Trombone Transfer Functions: Comparison Between Frequency-Swept Sine Wave and Human Performer Input

Source/filter models have frequently been used to model sound production of the vocal apparatus and
musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission
response or filter characteristic) of a trombone while being played by expert musicians, sound pressure
signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and
then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes
plotted vs. harmonic frequency then became points on the trombone’s transfer function. The first such
recordings were made on analog 1/4 inch stereo magnetic tape. In 2000 digital recordings of trombone
mouthpiece and anechoic output signals were made that provide a more accurate measurement of the
trombone filter characteristic. Results show that the filter is a high-pass type with a cutoff frequency
around 1000 Hz. Whereas the characteristic below cutoff is quite stable, above cutoff it is extremely
variable, depending on level. In addition, measurements made using a swept-sine-wave system in 1972
verified the high-pass behavior, but they also showed a series of resonances whose minima correspond
to the harmonic frequencies which occur under performance conditions. For frequencies below cutoff the
two types of measurements corresponded well, but above cutoff there was a considerable difference. The
general effect is that output harmonics above cutoff are greater than would be expected from linear filter
theory, and this effect becomes stronger as input pressure increases. In the 1990s and early 2000s this
nonlinear effect was verified by theory and measurements which showed that nonlinear propagation takes
place in the trombone, causing a wave steepening effect at high amplitudes, thus increasing the relative
strengths of the upper harmonics.