Annotation for Westergaard, Peter
Notes, Beats and Measures
From Part III, "A Little Closer to the Real Thing--A Theory of
Tonal Rhythm" in An Introduction to Tonal Theory,
Annotation (by Jonathan E. Brooks):
- This text is designed for a first year theory course and is based
on a species counterpoint method which is derived mainly from Schenker and Fux.
A theory of tonal rhythm is discussed for determining the duration of a newly generated note.
Westergaard begins by stating the order and size principles to represent the durations a composer can provide for a listener
and still expect this person to understand a configuration of notes as segments of a longer span.
The order and size principles indicate that a listener, given
two time-points, will tend to think of the second note in terms
of the first, and the shorter note in terms of the longer.
From these initial premises, Westergaard deduces the Law of
Segmentation which states that the initial note in a time-span must be equal
to or greater than the length of a note in the the final portion of that time-span.
As corollaries to the Law of Segmentation, Westergaard demonstrates that a delayed note must be greater than
half the time-span into which it is being delayed while an anticipated note must be less than
half the time-span which it precedes. For a listener to understand that a note is
delayed or anticipated, he or she must have foreknowledge of
the length of time-spans these notes will occupy and the location of
the attack points. This foreknowledge is provided by the framework created by
the evenly spaced beat. Since a listener can understand a
pitch configuration as being derived from a prior configuration
in more than one manner, Westergaard considers the criteria
a listener will use in preferring one analysis to another.