3x5 for concert band ; an analysis of the numerical bases of rhythm, gesture, melody and form
3x5 for Concert Band uses the numbers three and five as the basis of many smalland large-scale aspects of the work. The two numbers act as generative numbers, underlying such features of the work as length of melodic and rhythmic gestures, polyrhythmic interaction, articulation of significant formal sectional changes, durational patterns of local and large-scale formal events, and the number and relative length of large formal sections. The two generative numbers and their interaction generate both the formal skeletal structure of the work and aspects of the content of the work as well. v The use of these generative numbers gives the piece a unifying framework and generates musical interest through gestures and events that correspond to the numbers. For example, the superimposition of odd-numbered patterns over even-numbered frameworks (such as rhythmic units of 5 eighth-notes over a 4/4 measure) creates tension in the form of syncopation or polyrhythm. The resulting rhythmic structures sound as if they could be created by intuitive means, but contain a sense of cohesiveness that may be lacking from such a constructive method. The numerically generated structures may be audible or inaudible to the listener depending on their time scale and their proximity to the surface level of the texture. However, the number of events that are easily recognizable as having been derived from the generative numbers creates a sense of continuity and accessibility. Structural details do not exist solely for the sake of intellectual exercise. A sense of spontaneity and unpredictability is also central to the conception of the work, as is a visceral impact. 3x5 for Concert Band is an attempt to reconcile the sometimes disparate worlds of structurally- and intuitively-based music. With a balance of intuitive and logical structure, a work of accessibility and spontaneity can be created without sacrificing structural integrity, intellectual interest and rigor.