Polytonal Closure in the Music of Darius Milhaud and Howard Swanson

Abstract

Recent years have seen a renewed interest in cadence and closure in post-Classical-era music, especially Romantic and neo-tonal repertoire (Caplin 2018 and 2024, Rodgers and Osborne 2020, Eng 2019). One subset of neo-tonal music that poses special challenges regarding closure is polytonal music. Polytonality relies on the establishment of separate key centers that can work both independently and in conjunction with one another, which raises many questions concerning cadence and closure—principally, what do we consider a cadence in polytonal music, and is closure possible in only one key or can it happen in multiple keys at once?My thesis addresses these questions by examining the closural strategies utilized by French composer Darius Milhaud and African-American composer Howard Swanson. Drawing upon studies of polytonality by Peter Kaminsky (2004) and studies of neo-tonal closure by Clare Eng (2019), I outline three types of closure that appear in Milhaud’s and Swanson’s polytonal works: (1) monoclosure, where closure is reached in one of the established keys, but the other key(s) does not achieve any closure, either stopping mid phrase or continuing uninterrupted; (3) polyclosure, where simultaneous closure occurs in two (or more) separately established keys; and (3) converging closure, where multiple established keys converge at the point of cadence to achieve closure in one unified key. After developing this analytical approach, I apply it to large-scale works by Milhaud and Swanson. First, drawing on the Sonata Theory of James Hepokoski and Warren Darcy (2006), as well as writings about twentieth-century sonata form by Joseph Straus (1990) and Damien Blättler (2024), I analyze the first movement of Darius Milhaud’s Sonata for Flute, Oboe, Clarinet, and Piano, Op. 47-I; this analysis includes a meta-narrative analysis founded on theories of agency theory by Robert Hatten (2018) and Edward Klorman (2016). Then, I turn to Swanson’s Fantasy for Soprano Saxophone and String Orchestra–a work that has never been published or performed, which I found among Howard Swanson’s papers in the Amistad Research Center at Tulane University. After developing a model of analyzing Swanson’s unique polytonal idiom in general terms, building upon Marsha Reisser (1989) and Lee Cronbach (1981), I use my theory of polytonal closure to show how multiple layers of formal function emerge out of this 350-measure single-movement work.