Harmonic rhythm plays a crucial role in the forward drive of Elliott Carter’s late music (1990–2012). Typically, the harmonies of these works involve only three set classes—the two all-interval tetrachords and the all-trichord hexachord (Link 2022). Harmonic rhythm thus refers to the durations of these sets on the musical surface. Harmonic rhythm occurs against a backdrop of pulse streams, evenly-spaced rhythmic attacks highlighted by accents (Roeder 1994). Carter often uses two pulse streams at once, and a stream may or may not align with the harmonic rhythm. If a stream drops out of the texture, the harmonic rhythm will often continue its durational span. The interaction of the pulse streams and harmonic rhythm generate momentum and create formal units (Krebs 1999).

This paper will demonstrate how harmonic rhythm takes shape in this music. I present a three-stage method for analyzing harmonic rhythm. Stage 1 identifies harmonies on the musical surface. Stage 2 locates pulse streams (if any). In Stage 3, the analyst interprets the interaction of the harmonies and pulse streams, focusing on how they combine in larger wholes.

Close attention to harmonic rhythm in Carter’s late music deepens our understanding of how harmonic rhythm can alternate between pulse streams, “stand in for” an absent stream by maintaining its speed, and create formal units of moderate size. The talk will also present an analysis of Carter’s song “Alba” (2008). In the absence of pulse streams, harmonic rhythm expands and contracts in duration to reinforce the poem’s four-stanza organization.

The omnibus progression has long intrigued musicians. Its voice leading, characterized by a minor-third double pedal and a chromatically filled-in voice exchange, results in tonally disorienting harmonic progressions that resist standard Roman-numeral analysis. Despite the many distinct forms the omnibus has taken from the late eighteenth to the early twentieth century, only prolongations of dominant-seventh and diminished-seventh chords have received substantial theoretical attention. Although a few examples of omnibus progressions beginning with a half-diminished seventh have been reported in late-tonal repertoires (Utne-Reitan 2021; Piché 2023), variants of the omnibus have not yet been systematically studied. This paper fills this gap by examining lesser-known omnibus types involving prolongations of various seventh chords (e.g., major seventh, minor seventh, dominant seventh with augmented fifth), drawing on examples from late-tonal music and from the writings of the German-American theorist Bernhard Ziehn (1845-1912).

I argue that expanding our understanding of the omnibus to include other seventh chords is crucial to appreciating how the omnibus’s voice leading underpins large-scale linear progressions in late-tonal repertoires. This paper analyzes examples from Taneyev’s Cantata At the Reading of a Psalm op. 36 and Medtner’s “Lieb Liebchen,” where different variants of the omnibus are juxtaposed.

Pierre Boulez’s development of transpositional “multiplication” is considered by many to be a hallmark of his mature compositional style (Koblyakov 1977, Heinemann 1998, O’Hagan 1997, Losada 2014, Scotto 2014, Salem 2018, etc.). It also stands as one of the more fecund harmonic methods among similar strategies by mid-century composers, with Boulez continuing to use variations of the method and its related outcomes (mainly, blocs sonores, or sequences of serially related pitch sets) as the structural basis for his music for the next sixty years.

Scholars currently date the beginning of Boulez’s use of “multiplication” with his work on Oubli signal lapide (1952). Although Boulez abandoned this work, its shares an important blocs sonores matrix with Le Marteau sans maitre (1952-56; Decroupet 2005). Anticipating the completion of Marteau as early as 1954, Boulez began planning a host of new pieces, including L’Orestie (1955), a second book of Structures, and a third piano sonata. Significantly, two of these works play an important role in many studies of Boulez’s “multiplication,” with Structures Book 2 Chapter 1 (1956) and the Third Piano Sonata (1957ff) both serving as iconic examples of new variations of the method. It is notable, however, that the Third Piano Sonata was first conceived as an extension of a pre-existing work (a lost piano concertante), while L’Orestie and another rarely discussed short film score, Symphonie mécanique (1955) were both conceived around the same time and share numerous blocs sonores sequences with the Third Piano Sonata (Salem 2019). Meanwhile, L’Orestie had its own, unique form of harmonic generation that offered an alternative to transpositional multiplication (Piencikowski 1993).

In my paper, I provide the first in-depth analysis of the harmonic structures of the (unpublished) Symphonie mécanique. I compare the sonorities found therein with the blocs sonores and related labelling systems found across at least two other works, L’Orestie and the Third Piano Sonata, to speculate on the interrelated generation of these works. In doing so, I attempt to provide evidence of Boulez’s changing approach to “multiplication” (and composition) during the mid-1950s.