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Figure 9. Input impedance curves for F horn with (red) and without (black) hand in bell. From Dell et al., 2010, with permission of the Australian Acoustical Society.
obtained from a human performer, was used to investi- gate the effect of hand technique on the input impedance curve of a French horn (Dell et al., 2010). The boost in the heights of the peaks in the input impedance curves, partic- ularly in the region around the cutoff frequency, is clearly shown. The strengthening of the high-frequency acoustic modes extends the range of pitches that can be sounded securely (Yoshikawa and Nabarra, 2017), reducing the risk that the player will “crack” or mis-pitch a high note.
The horn mouth can be almost completely closed by a movement of the player’s wrist, as shown in Figure 8B (see Multimedia 4 at acousticstoday.org/campbellmultimedia). A note played with this hand position is described as
“stopped.” The hand is then behaving acoustically as an internal transposing mute; on a horn in F with a sounding length of approximately 4 meters, the effect is to provide the player with a new set of natural notes a semitone higher than the unstopped set. The tutorial by the virtuoso hornist Frank Lloyd (see bit.ly/3uitBs3) includes excellent demon- strations of hand stopping on a modern horn, especially from around 5 minutes 40 seconds.
Nontransposing Internal Mutes
The invention of a mute that could be inserted into the bell of a brass instrument without seriously modifying the pitches of the natural notes is usually credited to the eighteenth century Dresden horn player Anton Joseph Hampel (Humphries, 2019). The simplest form of a nontransposing mute is simply a hollow truncated cone,
closed at the wide end and open at the narrow end. A trumpet mute of this type is illustrated in Figure 1B, and a spectacularly large tuba straight mute is demonstrated in Multimedia 5 (acousticstoday.org/campbellmultimedia). When the open end of the mute is inserted into the bell, it is held in position by three cork spacers. The sound can radiate only through the narrow annular space between the outer surface of the mute and the inner surface of the bell, resulting in a strong attenuation of the low-fre- quency components in the sound.
The straight-sided cone mute is usually described simply as a “straight mute.” The same term is often applied to the metal mute shown in Figure 1C, although in this common design, the conical part is tapered to match the internal profile of the trumpet bell. Straight mutes are widely used in most genres of brass performance, and a player will normally use a straight mute unless some other type is specified in the score.
The hollow cavity inside a straight mute has a range of inter- nal resonances. The lowest frequency acoustic mode of the cavity is the Helmholtz resonance, whose frequency can be estimated by blowing across the open end of the mute (Multimedia 3 at acousticstoday.org/campbellmultimedia). There is also a series of standing wave resonances at much higher frequencies. On a well-designed mute, these internal standing waves do not significantly modify the frequencies oftheacousticmodesoftheinstrument.Theinfluenceofthe Helmholtz resonance can, however, be seen in the appear- ance of an additional peak in the input impedance curve. This behavior has been studied by Sluchin and Caussé (1991), who described the additional peak as “parasitic” because it can disrupt the sounding of low pitches on the muted instrument.
Figure 10 illustrates the changes that occurred in the input impedance curve of a tenor trombone when a straight mute was inserted in the bell (Campbell et al., 2021). In the measurements shown in Figure 10A, the slide was in first position (fully retracted). Figure 10A, blue curve, shows the first five impedance peaks with the mute removed. Figure 10A, red curve, measured with the mute in the bell, shows that the pitches of the second, third, and fourth peaks have been slightly raised in frequency by the mute. More significantly, a small addi- tional peak, corresponding to the parasitic resonance, has appeared at 77 Hz. The second natural note, B♭2, played with the slide in first position, relies on the coupling of
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