Mutes of brass instruments—Experiments and calculations

We have performed precision measurements to determine the effects of various mutes on the input impedance, external averaged spectra, and radiation patterns of brass instruments. A straight mute introduces a parasitic impedance peak and causes frequency shifts in neighboring impedance peaks. For horns which are approximately conical (e.g., tubal) the parasitic peak lies near the lowest resonance. For horns which are approximately hyperbolic (e.g., trumpet and trombone) the parasite normally lies near the second resonance. With increasing penetration of the mute the parasite frequency decreases. In general, the parasite frequency varies as the inverse square root of the mute volume. A cup mute and a Harmon mute may introduce two parasitic peaks. These effects of a mute may be calculated by modeling both horn and mute as a series of truncated cones and computing the input impedance by an iterative procedure. Calculations to date are in reasonable agreement with experiment. The external spectrum of a muted instrument, averaged over radiation direction and playing frequency, shows up to six prominent minima. These correspond well with calculated impedance minima of the mute itself. The mute material may also significantly affect the radiated spectrum. We have, therefore, studied four geometrically identical straight mutes constructed from wood, plastic, aluminum, and cardboard.