## 1pMU6. A linearized model of bassoon sound production: The role of auxiliary fingerings.

### Session: Monday Afternoon & Evening, May 13

### Time: 4:00

**Author: Douglas H. Keefe**

**Location: Boys Town Natl. Res. Hospital, 555 N. 30th St., Omaha, NE 68131**

**Author: Robert H. Cronin**

**Location: Menlo Park, CA 94025**

**Abstract:**

A quantitative theory of sound regeneration in the bassoon helps explain
differences in the playing frequency and mouthpiece spectra associated with the
use of auxiliary fingerings. The linearized condition for steady-state
oscillations at a frequency f is 0=Y(f)+Y[inf G](f); the air-column input
admittance is Y(f) and the double-reed generator admittance is Y[inf G](f),
whose real part is negative (Fletcher, 1979; Thompson, 1979). The generator
admittance is based upon a simple Bernoulli-type flow model, and the cane reed
is modeled as a damped oscillator. Model parameter values are empirically
determined and combined with measured input admittances, allowing direct
comparison of Y(f) and -Y[inf G](f) at frequencies below and above the open
tone-hole lattice cutoff frequency (Benade, 1960). Auxiliary fingerings produce
significant differences in input admittance magnitude and phase above cutoff,
and sound production is stabilized for a fingering such that the linearized
condition is satisfied near a harmonic multiple of the playing frequency. The
model accounts for intonation shifts associated with changes in auxiliary
fingerings. While sound production in the bassoon is highly nonlinear, the fine
structure of the linear air-column response at frequencies above cutoff is an
essential contributor. [Work partially supported by the International Double
Reed Society.]

from ASA 131st Meeting, Indianapolis, May 1996