra, swells... etc.

--Georg Friedrich Haas

Art by Georgia O'Keeffe