Conference Agenda

Eighteenth-century Spanish keyboard music reflects a blend of native traditions and external influences, notably the Italian Galant style. Central to this influence is the partimento tradition—a pedagogical method emphasizing harmonic practice and improvisation, originating in Italy around 1700. Despite its importance, the presence of partimento in Spain has been underexplored. This paper investigates the only known work in the partimento tradition by a Spanish composer: Reglas Generales, o Escuela de Acompañar de Órgano o Clave (c. 1780s), an unpublished manuscript by Félix Máximo López, fourth organist of the Royal Chapel in Madrid. Reglas Generales is concise in its language but abundant in musical examples and exercises, reveals a sophisticated understanding of partimento pedagogy, and offers a clearer window into harmonic practice than modern methods typically allow. The findings not only enrich our understanding of eighteenth-century Spanish music but also invite a broader perspective within historically-informed analysis.

Recent music theory scholarship has called for the examination of music-theoretical discourses hidden in linguistic enclaves, to decenter the history of music theory (Rehding, 2020), to make it global (Martin, 2022), and to make it plural (Li, Stover, and Yu Wang, 2024). This presentation examines the origins of one such discourse—the twentieth-century Prague-based school of theorizing harmonic function, typified by writers such as Karel Janeček (1903–1974), Karel Risinger (1920–2008), and Vladimír Tichý (b. 1946). These authors represent perhaps the most significant music-theoretical tradition in the Czech lands, seeking to account for the chromaticism of twentieth-century music with a veritable menagerie of function symbols, such as modal functions, chromatic third–related functions, and even an anti-tonic function. This tradition began with Otakar Šín (1881–1943), who provided the first Czech-language account of harmonic function in Nauka o harmonii na základě melodie a rytmu (The Study of Harmony on the Basis of Melody and Rhythm, 1922) and in a revised second edition under the title Úplná nauka o harmonii (The Complete Study of Harmony, 1933). While clearly indebted to Hugo Riemann, these texts were in no sense translations of Riemann’s work—Šín went to great lengths to reimagine Riemann’s theory of harmonic function without the Harmonieschritte and, to some extent, without harmonic dualism.

In this presentation, I examine how Šín’s theory of harmonic function departs from Riemann’s original. Specifically, I demonstrate how Šín’s decision to jettison Riemann’s Harmonieschritte caused a host of music-theoretical problems; how he addressed those problems across the two editions of the Nauka; and how his superficial commitment to harmonic dualism led to a variety of conceptual tensions. In so doing, I treat Šín’s theory of harmonic function as a work of Riemann reception, showing how Šín’s reinterpretation of Riemann’s theory serves as an implicit commentary on Riemann’s approach and the concept of harmonic function in general.

Herman Berlinski, a student at the Leipzig Conservatory, witnessed a conflict between the institution’s two professors of Tonsatzlehre, Sigfrid Karg-Elert and Hermann Grabner. Berlinski recalled that in 1932, “Karg-Elert’s harmonic theories were to be established as an examination subject. However, someone circulated a petition against Karg-Elert; I believe that Grabner’s supporters organized the petition. Karg-Elert’s theories were removed from the examinations.” Karg-Elert died in 1933; his methods vanished from the Conservatory curriculum, replaced by those of Grabner.

To consider why Grabner won decisively over Karg-Elert, I will compare the basic elements of their function theories (Karg-Elert 1921 and 1931; Grabner 1923, 1924 and 1944). I will focus on the three basic functions in major and minor, and of the Parallel and Leittonwechsel of those functions. Karg-Elert’s conception is uncompromisingly dualist. His Principalklänge are polar opposites in major and minor, indicated by the directions of his function labels. He uses Arabic numerals to indicate chord tones; the numerals reflect just-intonation intervals above or below the Prime. His examples employ arrows to highlight energetic tendencies: upward in major, downward in minor. For the Parallel and Leittonwechsel, Karg-Elert uses vertical placement to indicate which tones from the original function are retained. Finally, he illustrates how the common tones involve inversional exchange, foreshadowing two features of neo-Riemannian transformations. Karg-Elert’s presentation is that of a speculative theorist, seeking to convey perception of functional relationships in a manner reminiscent of recent transformational theory.

Grabner’s system eliminates most traces of dualism. His functions are the same in major and minor, and his Parallel and Gegenparallel are simply shown as third-relations of the basic functions. He equates the three functions with their corresponding Stufen, again reflecting his monistic conception. In 1943 Grabner eliminated the Gegenparallel altogether, simplifying his system even further. His primary concern is for pedagogical directness, and thus he reduced theoretical detail to the absolute minimum. For students, it is clear which system would be easier to learn and use. While it is perhaps not surprising that Karg-Elert’s complex theories were not widely adopted, his presentation of harmonic function is both deeply searching and strikingly modern.

This paper examines some of the key tensions that arose as music theorist Abū Naṣr al-Fārābī (fl. in Baghdad, d. 950) sought to reconcile the universalizing impulses of the Classical Greek theoretical system with the musical practices indigenous to the Abbasid Caliphate. While much of Greek music theory focused on construing the eternal laws of music in mathematical terms, Fārābī believed that music could only be theorized through the repeated encounter (sensual experience) of musical phenomena, necessitating a richer engagement with practice. Only once the principles behind these local phenomena were established that the theorization could be completed through the logical means of demonstration (Druart 2020). But this meant that Fārābī had to somehow find a way to bridge two incommensurate realms: the physical one—i.e., the sublunary world of continuous and changing phenomena—and the purely theoretical one, in which musical principles could ultimately be reduced to quantitative terms (ratios).

I argue that Fārābī's treatment of rhythmic theory is key to understand how he reconciled the tension towards the construction of an immutable and universal theoretical apparatus with embodied feelings, sensual phenomena, and indigenous musical practices. First, I show how his rhythmic system managed to harmonize two incommensurable music-temporal aspects, which can be respectively mapped onto the physical and the purely theoretical realms: 1) the notion of music as movement, appreciated as qualitative changes in degrees of “speed;” and 2) the notion of music as a succession of proportional durations, ultimately reducible to ratios. I demonstrate how his system derives duration as a consequence of motion, speed, and weights applied in the performance of attacks, i.e., the instantaneous point in which a sound is struck. Thus duration can be computed a posteriori as the space of time between two successive notes. Second, I show how Fārābī's system of rhythmic modes and their notation was designed to be generative so that it might accommodate potentially new local forms.

Ultimately, al-Fārābī's writings illustrate how we might begin to historicize the universalizing—and thus fundamental ahistorical—impulse of music theory. This proves particularly important when conducting comparative work between music theoretical systems belonging to different traditions.