Page 18 - Summer 2021

MUTES FOR MUSICAL HORNS
fundamental pitch (EFP) plot, which can be derived from the input impedance curve (Campbell et al., 2021). An EFP plot for the natural trumpet without a mute is shown in Figure 7C, blue circles. Each impedance peak is assigned an index number (n) starting from the lowest frequency mode. The nth mode, with peak frequency (fn),
has an equivalent fundamental pitch
EFP(n) = (1200/log2) log(fn/nfref) (1)
where fref is the frequency of a reference pitch. EFP(n) is the deviation in cents (hundredths of a semitone) of the pitch of the nth mode from the exact nth harmonic of fref. For an ideal harmonic series with fundamental frequency fref, EFP(n) = 0 for all n, and all the points on the EFP plot lie on a vertical line at frequency fref.
The EFP plot for the unmuted trumpet shows that the impedance peaks from the 3rd to the 16th lie very close to the dashed blue line in Figure 7C, marking a perfect harmonic series with a fundamental frequency of 65.4 Hz, corresponding to the pitch C2, 2 octaves below “middle C.” This is expected because the length of the removable crook at the input of the instrument has been chosen to allow it to play “in C.” Figure 7C, red squares, shows the EFP values when the mute is inserted, confirming that the pitches of the acoustic modes from the eighth downward are increasingly flattened by the insertion of the mute.
The EFP plot also reveals why an acceptable quasi- harmonic set of resonances with a higher pitch can be found on the muted trumpet (Multimedia 3 at acousticstoday.org/campbellmultimedia). Figure 7C, black diamonds, shows recalculated EFP values obtained by discounting the small second peak in the muted input impedance curve and reassigning the index numbers so that the third peak corresponds to n = 2, the fourth peak to n = 3, and so on. This reinterpretation of the pitches of the acoustic modes shows that they lie close to the dashed black line in Figure 7C, representing a perfect harmonic series with a fundamental pitch around 170 cents above C2. A skilled trumpet player can compensate for the residual deviations by adjusting the natural resonance frequency of the lips, a technique known as “lipping.”
Hand Technique on the Horn
A brass instrument can be muted simply by using a hand to partially close the bell. In the eighteenth century, players
of the French horn developed a sophisticated technique in which precise positioning of the hand in the bell was used to modify the loudness, timbre, and pitch of individual notes during a performance. At this time, French horns, like trumpets, were natural instruments whose sounding length could be varied only by removing one crook and inserting another; the pitch-changing property of internal muting was in this case an advantage rather than a prob- lem because it could be used to make musically desirable changes to the pitches of the natural notes of the instru- ment. Although modern French horns have valve systems allowing for almost instantaneous changes of sounding length, the hand technique remains an important aspect of horn performance. The normal position of the player’s hand in the bell is illustrated in Figure 8A.
The partial obstruction of the horn mouth by the player’s hand increases the fraction of the sound energy reflected back into the instrument tube, to an extent that increases with frequency. Figure 9 shows the result of an experiment in which an artificial hand, cast in gelatin from a mold
Figure 8. Placement of a French horn player’s hand in the bell of the instrument. A: normal position. B: stopped position. Photographs courtesy of Lisa Norman.
18 Acoustics Today • Summer 2021