The "Wave Meter Model": A Graphic Notation for Metric Phenomena

Douglas Donley, University of North Texas

Danuta Mirka presents a linear view of musical time while Justin London encourages a cyclic view of musical time. Each of these views has its own strengths and weaknesses: linear time favors the understanding that time cannot regress while cyclic time expresses the recurring nature of musical meter. Is it possible to produce a graphic that expresses both the continuous and cyclic nature of musical time? If one of London's time circles is projected forward such that it maintains its curved path but is not permitted to regress to its starting point, the result would be a familiar shape: a cosine wave. This study will discuss the utility of cosine waves as a model for metric analysis, identify and explain the mechanics of the "Wave Meter Model," and explore the use of the model as a tool for describing:

1) Multiple levels of metrical organization (hypermeter);
2) Metrical coexistence (hemiola);
3) Metrical disturbances (time change, expansions, deletions, etc.).

The ability to express such a wide variety of metrical phenomena makes the "Wave Meter Model", a flexible tool for analyzing and expressing the attributes of musical time, explicating tonal music's temporal hierarchy from the micro-level (a measure) to the macro-level (an entire work).