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Figure 3. Schematic diagram of brass instrument sound production.
brass instrument, however, the resonances of the horn strongly influence the pitches that can be easily played on the instrument. This is because the player’s lips are coupled to the resonant modes of the instrument’s inter- nal air column in a feedback loop, (Figure 3, red arrow). To play a note, the performer presses the lips against the mouthpiece, using facial muscles to set the lip mechani- cal resonance frequency close to the frequency of one of the air column resonances. When air is blown through the aperture between the lips, the coupled system of lips and acoustic resonance is destabilized, and an oscillating regime is established at a frequency near but not exactly equal to the selected acoustic mode frequency (Benade, 1973; Moore, 2016). If the insertion of a mute changes the frequency of the acoustic mode, the frequency and pitch of the played note will also change.
The acoustic resonance frequencies of a brass instru- ment correspond to maxima in the input impedance, which is the ratio of pressure to volume flow rate mea- sured in the mouthpiece (Backus, 1976). A trumpet bell is carefully shaped so that most of the acoustic reso- nances have frequencies close to a harmonic series, as shown in Figure 4 (Campbell et al., 2021). When no valves are activated, the resonance frequencies are simi- lar to those on a B♭ bugle, and the corresponding set of natural (easily playable) notes include those required to play familiar bugle calls such as “Taps” (Figure 5). An experiment with a trumpet and a sock quickly confirms that when the sock is pressed firmly into the bell, the sound level is reduced, but the pitches of the natural notes are so distorted that it is impossible to play a well- tuned bugle call.
Figure 4. Blue line, input impedance of a B♭ trumpet. Red lines, B♭ harmonic series (integer multiples of 116.5 Hz).
Figure 5. The bugle call “Taps,” sounding a tone lower than written when played on a B♭ instrument (available at bit.ly/3at4lqZ).
Summer 2021 • Acoustics Today 15