THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

Stockhausen also permutes dynamic levels serially, and in elaborate detail,
especially in his Studie I. Studie I differs from Studie II in that it varies the number of sine
tones per tone-mixture. Each tone-mixture has its maximum amplitude determined
serially, and furthermore, each element of a tone-mixture will differ in amplitude. In fact,
the length of his Studie I is partially due to Stockhausen’s decision to repeat the
succession of structures, rotating through each note of the tone-mixture as the dynamically
strongest element. In both Studie I and Studie II, Stockhausen also uses different dynamic
envelopes (crescendo, decrescendo, steady) to vary the presentation of these tone-
mixtures.
Ligeti’s Pièce électronique no. 3 uses many of the same principles as Koenig’s
Essay and Stockhausen’s studies, although Ligeti’s practice differs in certain regards.
First of all, rather than using complicated calculations for his choice of pitches, Ligeti
selects only harmonic and sub-harmonic arrangements of sine tones. Secondly, while
Ligeti does use many of the modes similar to Stockhausen, he does not arrange them
serially. Thus in a spectrograph of the realization of what Ligeti terms “Structure 2" of
that piece, we find a pitch-space divided into two octaves from 500 to 1000 Hz, and from
1000 to 2000; each octave has 16 sine tones (counting 1000 Hz in both octaves), which
are arranged harmonically from 1000 up to 1937, and sub-harmonically from 1000 down
to 517 Hz (see Figure 4.4). These filter towards frequencies of 667, 1000, and 1500, the
center frequency of the whole, and the center frequencies of each of the octaves. This rate
of decay resembles Stockhausen’s use of “modus” which would sometimes define tone-
mixtures with a single coordinated attack, but different ending points, which often
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