Teresa D. Wilson
Douglas H. Keefe
Systematic Musicol. Program, School of Music DN-10, Univ. of Washington, Seattle, WA 98195
Nonlinear dynamics offers a nontraditional but useful viewpoint from which to study tone production in the clarinet, and its applications have not been fully explored. A qualitative and quantitative analysis using nonlinear dynamics was done on pressure time series for single (monophonic) and multiphonic tones performed by a professional clarinetist. The pressure was measured by a piezoresistive pressure transducer inserted flush with the inner mouthpiece wall 4.5 cm from the tip. Phase portraits and Poincare sections were produced, and pressure spectra, correlation dimensions D, and Lyapunov exponents were calculated. The multiphonic spectra were biperiodic and phase-locked. For single tones D=1.0--1.1, and for multiphonics D=2.2--2.5. The largest exponent for both single tones and multiphonics was small and positive; for example, the information loss was 1 bit per 44 periods for the written note E[sub 3] and 1 bit per 68 periods for E[sub 5]. The slightly positive Lyapunov exponent and the values D>1 for single tones, and D>2 for multiphonics, may be interpreted as the information loss due to slight fluctuations of a performer who maintains a steady tone. This result represents a significant difference between human performance and physical modeling of musical tone production.