THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

Here the letter names correspond to the rehearsal letter which ends that section, thus “A”
designates from the beginning to Letter A, “B” from Letter A to B, and so forth, with
“V” standing for the Hungarian “vége” meaning “end.”
A careful examination of these numbers reveals that Ligeti has modified the
distribution slightly, leaving out nine instances of the number 2, four 3s, two 4s, and one
10. The rationale for this division and modification of the numerical scheme, may be
related to the proportions between the lengths of these larger sections; in interviews Ligeti
states that,
In the first movement of Apparitions, I applied Bartók’s golden section as
interpreted by Lendvai. Its first part is in a low register and the second in a high
register; the relative duration of the two parts corresponds to the golden section.
Subsequent shorter parts of the movement are also divided in the same proportion.
The golden section is in fact the dominant formal principle of the work. Looking
back on it, I must say that I could have applied any other principle of proportions
just as well. 8
This last sentence is particularly telling, since it turns out that the actual division reflects
the proportion of 2:3 (or approximately 0.667) rather than the golden section
(approximately 0.618). The sums of the individual values for each of the four sections are
shown in Table 4.3.
Table 4.3a. Proportions Between Sections of Apparitions, mvt. 1
A B C V
585 390 195 877
V:A = 877:585 = 3:2
A:B = 585:390 = 3:2
B:C = 390:195 = 2:1
8
Ligeti, Ligeti in Conversation, 43. Toop (Ligeti, 68) also reports this as the golden section. See also Ernö
nd
Lendvai, Béla Bartók: An Analysis of His Music 2 ed. (London: Kahn & Averill, 1979), especially 17-26
which deal with the golden section in determining proportions of large forms.
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