Teresa Wilson Douglas Keefe
Systematic Musicology Program, School of Music, DN-10, Univ. of Washington, Seattle, WA 98195
There exist few measurements on the acoustical response of tone holes in conical-bore air columns. For practical application to woodwind design, the accuracy of predictive models is said to be insufficient [McCann and Mathews, J. Acoust. Soc. Am. 91, 2449 (A) (1992)]. Experiments performed test the transmission line model of air columns and tone holes. The input impedance was measured over the range 150--10 000 Hz for a single tone hole in a cylindrical bore and in a conical bore. The cylindrical bore had length 920 mm and radius 7.2 mm, and the conical bore had length 630 mm, entry radius 6.5 mm, and exit radius 12.5 mm. In woodwinds, the low-frequency resonances control the playing frequencies. Hence, the resonance frequencies under 1 kHz were predicted from a model of the air column and tone hole. The measured and predicted resonance frequencies for the cylindrical bore agreed to within 6(plus or minus)6 cents and for the conical bore agreed to within 23(plus or minus)18 cents. The errors in the conical-bore theory are largest at low frequencies. Work is underway to refine the theory of tone holes in conical bores.