THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

2'38") dramatically reduces the reverberation while the sine tones trail away, leaving the
invariant gestures, in both whole and fragmentary form.
The invariant gestures found in Event 1 are symmetrical around both horizontal
and vertical axes, and thus would be invariant under both inversion and retrograde. The
gesture can be idealized as a diamond shape, and was most likely created by the use of
ring-modulation of a band of 20 Hz noise with a low frequency glissando which would
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produce bands symmetrically around the center frequency.
These gestures are also arranged in specific registers, their center frequencies are
arranged in octaves at 3200 and 6400 Hz. and in the lower register at 335 and 670 Hz.
This suggests that this type of material was created all at once in the studio and then later
distributed through the piece. Due to the noisy character of these gestures, the specific
frequencies will not be heard; the most prominent feature of these gestures is a
characteristic envelope, crescendoing to the peak of the divergence and then
decrescendoing again–yet another invariant feature when retrograded. This combination
of registral and dynamic expansion and contraction creates a Doppler-like effect, and even
in a mono presentation creates an illusion of objects approaching and fading away,
moreover, the gestures’ presentation in rapid succession, or overlapping with one another
makes this new type of material all the more prominent.
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Given two input frequencies, ring modulation will yield the sum and difference of these frequencies, so
that if the center frequency of 3200 was ring modulated with a glissando from 50-100 Herz, one would get
mirror-image glissandi from 3250 Hz up to 3300 and from 3150 down to 3100 Hz. A thorough discussion
of ring-modulation can be found in Charles Dodge and Thomas Jerse, Computer Music: Synthesis,
nd
Composition, and Performance, 2 ed. (New York: Schirmer Books, 1997), 92-94.
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