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No composer’s harmonic practice has been more closely studied than J. S. Bach’s, yet techniques remain in Bach’s music that demand further attention, one of which is the composer’s use of the subdominant. As in the music of other composers, a subdominant in Bach could appear locally, especially near the beginnings and endings of compositions, or in extended form, as in the concertos and concerto-style sonata movements that state the ritornello in the key of the subdominant. This paper describes a particular way in which Bach will sometimes coordinate small- and large-scale uses of IV within a single composition. In some works, especially those in the minor mode, one hears a process whereby an early gesture toward IV is recomposed more than once, gaining intensity until it becomes the harmonic goal of a section. Working together with other factors, such as voice leading and thematic repetition, the gradual realization of the tendency toward the subdominant may form one of the guiding ideas for an entire composition.
Works by Bach organized to a greater or lesser degree around such tendencies include the sarabandes from the D-minor French Suite and from the D-minor Partita for Solo Violin. An extraordinary case is the Fugue in F-sharp minor from Book I of the Well-Tempered Clavier, where the subdominant tendency, hinted at in the subject and countersubject, is realized at the moment when Bach reveals a crucial relationship between the two themes.
A Perfect Ten: Invertible Counterpoint at the Tenth and Its Relationship to Reaching-Over
Invertible counterpoint at the tenth can be utilized within the voice-leading complex comprised of fugal subjects and countersubjects.In this light, Renwick 1995 illustrates that invertible counterpoint at the octave is tightly connected to this complex and hierarchical levels of structure, but that invertible counterpoint at the tenth is only loosely related to such concepts. Invertible counterpoint at the tenth, however, appears within this complex in some fugues of J. S. Bach. This paper, therefore, reappraises how invertible counter-point at the tenth engages not only foreground levels via the subject/countersubject complex, but also middleground levels through the Schenkerian voice-leading transformation of reaching-over (Übergreifen). The paper is divided into four sections. First, it reevaluates the definition of invertible counterpoint at the tenth so that it includes the inversion of harmonic tones, not just intervals. Second, it identifies applications of this contrapuntal device within Bach’s Fugue in Bb Major from the Well-Tempered Clavier, Book II, the result of which produce supposed parallel perfect consonances. Third, as a way of resolving these parallels, the paper shows how invertible counterpoint at the tenth engages reaching-over, a transformation that places inner voices into higher registers, thus enabling voices to cross over each other. Fourth, the paper integrates reaching-over, and by association, invertible counterpoint at the tenth, into middleground levels of the aforementioned fugue, thus demonstrating that both techniques participate at earlier and later levels of derivation. Both techniques, it is hypothesized and shown, appear in other fugues with similarly structured subjects.
A Comparative Study of the Fugue Subjects of Felix Mendelssohn and Robert Schumann
Felix Mendelssohn and Robert Schumann made significant contributions to the fugal genre in the first half of the nineteenth century. This paper examines the subjects in their fugues for piano and organ. Mendelssohn’s fugues for piano tend to be longer and freer in their overall style compared to those for organ. Despite the differences, his fugue subjects display remarkable consistency in their voice-leading implications. By contrast, Schumann’s fugue subjects do not show such consistency. Indeed, his fugue subjects are often ambiguous in length and harmonic implication.
The paper is in two sections, both of which focus on voice-leading patterns. Section One provides an overview of the subjects in the fugues of Mendelssohn and Schumann. Section Two examines selected fugal expositions, noting the differences in which the two composers treat their subjects against other voices. Mendelssohn’s fugues seem closer to the Baroque models in that they favor a small number of voice-leading patterns. Schumann’s fugues, by comparison, are not as close to the Baroque models from a voice-leading perspective. Instead, motivic unity on the surface seems to be Schumann’s main concern.