Multidimensional Musical Objects and the One-Dimensional Musical Space

Jason Patterson, University of North Texas

In the Schenkerian model the triad is what undergoes all of the processes of diminution, prolongation, composing-out, etc.; the Ursatz is a temporal expression of the tonic triad. My model suggests that a multidimensional musical object (MMO) can substitute for a triad in these traditional compositional roles, particularly in works that challenge a monotonal reading. The MMO can best be thought of as an expansion of the triad, but not in the sense of a tertian extension like a 7th or 9th. Rather, an MMO is a more complex set of pitches that functions similarly to a triad as a compositional component. In order to visualize the MMO as it exists in a composition I have defined the musical surface (what can be heard at any one moment) as one-dimensional, where a one-dimensional musical object sounds consonant. When two- and three-dimensional musical objects are compressed onto the one-dimensional musical surface their geometric shape is distorted and, as a result, sound dissonant. Subsequently, a higher-dimensional musical object must rotate through time (composed-out) to be heard in consonant, one-dimensional slices. Through various examples, I will disclose how Mahler's Seventh Symphony employs a three-dimensional tonic object that influences the structure at every level, most notably in its "progressive" design from E minor in the first movement to C major in the finale.