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. . . counterpoint means
an ‘opposing point’
whose combination with the original point is needed if the idea
is to exist. The opposing point may contain the completion:
(a + b)(a – b) = a2 – b2,
so that a2 – b2
means, as it were, the idea represented
by the point (a + b) and opposite point (a – b).
Or things may be in the
manner of diophantine equations, where there are many solutions, many ways
to bring together point and opposing point (polymorphous canon; polymorphous
texture)—here point and opposing point are placed as if right and left
of the ‘equals’ sign, hinting at many possible solutions,
or sound-combinations.
Or their relationship may be something like that of subject and
predicate—literally ‘changing the subject’ has, then,
to change the predicate,
in music it is enough to change the layout (in space and time).
Arnold Schoenberg
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