THE ELECTRONIC WORKS OF GYÖRGY LIGETI AND THEIR ...

etween three-object sets; a move from ff to pp to mp can be understood as very similar to
a forte-piano accent, followed by a crescendo to mf. While the former might be
understood as an exaggeration of the later, and the later a compression (perhaps both in
time and in range) they have a similarity in their shape from loudest, to softest, to mid-
range.
Morris numbers each element of a set from lowest to highest using numbers from 0
to n-1, so that the three levels involved in this shape could be described as , and
then goes on to describe operations one can perform to transform recognizable contours.
Morris’s list includes the standard twelve-tone operators of inversion, retrograde, and
retrograde-inversion, so that a low-high-middle contour, describable as , could be
inverted to . This formality simplifies calculations for longer sets, but is often
unnecessary for shorter elements; moreover this outlook often presents the temptation to
over emphasize these connections even when they are not musically presented as related,
or to ignore other relations or transformations which do not fall into these prototypes.
While I will maintain Morris’s rigorous outlook, the three and four element sets that we
will find later in this study can often be described in either simple prose or graphical
notation.
Morris’s theories have been expanded substantially since the publication of
Composition with Pitch-Classes to include a number of similarity relations and to be
38
applied to a number of differing parameters. While none of these analyses have applied
38Elizabeth
West Marvin and Paul A. Laprade, “Relating Musical Contours: Extensions of a Theory for
Contour,” Journal of Music Theory 31, no. 2 (Autumn 1987), 225-67; Elizabeth West Marvin, “The
Perception of Rhythm in Non-Tonal Music: Rhythmic Contours in the Music of Edgard Varèse,” Music
28