THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

The duration scheme of Section B is built from an additive series of numbers,
similar to the plan for the large-scale form of the first half in that it achieves an exponential
rate of growth. In Ligeti’s sketches, the following diagram is found where numbers on the
top line list the seconds in order and the bottom line gives the number of events which
occur in that second.
Seconds
x2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 1 1 1 2 2 3 4 5 7 10 15
The pacing of these events in seconds relies on the Fibonacci series at first to determine
the spacing of entries. The first event begins at 1", the second at 6", and the following at
9" and 11" so that they are spaced 5, 3, and 2 seconds apart, corresponding to the
descending Fibonacci series.
After achieving the rate of one event per second, Ligeti piles up multiple events
per second using a similar distribution. The events in 11" and 12" occur at 1 per second,
those in 13" and 14" double this rate, and the following events return to Fibonacci
distribution, this time with the number series determining the rate at which the number of
events per second increases. The events from 15" on begin with 3 per second, and
continue by adding 1, 1, 2, 3, and 5 events as shown below.
second 15 16 17 18 19 20
events 3 4 5 7 10 15
difference 1 1 2 3 5
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