Conference Agenda

William Herschel (1738–1822) was more famous for his astronomical accomplishments, such as discovering Uranus in 1781, than for his music. Prior to this Herschel was a successful musician in England, and although his works do not strike us as particularly experimental or related to his science, Herschel’s unpublished (and unfinished) music theory treatise [1763-6], combined with his previously untranscribed letters [1761-3], hints at an underlying empirical approach to music. The treatise, organized into six sections (Melody, Harmony, Modulation, Relation, Invention, and Composition) lays out what Herschel calls his “gravitational” theory of music, which ranks an interval’s resolution tendency and ascribes greater expressiveness to those with higher “gravity” – i.e. whose pitches are further away on the circle of fifths. Although he only finished the section on Melody, it is clear that the “Gravitational” theory explicated there has strong implications for his unwritten section on Modulation, which is sketched out in a table of contents. Fortunately Herschel’s letters also comment extensively on modulation and can be used to project his ideas further.

This paper will draw together Herschel’s treatise, letters, and compositions to codify Herschel’s ideas of modulation (which he divides into transitions, modulations, and arbitrary modulations). The paper also attempts to situate Herschel’s ideas with regard to contemporary music theory. Evidently in his Hanover childhood he had absorbed, if not “all what had been written [in Germany] on the subject of Harmony” as he claimed, at least writings from Rameau, Euler, Daube, Sorge, and likely Mattheson. Herschel’s explanations to his brother, also a composer, give a window into a formative period in which the concepts of related keys and tonal hierarchies are still being established.

Herschel’s use of the term “Gravity” predates any of his telescope-building or astronomical activities, but the treatise and letters do show the systematic yet unorthodox thinking that would lead to his astronomical discoveries. Though the relative acceptance of complex dissonances and unusual modulations in his theory is blunted in his symphonic compositions [1760-64], some of his works, such as the organ prelude marked “Arbitrary Modulations,” are clearly attempts to illustrate his theoretical thinking.

Studies of harmonic dualism have centered almost exclusively on German-speaking theorists, notably Moritz Hauptmann, Arthur von Oettingen, and Hugo Riemann (Harrison 1994; Clark 2001; Rehding 2003; Klumpenhouwer 2011). Consequently, non-German developments of harmonic dualism have received minimal scholarly attention. This paper provides the first study of dualist methodologies in twentieth-century France: I show how harmonic dualism extends beyond Vincent d’Indy’s Cours de composition musicale (1902–50) to become an important and multivalent topic in French music-theoretical discourse. I argue that engagement with these varied dualisms deepens our understanding of French music theory and of dualism itself.

I divide twentieth-century French dualists into two camps: those who engage with d’Indy’s approach and those who present idiosyncratic methods. Auguste Sérieyx (1910, 1925), Antoine Auda (1930), and Albert Bertelin (1931) extend d’Indy’s theories. While rebutting d’Indy’s acoustical justification for undertones, Amy Dommel-Diény (1953) accepts his dualist scale system. Xavier Perreau (1908), Louis Villermin (1911), and Edmond Costère (1954) do not engage with d’Indy’s dualism. Rather, they use individualistic dualisms to serve novel music-theoretical agendas. For Perreau, dualism explains modern compositional practice. Recalling Oettingen’s “tonicity” and “phonicity,” his approach equates major and minor triads via their common upper partials and lower resultants. Villermin uses unitonic thirteenth chords—comprised of superimposed major and dual minor triads—to explain “ultra-modern” harmony. Costère merges dualism with his own cardinal attraction theory.

Beyond revealing the significance of French harmonic dualism, these diverse methodologies prompt us to expand our perception of dualism itself. Dualism does not represent a single project but an assortment of projects. The equal generation of major and minor objects is central to any dualism; however, the musical objects under consideration vary—dualist principles can influence theories of intervals, melody, triad generation, tonality, or function. This dualist influence can be localized or systemic, impacting a single theory or permeating an entire music-theoretical worldview. I contend that a more flexible notion of dualism not only reflects practice but opens the door to wider and more complex music-historical narratives.

Ernst Friedrich Richter (1808–79) was arguably the most influential music theorist in the Western world during the second half of the nineteenth century. He was hired as a theory professor at the Leipzig Conservatory when it opened in 1843, and was central in forming this institution’s theory curriculum. Richter’s most influential work, the Lehrbuch der Harmonie (1853), has an impressive publication history, with new editions appearing regularly over a century-long period and translations to numerous languages. For instance, Richterian harmony pedagogy retained a dominant position in the United States from the 1860s until the early twentieth century and was central in popularizing Roman numeral analysis in this context.

Although Richter is often—albeit briefly—mentioned as an influential textbook author in the history of music theory literature, comprehensive research on him and the broad international success of his works remains limited. One possible reason is that Richter’s reputation is colored by the many negative judgments of his works by later theorists. Both Schenker and Schoenberg specifically targeted Richter to demonstrate what was wrong with the then-current theory pedagogy. However, the constant targeting of Richter reflected his pedagogy’s dominance. In 1906, Louis claimed that Richter had a “monopoly” on theory pedagogy. Negative judgments of Richter persisted in the twentieth century. Dahlhaus, for example, reduced Richter to a “banal pragmatic.”

This paper seeks a more positive outlook by asking: Why did Richter’s works become so influential in the first place? It briefly outlines key characteristics of Richter’s pedagogy, with reference to recent studies of his textbooks and student exercises, before exploring possible reasons for its widespread success. As a case study, the paper looks to Norway—where Richterian harmony pedagogy retained a dominant position until the middle of the twentieth century. One peculiar (and possibly unfortunate) aspect of the transmission and reception of Richterian pedagogy is highlighted, namely that the harmony textbook was often separated from its larger pedagog­i­cal context (the three-volume Die praktischen Studien zur Theorie der Musik), thus losing one of the biggest strengths of Richter’s own pedagogy: the smooth transition from harmony to counter­point studies.