Conference Agenda

In musical settings with ambiguous chromaticism, it can be difficult to identify the tonality and, thus, the scale-degree motion among voices. In this paper, I propose a new methodology to describe motion that occurs when the voices of one chord reposition themselves into different positions of another chord (e.g., root, 3rd). I generalize a chord-member space with accompanying intervals that form a “mod-7” group structure, inspired by David Lewin’s definition of a Generalized Interval System, or “GIS” (1987). By combining Richard Bass’s (2007) enharmonic position-finding nomenclature and Steven Ring’s (2011) “heard” scale-degree GIS, my methodology introduces the concept of heard chord members. I argue that through this apparatus, one can hear changes in vertical placement as characteristic linear gestures, even in progressions that do not convey a clear tonal center. In my proposed system, I represent any given note as an ordered pair derived from the direct product CM × PC, where CM is chord-member space (newly introduced here), and PC is the usual pitch-class space. The ordered pair is of the form (cm, pc), where cm represents the heard chord member, and pc represents its regularly assigned pitch-class integer. To describe the interval between two notes, I use a different ordered pair of the form (cmint, pcint), where cmint represents the ascending chordal interval (the designation “3rd” denotes an ascending chordal third, “3rd²” denotes two ascending chordal thirds, and so forth), and pcint represents the ascending chromatic interval. I additionally argue that this system illustrates characteristics of chromatic progressions that are not so easily detected by previously established transformational approaches. For example, this system describes types of individual voice motions across chords of different qualities (e.g., major and diminished triads) and cardinalities (e.g., triads and seventh chords). By analyzing the chord-member transformational activity of a sample of ambiguously chromatic nineteenth-century musical passages (from Frédéric Chopin’s Etude in A-flat major, Op. 25, No. 1; and Franz Schubert’s “Die junge Nonne,” D. 828), I show that this system offers a newly instructive way of thinking about chord progressions and voice leading. In so doing, this approach closely reflects the transformational attitude.

This paper examines harmonic organization systems in two songs by the French composer Mel Bonis (1858–1937): “Noël pastoral” (1892), a Christmas-themed song whose text fuses sacred and secular content, and “La mer” (1903), whose message about the value of divine love is made clear only at the end. While both songs generally adhere to the Romantic tonal-harmonic idiom that was prevalent throughout Bonis’ oeuvre, they contain remarkable passages that switch to a kind of harmonic organization that I call “transcendent triadic chromaticism.” In these passages, harmonic successions are not based in tonal relationships; instead, common tones and symmetrical pitch collections form a basis for chord relationships beyond the bounds of tonality. The fact that these chromatic passages can be found in passages of her songs in which the texts present spiritual themes, further, leads me to propose the term transcendent triadic chromaticism, which both identifies the harmonic organization systems employed by Bonis in these passages and enables exploration of their significance to the composer in both musical and personal terms.

Specifically, I examine these passages by employing an approach grounded in neo-Riemannian analysis methods that considers harmonic organization in terms of triadic transformations (Hyer 1995), hexatonic and octatonic systems (Clough and Douthett 1991, Cohn 1996), and pivots between these systems. I also examine how the relationships between these harmonic structures and the lines of text set in these passages support an interpretation of this kind of harmonic organization as being aligned with the divine and the transcendent for Bonis.

Finally, I contextualize the stylistic tension between these transcendent triadic-chromatic passages and Bonis’ overall more traditional Romantic style, considering internal conflicts in Bonis’ musical aesthetic viewpoints as well as tensions in her personal life related to her musical activities, and speculating about how transcendent triadic chromaticism could be read as a strategic method for responding to a variety of coinciding challenges.

Within the growing literature on instrumental spaces, scholars have employed set theory and transformational theory to study the left-hand shapes used to play chords on the fingerboards of string instruments: Koozin’s fret-interval type (2011) serves as a kind of prime form to describe “equivalent” fingerboard shapes, and De Souza’s (2018) fretboard transformations capture relationships between such shapes. Nonetheless, transformational theory’s algebraic constraints pose challenges for relating certain kinds of fingerboard shapes—just as they do with traditional pitch-class sets. In comparison to transformational approaches, the methods employed in the area of geometric music theory (Callender, Quinn, and Tymoczko 2008) don’t face this same limitation: they use geometry and topology (rather than abstract algebra) to capture relationships between any set-classes containing the same number of notes. This paper—which connects these instrumental and mathematical approaches—employs geometric voice-leading techniques to study relationships between fingerboard shapes on the violin and the corresponding chords that they produce in pitch space.

Chords played with similar shapes on the violin’s fingerboard are represented by the same fret-interval type. Drawing on techniques that combine geometric theory and diatonic set theory (Frederick 2019), we construct a voice-leading space of all possible triple-stop fret-interval types. Each point in this space represents a different abstract shape on the fingerboard, and paths through the space represent voice leadings within the instrumental space. Comparing the space of fret-interval types to a geometric voice-leading space whose points represent chord spacings illustrates how fingerboard shapes map onto traditional sonorities in pitch space. These theoretical relationships are explored through analysis of the opening of J.S. Bach’s Violin Sonata in G minor, BWV 1001. Compositional implications are also addressed: guidelines in orchestration treatises for writing triple stops on string instruments (e.g., Blatter 1997) suggest that the playability of chords relates to where they lie within the fret-interval space.