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

Open access

Abstract

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.

1. Backus J. (1974), Input impedance curves for the reedwoodwind instruments, J. Acoust. Soc. Am., 56, 4, 1266-1279.

2. Backus J. (1976), Input impedance curves for the brassinstruments, J. Acoust. Soc. Am., 60, 2, 470-480.

3. Backus J., Hundley T.C. (1971), Harmonic generation in the trumpet, J. Acoust. Soc. Am., 49, 2, 509-519.

4. Beauchamp J.W. (1969), Nonlinear characteristics ofbrass tones, J. Acoust. Soc. Am., 46, 1, 1, 76.

5. Beauchamp J.W. (1980), Analysis of simultaneousmouthpiece and output waveforms of wind Instruments, Audio Eng. Soc. Preprint No. 1626.

6. Beauchamp J.W. (1996), Inference of nonlinear effects from spectral measurements of wind instrumentsounds, J. Acoust. Soc. Am., 99, 4, 2, 2455.

7. Beauchamp J.W. (1988), Wind instrument transfer responses, http://ems.music.uiuc.edu/beaucham/trombone/Beauchamp.ASA.s88.pdf

8. Beauchamp J.W. (2007), Analysis and Synthesis ofMusical Instrument Sounds, [in:] Analysis, Synthesis, and Perception of Musical Sounds: Sound of Music, J.W. Beauchamp [Ed.], pp. 1-89, Springer.

9. Benade A.H. (1976), Fundamentals of Musical Acoustics, Oxford Univ. Press, p. 421.

10. Caussé R., Kergomard J., Lurton X. (1984), Inputimpedance of brass musical instruments - Comparisonbetween experiment and numerical models, J. Acoust. Soc. Am., 75, 1, 241-254.

11. Cooper C.M., Abel J.S. (2010), Digital simulationof “brassiness” and amplitude-dependent propagationspeed in wind instruments, Proc. 13th Int. Conf. on Digital Audio Effects (DAFx-10), pp. 1-6.

12. Elliot S., Bowsher J., Watkinson P. (1982), Input and transfer response of brass wind instruments, J. Acoust. Soc. Am., 72, 6, 1747-1760.

13. Fletcher N.H., Rossing T.D. (1991), The Physicsof Musical Instruments, pp. 374-375, Springer-Verlag, 1st ed.

14. Hirschberg A., Gilbert J., Wijnands A.P.J. (1996), Shock waves in trombones, J. Acoust. Soc. Am., 99, 3, 1754-1758.

15. Kinsler L.E., Frey A.R., Coppens A.B., Sanders J.V. (1982), Fundamentals of Acoustics, p. 185, Wiley, 3rd ed.

16. Smyth T., Scott F.S. (2011), Trombone synthesisby model and measurement, EURASIP J. Advances in Signal Processing, Vol. 2011, Article ID 151436, pp. 1-13.

17. Thompson M.W., Strong W.J. (2001), Inclusion ofwave steepening in a frequency-domain model of trombone sound production, J. Acoust. Soc. Am., 110, 1, 556-562.

Archives of Acoustics

The Journal of Institute of Fundamental Technological of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 0.816
5-year IMPACT FACTOR: 0.835

CiteScore 2016: 1.15

SCImago Journal Rank (SJR) 2016: 0.432
Source Normalized Impact per Paper (SNIP) 2016: 0.948

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 95 77 3
PDF Downloads 46 44 4