Arvo Pärt's strict and elemental compositional procedures, which have been described and evaluated critically by several scholars, are here expressed via a mathematical formalism drawn from theories of musical transformations. The analytical opportunities that this perspective provides are demonstrated by attributing the melodic and harmonic structures of complete pieces—Fratres, Passio, and The Beatitudes—to the interaction of a very small set of transformations. This representation reveals similarities of form as well as of process among them. It also shows how Pärt's signature harmonic procedure, tintinnabulation, sometimes governs melodic procedure and has melodic meaning while also making it possible to define and recognize harmonic areas, distinctions among harmonies, and systematic reasons for cadences. For instance, transformational expressions for Passio show the interpenetration of melody and harmony and define the field of possibilities in which each melodic/harmonic change takes place—a “space” in which the changes can be heard as meaningful in relation both to themselves and to the text. Overall, these results suggest how the ostensibly mechanical melodic and harmonic processes in this music can be heard as nuanced and expressive. More theoretically, the transformational representation reveals some formal properties of tintinnabulation that suggest some interesting generalizations.

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