Musical logic acts through conflict. Under the rubric "musical dialectic," Greenbaum has traced the evolution of dialectical opposition through a series of analytical articles focusing on works of Bach, Beethoven, Debussy, Schoenberg, Varèse, and Stefan Wolpe. Here is an overview:
We tend to think about musical structure from one of two perspectives: as an instantiation of an abstract form—ternary, for example—or as a rhetorical entity with a unique dramatic arc. The rhetorical view is one of dramatic conflict and resolution; or, to use a Hegelian term, resolution of contradiction.
But of what exactly does musical contradiction consist? Is it the result of concrete musical operations or is it merely an explanatory construct? Two related disciplines provide a conceptual framework to resolve this question: classical rhetoric and Hegelian logic. The former lies at the basis of musical structure up through the Classical period, with the music of Bach as both a culmination of Aristotelian practice and a harbinger of the Hegelian era exemplified in the music of Beethoven.
Musical structure until and including Bach followed archetypical models derived from Aristotelian dialectic and forensic rhetoric. The figures of classical rhetoric were forensic, oratorical tools and were meant to persuade: the orator presented antithetical arguments in order to defeat them. But the nexus of Hegelianism and the dialectical organicism of Goethe at the end of the eighteenth century subsumed the old rhetorical structures into a more subjective dynamic of forces. And as Romanticism developed an imagery of the subjective, a new oppositional structure--“dialectical form”--came into being, characterized by a process of emergence. Finally, various twentieth-century “modernisms” treated musical structure as analogous to physical laws.
A dialectical approach explains musical form and structure as the result of the play of forces rather than the completion of a template. Many aspects of music depend on an assumed reciprocal relationship. Such polar opposites include the tension between harmonic and melodic ideas, the tonic/dominant relationship, diatonicism and chromaticism, and enharmonic relationships.
The articles below examine the historical interaction of musical and philosophical conceptions of form and structure.
“Dialectic in Miniature: Schoenberg’s ‘Sechs Kleine Klavierstücke Op. 19.’” Ex Tempore Summer 2010
“The Music of the Critique of Pure Reason.”
Hawaii International Conference on Arts & Humanities 2008
“Debussy, Wolpe and Dialectical Form.”Contemporary Music Review: Stefan Wolpe Issue (Spring 2008)
”The Proportions of Density 21.5: Wolpean Symmetries in the Music of Edgard Varèse” in On the Music of Stefan Wolpe, Austin Clarkson, ed. Pendragon (Hillsdale, New York: 2003)
“Stefan Wolpe’s Dialectical Logic: A Look at the ‘Second Piece for Violin Alone.’” Perspectives of New Music Vol. 40/2 (2002)