Babbitt's Canonical Form Revisited: Codes and Metaphors for Epistemology

Even among Milton Babbitt's composition titles (such as It takes Twelve to Tango, Whirled Series, and the Joy of More Sextets) his title Canonical Form is unusually mysterious, not for being abstruse or impenetrable, but rather for being so multiply penetrable; that is, for being so easily unwrapped to reveal several possible meanings. Until recently, the titles of Babbitt's compositions have not been subject to much scrutiny, usually being treated merely as casual diversions, prompting mere casual speculation. Alison Maggart's (2017; 2021) recent work, however, delves into aspects of Babbitt's biography, identity, and personality to develop an unprecedented hermeneutical account of his music, foregrounding Babbitt's predilection for wordplay in the form of puns, considering the possible power dynamics of humor, Babbitt's Jewish identity, and his nostalgia for baseball. The present essay pursues such a hermeneutical account, focusing on Babbitt's solo piano work Canonical Form (1983).

The third of Joseph Dubiel's "Three Essays on Milton Babbitt" (1990; 1991; 1992) addresses the overall grandeur of Babbitt's Canonical Form, suggesting some possible meanings of the title, which provide part of the foundation that my remarks build on. Yet since the time of Dubiel's writing, not only have Babbitt's titles begun to be scrutinized more closely (Maggart 2017; 2021), but also a number of analytical technologies and attitudes have arisen which enable, or underwrite, an even broader spectrum of interpretations than was perhaps possible, or tenable. For instance, Gilles Fauconnier and Mark Turner's (1998; 2002) conceptual blending theory, including the analytical technology of conceptual integration networks (CINs), is enlisted to model the multifaceted, multivalent nature of Babbitt's music and titles.¹ It provides a framework for interpreting various analytical results, as I've demonstrated before. For instance, as I showed previously (Mailman 2020) and show below, Schenkerian analysis can be deployed to reveal tonality in Babbitt's music, such that it can be read as a conceptual blend of serial and tonal syntaxes. Later in the analyses below I also apply, to pitch registers, both oscillator modeling and David Lewin's (1995) technique of binary state operators, which he had applied specifically to rhythms and instrumentation in two other Babbitt works. Finally I present a technique of cumulative pattern matching (across domains of pitch class and pitch register) based on Boolean functions (Boolean algebra) which reveals a hidden meaning in Babbitt's title. Yet another arises from an important matrix pattern in linear algebra.

Ultimately, I suggest, as one aspect of Babbitt's compositional poetics, a certain pragmatism regarding ontologies in music theoretical discourse. That is, this piano work and its title, taken together, endorse a certain pragmatism as instrumental to the progress of musical inquiry.

Canonicity

One of the possible meanings of the title "canonical form" that is at least worth considering is the work's engagement with canonical repertoire, not in terms of anything as overt as quoting, but rather through subtler means. In this work, and others from the 1980s, Babbitt's pitch configurations dance with the tonal languages of canonic repertoire, by eluding to brief triadic chord progressions and even longer voice-leading motions.

Canonical Form is based on the same array as Whirled Series, Quartet No. 5, and Around the Horn (Mead 1994; Dubiel 1997), an array whose row features three consonant triads as consecutive segments. Furthermore these works are based on superarrays, which enable a surprisingly vast flexibility in aligning pitches to create various configurations (Mailman 2019). This is because these superarrays feature three or more simultaneous arrays whose ordering relative to each other is undetermined. Thus Babbitt can choose to align pitches from different array lynes, not only to forge consonant triads but also to suggest cadential tonal gestures and, in some cases, longer chromatic tonal progressions.

A passage near the beginning of Canonical Form exemplifies this strikingly. Shown in Example 1, a perfect authentic (I-V-I) cadence in F# minor launches m. 21, prepared by a melodic lead-in (A and G# from m. 20). In m. 22, six pitches, drawn...