Aggregates

The term aggregate is used in two ways by musicians.

The first, associated with Cage and Harrison, but probably coming from Cowell and Seeger, indicates an ensemble or complex of tones, articulated together. In Cage's music, the complex tones of the prepared piano lead directly - and explicitly so in the Concerto for Prepared Piano and Chamber Orchestra - to the use of collections, or gamuts, including combinations of single tones, aggregates, noises, and silences. A melody may then be composed not only of a single tones, but of a succession of events including single tones, aggregates, noises, and silences. (Christian Wolff has written about this best, and applied the ideas consequently in his own music).

The second usage, associated with Babbitt, indicates the consumption, horizontally and/or vertically, of complete sets of all of the pitch classes in the temperament. In Babbitt's music, this number is inevitably 12, although some relatively recent techniques for creating arrays of aggregates have introduced the possibility of so-called weighted aggregates, in which successive or simultaneous sets of 12 tones are deficient by at least one pitch class and, consequently, redundant by at least one pitch class.

The two usages are markers of fundamentally different ideas about how a musical universe is put together, as well as different ideas about the identity of the elements that make up that universe. In the Babbitt-style usage, all elements are "notes", sharing all properties and potentiality except for pitch, and aggregates measure successive exhaustions of the supply. The fundamental issues in this music are determining which aggregate should follow another, and making a case for that determination through through the way in which the successions are articulated. In the Cagian usage, aggregates are themselves elements in the gamut of a piece, and sets of elements do not necessarily share any properties such that exhaustion of a set would have any particular significance.

(There is, incidentally, some middle ground in this terminological field, in Stravinsky's "verticals" - in which simultaneously played rotations of row segments fan out from the unisons found on the diagonal of a row matrix -, for example, or in the "chord multiplication" technique associated with Boulez. The latter, of course, knew the aggregate idea directly from his exchanges with Cage, and there is some resemblance between chord multiplication and the aggregate techniques of Cage found in Winter Music, the vituosic piano and violin Etudes, and in the "Number" pieces for keyboards, the use of lists of possible chords. However accidental, there is also a certain aural affinity between late Stravinsky and the music of Cage in the late 1940's and early 1950's.)