Abstract
In this chapter describes the resonant properties of the air column contained within a brass instrument and the nature of the sound radiated from it. The wave equation is presented. Lumped and distributed resonators are defined; travelling and standing waves are explained, and the relationship between standing waves and acoustic resonances is discussed. Time domain and frequency domain descriptions of acoustic processes are compared, and the related concepts of impulse response and input impedance are introduced. Experimental techniques for measuring the input impedance of a brass instrument are described, and the technique of pulse reflectometry is outlined. The concepts of equivalent cone length and equivalent fundamental pitch are explained. The different types of bore profile which are found in brass instruments (cylindrical, conical and flaring) are reviewed, and the Bessel horn model of a flaring tube is examined. The ‘horn function’ is defined and its properties discussed. The effects of the mouthpiece and flaring bell on intonation and timbre are outlined, and the modifications introduced by opening toneholes, muting and hand stopping on horns are explained. The nature of sound radiation from brass instruments is reviewed. In a Going Further section, mathematical techniques for calculating input impedance are discussed, including transfer matrix methods taking into account the effects of losses and bends.
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References
Amir, N., Rosenhouse, G. and Shimony, U. (1995). A discrete model for tubular acoustic systems with varying cross-section – the direct and inverse problem. Parts I and II: theory and experiments. Acustica 81, 450–474.
Amir, N., Pagneux, V. and Kergomard, J. (1997). A study of wave propagation in varying cross-section waveguides by modal decomposition. Part II. Results. J. Acoust. Soc. Am. 101, 2504–2517, https://doi.org/10.1121/1.419306.
Artim GmbH (2020). A-2230 Gänserndorf, Ziehrergasse 4, Austria. http://artim.at. Accessed April 2020.
Backus, J. (1974). Input impedance curves for the reed woodwind instruments. J. Acoust. Soc. Am. 56, 1266–1279, https://doi.org/10.1121/1.1903418.
Backus, J. (1976). Input impedance curves for the brass instruments. J. Acoust. Soc. Am. 60, 470–480, https://doi.org/10.1121/1.381104.
Barbieri, P. (2013). Physics of Wind Instruments and Organ Pipes 1100-2010, Chap. C. Latina, Il Levante Libreria.
Benade, A. H. (1960). On the mathematical theory of woodwind finger holes. J. Acoust. Soc. Am. 32, 1591–1608, https://doi.org/10.1121/1.1907968.
Benade, A. H. (1968). On the propagation of sound waves in a cylindrical conduit. J. Acoust. Soc. Am. 44, 616–623, https://doi.org/10.1121/1.1911130.
Benade, A. H. (1973). The physics of brasses. Scientific American 229(1), 24–35.
Benade, A. H. (1976). Fundamentals of musical acoustics. New York, Oxford University Press. 2nd ed. Mineola, Dover, 1990.
Benade, A. H. and Ibisi, M. I. (1987). Survey of impedance methods and a new piezo-disk-driven impedance head for air columns. J. Acoust. Soc. Am. 81, 1152–1167, https://doi.org/10.1121/1.394636.
Benade, A. H. and Jansson, E. V. (1974). On plane and spherical waves in horns with non-uniform flare: I. Theory of radiation, resonance frequencies, and mode conversion. Acustica 31, 79–98.
Bouasse, H. (1929). Instruments à vent tomes I et II). Paris, Delagrave; repr. with additional material by Jean Kergomard, Paris, Blanchard (1986).
Braden, A. (2006). Bore optimisation and impedance modelling of brass musical instruments Ph.D. Thesis, University of Edinburgh.
Braden, A., Newton, M. and Campbell, D. M. (2009). Trombone bore optimization based on input impedance targets. J. Acoust. Soc. Am. 125, 2404–2412, https://doi.org/10.1121/1.3087423.
Bruneau, M. (2006) Fundamentals of Acoustics. London, Wiley-ISTE.
Buick, J. M., Kemp, J., Sharp, D. B., van Walstijn, M., Campbell, D. M. and Smith, R. A. (2002). Distinguishing between similar tubular objects using pulse reflectometry: a study of trumpet and cornet lead pipes. Meas. Sci. Technol. 13, 750–757. https://10.1088/0957-0233/13/5/313.
Campbell, M. and Greated, C. (1987). The Musician’s Guide to Acoustics. Oxford University Press.
Campbell, D. M. and MacGillivray, T. (1999). Acoustics of the Carnyx. In Hickmann, E., Laufs, I. and Eichmann, R. (Eds) Studies in Musical Archaeology II: Music Archaeology of Early Metal Ages, pp. 357–363. Berlin, Deutsches Archaeologisches Institut.
Caussé, R., Kergomard, J. and X. Lurton (1984). Input impedance of brass musical instruments—Comparison between experiment and numerical models. J. Acoust. Soc. Am. 75, 241–254, https://doi.org/10.1121/1.390402.
Caussé, R., Eveno, P., Gilbert, J. and Petiot, J. F. (2013). What can we deduce from measured resonance frequencies of trumpets concerning their playing frequencies? Proc. Mtgs. Acoust. 19, 035066.
Chaigne. A. and Kergomard, J. (2016). Acoustics of Musical Instruments. New York, Springer.
Chung, J. Y. and Blaser, D. A. (1980). Transfer function method of measuring in-duct acoustic properties. I: Theory. II: Experiment. J. Acoust. Soc. Am. 68, 907–921, https://doi.org/10.1121/1.385211.
Dalmont, J. P. (2001). Acoustic impedance measurement, Part I: a review. J. Sound. Vib. 243, 427–439.
Dalmont, J. P. (2001) Acoustic impedance measurement, Part II: a new calibration method. J. Sound. Vib. 243, 441–459.
Dalmont, J. P., Joly, N. and Nederveen, C. J. (2001). Radiation impedance of tubes with different flanges: numerical and experimental investigations. J. Sound Vib. 244, 504–534.
Dalmont, J. P., Curtit, M. and Yahaya, A. F. (2012). On the accuracy of bore reconstruction from input impedance measurements: Application to bassoon crook measurements. J. Acoust. Soc. Am. 131, 708–714, https://doi.org/10.1121/1.3651793.
Dickens, P., Smith, J. R. and Wolfe, J. (2007). Improved precision in measurements of acoustic impedance spectra using resonance-free calibration loads and controlled error distribution. J. Acoust. Soc. Am. 121, 1471–1481.
Dubos, V., Kergomard, J., Khettabi, A., Dalmont, J. P., Keefe, D. H. and Nederveen, C. (1999). Theory of sound propagation in a duct with a branched tube using modal decomposition. Acta Acust. united Ac. 85, 153–169.
Elliott, S. J. and Bowsher, J. M. (1982). Regeneration in brass wind instruments. J. Sound Vib. 83, 181–217.
Eveno, P., Dalmont, J. P., Caussé, R. and Gilbert, J. (2012). Wave propagation and radiation in a horn: Comparisons between models and measurements. Acta Acust. united Ac. 98, 158–165, https://doi.org/10.3813/AAA.918501.
Félix, S. and Pagneux, V. (2001). Sound propagation in rigid bends: A multimodal approach. J. Acoust. Soc. Am. 110, 1329–1337, https://doi.org/10.1121/1.1391249.
Félix, S., Dalmont, J. P. and Nederveen, C. J. (2012). Effects of bending portions of the air column on the acoustical resonances of a wind instrument. J. Acoust. Soc. Am. 131, 4164–4172, https://doi.org/10.1121/1.3699267.
Fletcher, N. H. and Rossing, T. D. (1998). The Physics of Musical Instruments, 2nd Ed. New York, Springer.
Gibiat, V. and Laloë, F. (1990). Acoustical impedance measurements by the two-microphone-three-calibration (TMTC) method. J. Acoust. Soc. Am. 88, 2534–2545, https://doi.org/10.1121/1.399975.
Giordano, N. (2017). Lip dynamics in a physical model of the trumpet. Proc. International Symposium on Musical Acoustics, Montreal, Canada, 101–104.
Gray, C. D. (2005) Acoustic pulse reflectometry for the measurement of the vocal tract, with application to voice synthesis. Ph.D. thesis University of Edinburgh.
Hall, W. M. (1932). Comments on the theory of horns. J. Acoust. Soc. Am. 3, 552–561, https://doi.org/10.1121/1.1915578.
Helmholtz, H. L. F. (1877). Die Lehre von den Tonempfingungen, 4th Ed. Braunschweig, Friedrich Vieweg. English translation with additional material: Ellis, A. J. On the Sensations of Tone, 2nd Ed. London, Longman, Green and Co. (1885); repr. New York, Dover (1954)
Hélie, T. and Rodet, X. (2003). Radiation of a pulsating portion of a sphere: application to horn radiation. Acta Acust. united Ac. 89, 565–577.
Hendrie, D. (2007). Development of bore reconstruction technique applied to the study of brass wind instruments. Ph.D. thesis, University of Edinburgh.
Hirschberg, A., Gilbert, J., Msallam, R. and Wijnands, A. P. J. (1996b). Shock waves in trombones. J. Acoust. Soc. Am. 99, 1754–1758, https://doi.org/10.1121/1.414698.
Kausel, W. (2001). Optimization of brasswind instruments and its application in bore reconstruction. J. New Music Res. 30, 69–82.
Keefe, D. H. (1984). Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions. J. Acoust. Soc. Am. 75, 58–62, https://doi.org/10.1121/1.390300.
Keefe, D. H. (1990). Woodwind air column models. J. Acoust. Soc. Am. 88, 35–51, https://doi.org/10.1121/1.399911.
Kemp, J. A. (2002). Theoretical and experimental study of wave propagation in brass musical instruments. Ph.D. thesis, University of Edinburgh.
Kemp, J. A., van Walstijn, M., Campbell, D. M., Chick, J. P. and Smith, R. A. (2010). Time domain wave separation using multiple microphones. J. Acoust. Soc. Am. 128, 195–205, 10.1121/1.3392441.
Kemp, J., López-Carromero, A. and Campbell, M. (2017). Pressure fields in the vicinity of brass musical instrument bells measured using a two dimensional grid array and comparison with multimodal models. Proc. 24th International Congress on Sound and Vibration, London.
Kent, E. L. (1956). The Inside Story of Brass Instruments. Elkhart, C. G. Conn Ltd.
Kergomard, J. and Caussé, R. (1986). Measurement of acoustic impedance using a capillary: An attempt to achieve optimization. J. Acoust. Soc. Am. 79, 1129–1140, https://doi.org/10.1121/1.393385.
Kinsler, L. E., Frey, A. R., Coppens, A. B. and Sanders, J. V. (1999). Fundamentals of Acoustics, 4th Ed. New York, Wiley.
Klaus, S. K. and Pyle, R. W. (2015). Trumpet mute pitch: an analysis of three historic trumpet mutes. Proc. Third Vienna Talk on Musical Acoustics, University of Music and Performing Arts, Vienna, 88–91.
Krehl, P. and Engemann, S. (1995). August Toepler – the first who visualized shock waves. Shock Waves 5, 1–18.
Kühnelt, H. (2007). Vortex sound in recorder- and flute-like instruments: Numerical simulation and analysis. Proc. International Symposium on Musical Acoustics, Barcelona, 1-S1-6.
Lefebvre, A. (2010). Computational acoustic methods for the design of woodwind instruments. Ph.D. thesis, McGill University, Montreal.
Levine, H. and Schwinger, J. (1948). On the radiation of sound from an unflanged pipe. Phys. Rev. 73, 383–406.
Li, A., Sharp, D. B. and Forbes, B. J. (2005). Increasing the axial resolution of bore profile measurements using acoustic pulse reflectometry. Meas. Sci. Technol. 16, 2001–2019, doi:10.1088/0957-0233/16/10/017.
Lokki, T. (2014). Tasting music like wine – sensory evaluation of concert halls. Physics Today 67(1), 27.
López-Carromero, A. (2018). Experimental investigation of acoustic characteristics of radiation and playing gestures for lip-excited musical instruments. Ph.D. thesis, University of Edinburgh.
López-Carromero, A., Campbell, D. M., Kemp, J. and Rendon, P. L. (2016). Validation of brass wind instrument radiation models in relation to their physical accuracy using an optical Schlieren imaging setup. Proc. Mtgs. Acoust. 28, 035003.
Lurton, X. (1981). Etude analytique de l’impédance d’entrée des instruments à embouchure. Acustica 49, 142–151.
Macaluso, C. A. and Dalmont, J. P. (2011) Trumpet with near-perfect Harmonicity: Design and acoustic results, J. Acoust. Soc. Am. 129, 404–414. https://doi.org/10.1121/1.3518769.
Martin, D. W. (1942). Lip vibrations in a cornet mouthpiece. J. Acoust. Soc. Am. 13, 305–308, https://doi.org/10.1121/1.1902242.
Mersenne, M. (1635). Harmonicorum libri XII, Paris.
Meyer, J. (2009). Acoustics and the Performance of Music, 5th Edn., English transl. Hansen, U. New York, Springer.
Meyer, J. and Wogram, K. (1969). Die Richtcharakteristiken des Hornes. Das Musikinstrument 18(6), 1.
Meyer, J. and Wogram, K. (1970). Die Richtcharakteristiken von Trompete, Posaune und Tuba. Das Musikinstrument 19, 171.
Nederveen, C. J. (1969). Acoustical Aspects of Woodwind Instruments. Amsterdam, Fritz Knuf.
Nederveen, C. J. (1998a). Acoustical Aspects of Woodwind Instruments, 2nd. Ed. with additional material, Northern Illinois University, 1998.
Nederveen, C. J. (1998b). Influence of a toroidal bend on wind instrument tuning. J. Acoust. Soc. Am. 104, 1616–1626, https://doi.org/10.1121/1.424374.
Noreland, D. (2002). A numerical method for acoustic waves in horns. Acta Acust. United Ac. 88, 576–586.
Ossman, T., Pichler, H. and Widholm, G. (1989). BIAS: A computer-aided test system for brass wind instruments. Audio Engineering Society Preprint No. 2834.
Otondo, F. and Rindel, J. H. (2004). The influence of the directivity of musical instruments in a room. Acta Acust. United Ac. 90, 1178–1184.
Otondo, F. and Rindel, J. H. (2005). A new method for the radiation representation of musical instruments in auralizations. Acta Acust. United Ac. 91, 902–906.
Pagneux, V., Amir, N. and Kergomard, J. (1996). A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I. Theory and validation. J. Acoust. Soc. Am. 100, 2034–2048, https://doi.org/10.1121/1.417913.
Pandya, B. H., Settles, G. S. and Miller, J. D. (2003). Schlieren imaging of shock waves from a trumpet. J. Acoust. Soc. Am. 114, 3363–3367, https://doi.org/10.1121/1.1628682.
Pätynen, J. 2011. A Virtual Symphony Orchestra for Studies of Concert Hall Acoustics. Ph.D. thesis, Aalto University.
Pätynen, J. and Lokki, T. (2010). Directivities of symphony orchestra instruments. Acta Acust. United Ac. 96, 138–187, https://doi.org/10.3813/AAA.918265.
Pelzer, S., Pollow, M. and Vorländer, M. 2012. Auralization of a virtual orchestra using directivities of measured symphonic instruments. Proc. Acoustics12, Nantes, France, 2379–2384.
Pierce, A. D. (1989). Acoustics, 2nd Ed. Acoustical Society of America, Woodbury, NY.
Poirson, E., Petiot, J. F. and Gilbert, J. (2005). Study of the brightness of trumpet tones. J. Acoust. Soc. Am. 118, 2656–2666, https://doi.org/10.1121/1.2006007.
Pratt, R. L., Elliott, S. J. and Bowsher, J. M. (1977). The measurement of the acoustic impedance of brass instruments. Acta Acust. United Ac. 38, 236–246.
Pyle, R. W. (1975). Effective length of horns. J. Acoust. Soc. Am. 57, 1309–1317, https://doi.org/10.1121/1.380607.
Pyle, R. W. (1991). A computational model of the Baroque trumpet and mute. Historic Brass Society Journal 3, 79–97.
Rayleigh, Lord (1894). The Theory of Sound. London, Macmillan; repr. Dover, 1945.
Schumacher, R. T. (1981). Ab initio calculations of the oscillation of a clarinet. Acustica 48, 71–85.
Settles, G. S. (2001). Schlieren and shadowgraph techniques: visualizing phenomena in transparent media. New York, Springer.
Sharp, D. (1996). Acoustic pulse reflectometry for the measurement of musical wind instruments. Ph.D. thesis, University of Edinburgh.
Sharp, D. B., Mamou-Mani, A. and van Walstijn, M. (2011). A single microphone capillary based system for measuring the complex input impedance of musical wind instruments. Acta Acust. United Ac. 97, 819–829, https://doi.org/10.3813/AAA.918462.
Singh, R. and Schary, M. (1978). Acoustic impedance measurement using sine sweep excitation and known volume velocity technique. J. Acoust. Soc. Am. 64, 995–1003, https://doi.org/10.1121/1.382061.
Sluchin, B. and Caussé, R. (1991). Sourdines des Cuivres. Paris, Editions de la Maison des Sciences de l’Homme.
Stradner, G. (2015). Transposing mutes for trumpets. Proc. Third Vienna Talk on Musical Acoustics, 16–19 Sept., University of Music and the Performing Arts, Vienna, 92–25.
van Walstijn, M. O., Cullen, J. S. and Campbell, D. M. (1997). Modelling viscothermal wave propagation in wind instrument air columns. Proc. International Symposium on Musical Acoustics, Edinburgh: in Proc. Institute of Acoustics 19(5), 413–418, 1997.
van Walstijn, M., Campbell, M., Kemp, J., Sharp, D. (2005). Wideband measurement of the acoustic impedance of tubular objects. Acta Acust. United Ac. 91, 590–604.
Vasari, G. (1568). Le vite de’ più eccellenti pittori, scultori, e architettore, 2nd Ed. Florence, Giunti.
Webster, J. C. (1947). An electrical method of measuring the intonation of cup-mouthpiece instruments. J. Acoust. Soc. Am. 19, 902–906.
Widholm, G. (1995). Brass wind instrument quality measured and evaluated by a new computer system. In Proc. 15th International Congress on Acoustics, Trondheim, Norway, Vol. III, 517–520.
Wogram, K. (1972). Ein Beitrag zur Ermittlung der Stimmung von Blechblasinstrument Dr.-Ing. diss., Technischen Universitat Carolo-Wilhelmina zu Braunschweig.
Yoshikawa, S. and Nobara, N. (2017). Acoustical modeling of mutes for brass instruments. In Schneider, A. (Ed.), Studies in Musical Acoustics and Psychoacoustics, Current Research in Systematic Musicology 4. New York: Springer, 143–186, https://doi.org/10.1007/978-3-319-47292-8.
Zorumski, W. E. (1973). Generalized radiation impedances and reflection coefficients of circular and annular ducts. J. Acoust. Soc. Am. 54, 1667–1673, https://doi.org/10.1121/1.1914466.
Zwicker, G. and Kosten, C. (1949) Sound Absorbing Materials. Amsterdam, Elsevier.
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Campbell, M., Gilbert, J., Myers, A. (2021). After the Lips: Acoustic Resonances and Radiation. In: The Science of Brass Instruments. Modern Acoustics and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-030-55686-0_4
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