THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

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728.904824 x (11/10) = 801.795306
801.795306 x (11/10) = 881.974837
881.974837 x (11/10) = 970.172321
970.172321 x (11/10) = 1067.189553
th
He continues this process until 1067.189553, the 50 value reached in such a scale, and
equal to about 14 seconds. These numbers were then rounded to the nearest whole
millimeter (10, 11, 12, 13, 15, 16, 18, 19... 802, 882, 970, 1067), although in many of the
sketches, Ligeti is inconsistent in the number of decimal places used, resulting in slight
variance in the values returned.
Significantly, Ligeti divided the materials into individual sounds with specific
9
durations by a means that he would later use for his orchestral work Apparitions . His
goal was to balance short and long durations within a given material, but not by giving all
durations an equal number of occurrences, as a serial duration row would do. Ligeti
explains that this would favor the longer durations, which, given an equal number of
occurrences, would make up a more substantial portion of the piece than the shorter ones.
Rather than this Ligeti chose a method by which the value of each duration, multiplied by
the number of occurrences of that duration, would equal a constant, and thus the sum of
each of the types of duration would make up an equal portion of the piece. As an example
of this Wehinger cites a simple case where, “there were, for one material, 150 bits of tape
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1 cm in length, and one bit of tape 150 cm in length.” Figuring a tape speed of 76
9See
Ligeti’s comments in “Metamorphosis of Musical Form,” trans. Cornelius Cardew, Die Reihe, Vol. 7
(1960) 14, n 28.
10Wehinger,
Ligeti – Artikulation, 17
97