THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

added my section labels and timings underneath, as one can see, the timings correspond
quite closely.
I II IIIa IIIb IIIc IIId
seconds 40-50 40-45 24 20 17 15
sum= 32
section A B C D E
40 44 30 17 33
IIIe IIIf IIIg IIIh IIIi IIIj IIIk III l IIIm IIIn IIIo
13 11 9.5 8 7 6 5 4 3 2 1
sum= 69.5
F
Furthermore, one can discern a logic–influenced by the use of Fibonacci numbers, in this
arrangement of durations. Beginning with roman numeral III, the subdivisions steadily
decrease in length, and the rate at which they do so is determined by a Fibonacci-like
series. Examining the differences in duration between sections yields the following
arrangement.
grouping 1 1 3 2
difference 4 3 2 2 2 1.5 1.5
duration 24 20 17 15 13 11 9.5 8
8
1 1 1 1 1 1 1 1
7 6 5 4 3 2 1 0
The interval by which durations decrease becomes steadily smaller; IIIa is 4 seconds
longer than IIIb, which is 3 seconds longer than IIIc, subsequent sections differ by 2, then
1.5, then 1 second in length. Moreover, the rate at which the interval decreases is based
groups of subsections which are bundled into Fibonacci numbered units; while the
straightforward arrangement would yield groups of 1, 1, 2, 3, 5, 8, there are some
69
42