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| 17. Ordered
sets; serial music. |
In analyzing atonal music, we often
pay no attention to the sequence in which pcs are represented in the analyzed
segments; we deal with unordered pc sets. At times, however, we may
notice that the order in which pcs appear is itself a structural feature.
For example, this order may be subject to patterned manipulation. If so,
we would likely want to draw attention to any patterns we perceive. Although
the word "set" is sometimes used for such ordered patterns, they
are more often referred to as series (or rows); and music
in which series are a prominent structural aspect is serial music.
Sets of any size can be manipulated serially, but the most significant
kind of serial music has been twelve-tone music, in which the 12-pc
aggregate set is so treated There is, of course, only one 12-pc
set class, so structural designs cannot be created here on the basis of
pc-content or ic-content alone. Only order manipulations can distinguish
one use of the aggregate from another (and hence relate one to another).
It was Arnold Schoenberg who, in the early 1920s, developed the basic
operations used in 12-tone composition: the common order permutations
of retrograde, inversion, and retrograde-inversion; and such secondary
features as complement relations among serial subsets. Analysis of 12-tone
music is beyond the scope of the present guide. In recent years, however,
pc set analysis has proved quite useful in revealing structural aspects
of serial music other than those dealt with by serial analysis alone.
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| Page last modified 10
July 2001 / GRT |
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