Georg Friedrich Haas: limited approximations

  • for 6 micro-tonally tuned pianos and orchestra
  • 4 1 4 1 - 6 1 4 0 - pno(6), vln.I(10), vln.II(10), vla(6), vc(6), cb(8)
  • Duration: 30’
  • Instrumentation details:
    1st flute
    2nd flute
    3rd flute
    4th flute
    1st clarinet in Bb
    2nd clarinet in Bb
    3rd clarinet in Bb
    4th clarinet in Bb
    1st horn in F
    2nd horn in F
    3rd horn in F
    4th horn in F
    5th horn in F
    6th horn in F
    trumpet in C
    1st trombone
    2nd trombone
    3rd trombone
    4th trombone
    1st piano (+(+1/6–Ton))
    2nd piano (+(+1/12–Ton))
    3rd piano (+(Normalstimmung))
    4th piano (+(-1/12–Ton))
    5th piano (+(-1/6–Ton))
    6th piano (+(-1/4–Ton))
    1st, 2nd violin I
    3rd, 4th violin I
    5th, 6th violin I
    7th, 8th violin I
    9th, 10th violin I
    1st, 2nd violin II
    3rd, 4th violin II
    5th, 6th violin II
    7th, 8th violin II
    9th, 10th violin II
    1st, 2nd viola
    3rd, 4th viola
    5th, 6th viola
    1st, 2nd violoncello
    3rd, 4th violoncello
    5th, 6th violoncello
    1st, 2nd contrabass
    3rd, 4th contrabass
    5th, 6th contrabass
    7th, 8th contrabass
  • Composer: Georg Friedrich Haas
  • Commission: Kompositionsauftrag des Südwestrundfunks

Work introduction

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 then 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.

Or: two different overtone chords, based on tones that sound entirely warped next to one another, fade in and out … etc.

Melodies recur again and again, wandering from piano to piano – as tremolo, as individual tones, as overtone chords.

Or: an interval (for example the fifth C-G) sounds in all octaves – but some of these octaves are expanded by a twelfth of a tone. The ear corrects the chord (or tries to correct it) – looked at horizontally, the intervals oscillate in twelve-tone steps, but stay in the same place after all …

Towards the end of the piece (after an “aria” of overtones) the principle that the traditional 12-tone system makes overtone scales sound flat is reversed: the overtones are intoned (approximately) correctly – but the bass tones are blurred together in a twelfth-tone cluster. The string instruments then maintain the overtone chord built up in the “aria” – uninterrupted by the “intermezzo” that follows, in which the pianos adjust the chord in parallel twelfth-tone intervals.

As central as the work with overtone chords is for limited approximations, at first it is built out of processes of diffusion, clouding, friction. As the piece progresses, the music returns to this initial situation, as if by accident – reminiscences, relapses, contrasts.

At the end, a quotation from Ivan Vishnegradsky’s harmonies (against the relics of an overtone chord in the strings) – not with the clarity of his composition “arc-en-ciel” (I was able to première this work for 6 pianos tuned in twelfth-tone intervals in 1988) but in the clouding over of twelfth-tone chords gliding gently towards the heavens. Even this approximation is only a limited one.

Georg Friedrich Haas


limited approximations

The complete perusal score (PDF-preview)

World première

Donaueschingen (DE)
SWR-SO Baden-Baden und Freiburg
Sylvain Cambreling
Main soloists:
Pi-hsien Chen, Christoph Grund, Florian Hoelscher, Akiko Okabe, Sven Thomas Kiebler, Julia Vogelsänger, pno

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