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Symmetry is as central to what I call twelve-tone
tonality as the triad and the key center are to the major/minor system,
and the meaning I impute to the term “tonality” in
“twelve-tone tonality”
derives only from the presence of an analogously central and all-pervasive
principle and not from any other shared properties of the two systems,
though there certainly are such shared properties. But to move from the
abstract precompositional structure of triadic and tonal relations to the
composition itself means to interrupt and then to restore those relations.
The same thing is true of symmetry in twelve-tone tonality. It is only
in the precompositional array that this symmetry is always literally and
uninterruptedly unfolded. The compositional interpretation of the precompositional
symmetrical array constantly interrupts and restores that symmetry.
In the last of a series of wise and brilliant lectures that Roger Sessions presented at the Juilliard School in 1949 he spoke of “the way that apparently self-sufficient currents of development coincide in a single historical movement. Different sets of facts, having no apparent connection with each other, seem over and over again to coincide in such a manner that it is tempting to seek, or perhaps to assume, connections and to find only specious reasons for them. Fundamental and far-reaching changes in one so-called ‘field’ of human activity are likely to coincide with changes of an equally far-reaching character in many others.” In spite of these evident connections, the “process of musical development [is one] which we can interpret in terms of music alone” and which we can explain as “the inevitable consequence of developments which had been taking place within the most self-contained musical sphere.” It is without being tempted to seek any reasons for it that I call attention to the fact that the concept of symmetry seems to have the same far-reaching significance in many other “ ‘fields’ of human activity” in our time that it has in music. Indeed, according to some cosmologists, symmetry and “broken” symmetry—what I have called “interrupted” symmetry in differentiating between actual musical compositions and the perfect background symmetry of interval cycles and inversional relations—may even take us all the way back to the “big bang.” Here is Timothy Ferris on the creation of the universe [in The Creation of the Universe: A Science Special for Television]: The mathematical symmetries that the unified theories have exposed at the foundations of natural law are more subtle and complex than those of snowflakes, but their principle is the same. They imply that we live in a crystallized universe of broken symmetries. Perfect symmetry may be beautiful, but it’s also sterile. Perfectly symmetrical space means nothingness. As soon as you introduce an object into that space, you break the symmetry. . . . Perfectly symmetrical time means that nothing can happen. As soon as you have an event, then you break the symmetry. . . . It may even be that we owe the very origin of our universe to the imperfection of the breaking of the absolute symmetry of absolute emptiness.
George Perle
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