THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

While such speeds are easily achieved in the electronic music studio, the limitations
of acoustic instruments make this impractical, to say the least. Ligeti has acknowledged
this fact: “Since you cannot play an instrument fast enough to produce a succession of
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notes at a rate of twenty per second, I built the rhythmic shifts into the music.” And
while he goes on to mention Atmosphères as a specific example of these rhythmic shifts,
one need look no farther than Apparitions.
In the second movement of Apparitions, one finds rhythmic shifts of the type that
Ligeti identifies. For instance, in measure 17 of this movement (see Figure 4.2) the cross
rhythm of 10 against 9 occurs in the violins. The second violins, playing 10 subdivisions
at a metronome marking of half-note = 40 (or quarter-note = 80) produce, 13.33 attacks
per second. The first violins, playing 9 subdivisions will reproduce only the first attack,
since there is no common factor between 10 and 9, and these two patterns will coincide
only at this point. The total number of independent attacks comes to 18 per quarter-note,
or an average of 24 per second, truly exceeding the limit of blurring. The different
groupings of violins also share part of the same range, in which it will be impossible to
perceive the individual instruments playing the notes, let alone discern any lines moving
within this cluster. All of these calculations are based on strictly accurate renditions, but
Ligeti seems to be inspired by instrumental mistakes, even counting on their occurrence.
He cites a precedent, which he realized retrospectively in Wagner, of all composers,
saying, “the string parts at the end of Walküre (Feuerzauber) are such that no violonist
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Ligeti, Ligeti in Coversation, 40.
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