In search for a source/filter model for brass instruments
James W. Beauchamp

Source/filter models are frequently used to model sound production of the vocal apparatus and musical instruments. They certainly seem to work very well for the voice and for instruments where there is loose coupling between excitation and resonator as in the case of classical string instruments, but it may be a different situation for wind instruments. Beginning in 1968, in an effort to measure a filter characteristic (aka transmission response) of a trombone while it is being played by an expert musician, sound pressure waveforms from the mouthpiece and the bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s filter characteristic. The first such recordings were done on professional 1/4 inch stereo tape. Results showed that the filter was a high-pass with a cutoff frequency around 900 Hz. Whereas the characteristic below cutoff was quite stable, above cutoff it was extremely variable. In addition, measurements made using a swept sine wave system verified the high-pass characteristic, but it also showed a series of resonances whose minima correspond to the harmonic frequencies under playing 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 900 Hz are greater than would be expected from linear filter theory, and this effect becomes stronger as performance dynamic increases. Indeed, this effect was verified by theory and measurements in the 1990’s and early 2000’s which showed that nonlinear propagation takes place in the trombone causing a wave sharpening effect at high amplitudes, thus increasing the strength of the upper harmonics [Hirschberg, Gilbert, Msallam, and Wijnands, J. Acoust. Soc. Am., 1996; Thompson and Strong, J. Acoust. Soc. Am., 2001]. Recently this author made new digital recordings of trombone mouthpiece and anechoic output signals which he believes will allow more accurate measurement of the trombone filter characteristic. Also, a real-time musical sound analysis program was developed that can be used to display the input/output filter response in real time [Madden and Beauchamp, Proc. 1999 Int. Computer Music Conf.].

Related experiments in the 1980s and 1990s were aimed at brass synthesis. The first used a source/filter model for brass synthesis where the source was created by nonlinear distortion of a variable-amplitude sine wave, and the filter was a second-order high-pass type with a cutoff frequency tailored to the particular instrument. In the 1990s a version using multiple waveforms which were interpolated to select spectral-envelope-indexed spectral envelopes and a spectral centroid-vs-time function was used for trumpet synthesis.