Sunday, 1:30 pm–3:00
PM
The music-theoretic community has a wide variety of useful analytical tools with which to examine rhythmic structures in traditional, beat-oriented music. However, we are left with very few tools that are designed specifically to deal with the analysis of music that eschews traditional notions of beat and meter.
This paper focuses primarily on the introduction of a new tool to aid in the analysis of such non-beat-oriented music: the relative duration vector (RDVEC). The paper is in two parts. Part one defines and formalizes the RDVEC, and part two applies RDVEC to analysis of the first movement of Edgard Varèse’s 1923 composition Octandre.
RDVEC analysis is a simple generalization of rhythmic contour theory. While traditional rhythmic contours represent relative durations of notes as they occur in temporal order, the RDVEC allows us to express the relative duration content of a motive in an unordered fashion.
In the analytical part of the paper, I apply the RDVEC to the first movement of Octandre. By comparing the RDVECs of successive statements of a repeated rhythmic motive, we will see certain patterns develop. An understanding of these patterns will lead us to a better understanding of the durational organization of this movement.
Ever since François-Joseph Fétis suggested that harmonic sequences—through the force of sheer repetition—“suspend” tonality, sequences have been viewed primarily as agents of transition. A natural consequence of this view was the development of a distinction between sequences that begin and end with the same harmony (prolongational) and those that begin and end with different harmonies (progressional). This paper generalizes this distinction by investigating the distance in number of patterns between the initial chord of a sequence and its first recurrence, and between an initial chord and a chord that stands in a particular (i.e., non-unison) root relationship to it. Building upon John Clough’s conception of sequences as interlaced interval cycles, I enumerate the possible two-chord diatonic sequences. I then propose two constructs to measure prolongational and progressional distance, respectively, and demonstrate how such constructs provide fresh insights into familiar sequences. Some rhythmic applications are also discussed.