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The twelve-tone system, as system, is indeed
“simple.” It is simple in its principles of formation and
transformation,
but enormously complex and deep in its ramifications, in the necessary
inferences that can be drawn from these principles, for it is of the formal
model of which it is an exemplification that Hermann Weyl has said: “From
these insignificant looking assumptions springs an abundance of profound
relationships; and mathematics offers an astounding variety of different
interpretations of this simple axiom system.”
. . . . an “exhaustion” of the resources of the twelve-tone system in the relevant future is not only unforseeable [sic], but unthinkable. . . . in its vastness of structural means, its flexibility, and its precision, the twelve-tone system cedes nothing to any musical system of the past or present that has engaged the mind of musical man.
Milton Babbitt
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