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procession in Florence in 1511. One of the floats in the procession was described as the “Chariot of Death.” On this chariot drawn by oxen, singers dressed as corpses rose from their tombs to sing a mournful song, accompanied by “muted trumpets with a hoarse and deadened sound” (Vasari, 1568). There is no record of the type of mute used by the Florentine trumpeters. In 1607, however, the com- poser Claudio Monteverdi clearly had a solid internal mute in mind when he suggested the use of mutes in the opening “Toccata” of his first opera Orfeo. In a note on the score for the trumpet ensemble that plays this fanfare, he comments that the use of mutes will raise the pitch of the instruments by a tone so that the accompanying strings will have to transpose their parts accordingly.
The trumpets of Monteverdi’s time were natural instru- ments (without valves) almost twice the length of a modern orchestral trumpet. A natural trumpet based on an instrument made in 1632 is illustrated in Figure 7A. No mutes have survived from this period, but a wooden mute of the type in use around a century later is also shown in Figure 7A. The mute fits snugly into the bell of the trumpet, allowing the sound to radiate only through a small internal cavity, terminating in a cylindrical channel around 6 mm in diameter (Pyle, 1991).
A playing experiment with this mute (Multimedia 3 at acousticstoday.org/campbellmultimedia) reveals that its insertion does indeed raise the pitches of the natural notes, although by a little less than the whole tone described by Monteverdi. It might appear surprising that the pitches are raised by the mute because the partial closure of a pipe end usually lowers the frequency of the acoustic modes. A close inspection of the measured input impedance curves of the trumpet with and without the mute provides an explanation for this apparent paradox (Figure 7B). Mea- sured without the mute, the peaks correspond to the first 18 acoustic modes, the highest at a frequency just below 1,200 Hz (Figure 7B, blue curve). These peaks are modified by the insertion of the mute (Figure 7B, red curve). In the frequency range from 500 Hz upward, each muted peak is indeed slightly lower in frequency than the corresponding unmuted peak. Below 500 Hz, however, the frequency shift increases, to the extent that the third red peak appears slightly above the second blue peak. The second red peak is greatly diminished, and the first peak is almost unaffected by the insertion of the mute.
A useful graphical illustration of the extent to which the acoustic mode frequencies of an instrument depart from a perfect harmonic series is provided by the equivalent
Figure 7. A: natural trumpet (after Hanns Hainlein, 1632) with a modern copy of a baroque mute. B: input impedance curves for a natural trumpet without a mute (blue curve) and with a mute (red curve). C: equivalent fundamental pitch (EFP) for a natural trumpet without a mute (blue circles), with a mute (red squares), and with reassigned peak numbers (black diamonds).
Summer 2021 • Acoustics Today 17