Iyer, Vijay vijay@cnmat.berkeley.edu
Bilmes, Jeff bilmes@icsi.berkeley.edu
Wessel, David wessel@cnmat.berkeley.edu
Wright, Matthew matt@cnmat.berkeley.edu
Center for New Music and Audio Technologies
1750 Arch Street
Berkeley, CA 94709
USA
phone (510) 643-9990, fax (510) 642-7918
Submission Type: short paper
Keywords: Rhythm, timing, expressive timing, feel, tripartite
Content Area: Music Data Structures and Representations
Resources Required for Paper Presentation: Overhead projector, DAT machine, (optional) Power Macintosh.
A majority of world musics are characterized by a collectively-determined and relatively isochronous salient pulse that can be inferred from a musical performance. In such contexts, musicians display a heightened, seemingly microscopic sensitivity to musical timing. Different apparent qualities are created by playing notes slightly late or early relative to the pulse. While numerous studies have dissected the nuances of expressive ritardandi and other tempo-modulating rhythmic phenomena, to our knowledge there have been few careful quantitative studies of expressive timing with respect to an isochronous pulse. In pulse contexts, this fine-scale rhythmic delivery becomes just as important a parameter as, say, tone, pitch, or loudness. All these various musical quantities combine dynamically and holistically to form what some would call a musician's "feel." A careful study of pulse-based music requires similarly integrative treatment of these parameters.
One of the authors has developed a tripartite model for expressive timing in performance of groove-based music. In addition to the salient moderate-tempo pulse or tactus, another important pulse cycle is defined at the finest temporal resolution. It is called the temporal atom or tatum, the smallest cognitively meaningful subdivision of the main beat. A performance is characterized by phenomena on three timescales: 1) at the tactus level, the musical referent or "score"; 2) tempo variation over a larger timescale; and 3) the tatum-relative temporal deviations. Signal-processing techniques were developed to extract each of these three quantities from a musical performance. This work revealed that deviations have a crucial effect on the musical feel. Analysis of deviations can shed light on musicians' internal representations of the rhythmic content of their performances.
More recently, we have elaborated upon the above model to develop a powerful representation for musical rhythm. Implemented in the MAX music-programming environment, the representation includes features such as pitch, accent, rhythmic deviations, tempo variation, note durations (which are found to carry important rhythmic information and are therefore treated independently), and probabilistic processes. We provide a way to exaggerate or de-emphasize rhythmic features by the use of non-linear compression and expansion. The system also employs a novel method for handling large numbers of complex rhythmic structures. This feature facilitates "bottom-up" combination techniques, such as the construction of large musical objects by assembling small musical "cells" in series or parallel, layering of different-length rhythmic cycles, creation of composite beat schemes, and most importantly, improvisatory manipulation of these structures.
The richness of control over many meaningful musical quantities distinguishes our representation from those in more common usage, such as music notation programs, sequencers, and drum machines. Our implementation may be used to collect rhythmic data from musicians for analysis, or to model hypotheses about rhythm cognition. In addition, one of the authors has demonstrated that the representation supports creative applications in improvised performance.