THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

5 6 30 4.95
5.5 6 33 5.5
6.1 5 30.5 6.05
6.7 5 33.5 6.71
7.4 4 29.6 7.37
8.2 3 24.6 8.14
9.1 3 27.3 9.02
10 3 30 10.01
11 3 33 11
12 3 36 12.1 rounds to whole numbers
13 2 26 13.2
14 2 28 14.3
15 2 30 sin obiekt, ugató 15.4
17 2 34 sin obiekt, ugató 16.5
19 2 38 sin obiekt, sin 18.7
21 1 21 20 hz obiekt 20.9
23 1 23 ugató 23.1
25 1 25 sin obiekt 25.3
28 1 28 sin obiekt 27.5
31 1 31 ugató 30.8
34 1 34 sin obiekt 34.1 uses a quasi-additive series
41 1 41 20 hz obiekt 37.4 +7
50 1 50 20 hz obiekt 45.1 +9
61 1 61 sin obiekt 55 +11
74 1 74 ugató 67.1 +13
91 1 91 20 hz obiekt 81.4 +15
130 1 130 ugató 100.1 +39
This duration series shows similar characteristics to the 11/10 scale used in the previous
example, but also shows some inconsistencies. I have added an additional column to this
chart showing the unrounded series generated by multiplying the previous number by
11/10. First of all, after reaching the duration of 10 cm, rounding applies to whole
numbers rather than tenths. Furthermore after the number 31 (significant because of the
index of 30), Ligeti appears to begin using an additive series of odd numbers, 7 through
15, followed by 39, whose appearance cannot be explained by either system, although
given the use of additive series here and elsewhere in Ligeti’s work, one could speculate
that it is equal to sum of the previous three additions (11+13+15). The reason for this
99