THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

harmonic categories that was common for composers working in the studio of the WDR
in Cologne, can be discussed in greater depth.
David Lewin has spent much time and effort defining musical transformations, and
discusses at least one model of timbre in his Generalized Musical Intervals and
Transformations, and in doing so calls attention to another problem of analytical discourse
on timbre–that of defining units. His system addresses timbre as a non-commutative
generalized interval system (GIS) that is, a system in which there is no commonly held
minimum unit of distance, such as the semitone for pitch or a beat for strictly metric music
(although music such as Elliott Carter’s, in which there are competing beats, is held as
another example of non-commutative GIS). The lack of a standard unit of difference
means that certain combinations of transformations, will yield different results depending
on order. Lewin’s model of timbre, however, applies only to very simple harmonic
spectra, and governs only the difference in amplitude between the first three odd partials.
Thus, in scope, Lewin’s model is limited and moreover, Lewin himself admits that the
formal intervals and transformations he is able to define, “match our sonic intuitions only
to a certain extent... The models suffer here by comparison with the constructs of Wayne
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Slawson, who has developed an elegant model for an ‘intuitive’ timbral space.” Only a
very specifically and limited musical context would support the results of Lewin’s
experiment, and even this would require the listener to learn how to hear these
relationships which do not model common experiences. An extension of Lewin’s model to
36David
Lewin, Generalized Musical Intervals and Transformations (New Haven: Yale Univ. Press,
1987), 85. See footnote 29 above for Wayne Slawson’s theoretical writings.
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