Dynamical systems and physical models of trumpet-like instruments. Analytical study and asymptotical properties

Acustica

Volumn 86, Issue 1, 2000, Pages 147-162

  Vergez, Christophe ^a   Rodet, Xavier ^a  

^a IRCAM   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); COMPUTER MUSIC; MATHEMATICAL MODELS; NONLINEAR SYSTEMS;

PHYSICAL MODELS;

ELECTRONIC MUSICAL INSTRUMENTS;

EID: 0040885721     PISSN: 00017884     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. J. Kergomard: Instruments de musique à vent: Comment éviter le chaos pour faire de la musique? Le Quatrième CFA, 1997, 15-22.
2. X. Rodet: One and two mass model oscillation for voices and instruments. ICMC proceedings, Banff, Canada, 1995.
3. X. Rodet: Flexible yet controllable physical models: a non-linear dynamics approach. ICMC proceedings, Tokyo, Japan, 1993.
4. A. H. Benade: The Physics of Brasses. Sci. Am. (1973) 299.
5. N. H. Fletcher: Excitation mechanism in woodwind and brass instruments. Acustica 43 (1979) 63-72.
6. N. H. Fletcher, T. D. Rossing: The physics of musical instruments. Springer Verlag, 1990.
7. S. J. Elliott, J. M. Bowsher: Regeneration in Brass Wind Instruments. Journal of Sound and Vibration 83 (1982) 181-217.
8. X. Rodet, P. Depalle, G. Fleury, F. Lazarus: Modèles de signaux et modèles physiques d'instruments: études et comparai sons. Actes du Colloque Modèles Physiques de Grenoble, 1990.
9. S. Adachi, M. Sato: Trumpet sound simulation using a two-dimensional lip vibration model. J. Acoust. Soc. Amer. 99 (1996) 1200-1209.
10. R. D. Federico, G. Borin: Synthesis of the trumpet tone based on physical models. proceedings ICMC'97, Thessalonike. ICMC, 1997.
11. D. W. Martin: Lip vibrations in a cornet mouthpiece. J. Acoust. Soc. Amer. 13 (1942) 305-308.
12. R. D. Weast: A stroboscopic analysis of lip function. The Instrumentalist 23 (1963) 44-48.
13. D. E. Hall: Musical Acoustics. Brooks/Cole, Pacific Grove, 1991. second edition.
14. C. Vergez, X. Rodet: Model of the trumpet functioning: real time simulation and experiments with an artificial mouth. Proceedings ISMA'97, Edinburgh, 1997.
15. R. D. Ayers: New Perspectives on the Brass Instruments. Proceedings 1SMA98. Acoustical Society of America and Catgut Acoustical Society, Leavenworth, Washington, USA, 1998, 129-134.
16. C. Vergez, X. Rodet: Experiments With An Artificial Mouth For Trumpet. ISMA'98 Proceedings, Leavenworth, Washington State, USA, 1998.
17. S. Yoshikawa: Acoustical behavior of brass player's lips. J. Acoust. Soc. Amer. 97 (1995) 1929-1939.
18. X. Rodet, I. Steinecke: One and two mass models oscillations for voice and instruments. unpublished internal report, IRCAM, 1994.
19. J. D. Dudley, W. J. Strong: A computer study of the effects of harmonicity in a brass wind instrument: impedance curve, impulse response, and mouthpiece pressure with a hypothetical periodic input. Applied Acoustics 30 (1990) 117-132.
20. A. Hirschberg, X. Pelorson, J. Gilbert: Aeroacoustics of Musical Instruments. Meccanica 31 (1996) 131-141.
21. S. Candel: Mécanique des fluides. Dunod, 1995.
22. W. J. Strong: Computer Simulation of a Trumpet. J. Acoust. Soc. Amer. 1 (1990).
23. A. Freed: Tools for rapid prototyping of Musical Sound Synthesis Algorithm. Proceedings of the International Computer Music Conference.
24. C. Vergez, X. Rodet: Comparison of real trumpet playing, latex model of lips and computer model. Procedings ICMC'97, Thessalonike, 1997.
25. M. E. McIntyre, R. T. Schumacher, J. Woodhouse: On the oscillations of musical instruments. J. Acoust. Soc. Amer. 74 (1983) 1325-1345.
26. H. L. F. Helmholtz: On the sensation of tone. Masson, 1954. Reprinted by Dover, from the first edition (1877).
27. J. W. S. Rayleigh: The theory of sound. Dover, New York, 1945. reprinted from the first edition (1877).
28. J. Backus: Small vibration theory of the clarinet. J. Acoust. Soc. Amer. 35 (1963) 305. and Erratum (61) (1977), 1381.
29. T. A. Wilson, G. S. Beavers: Operating modes of the clarinet. J. Acoust. Soc. Amer. 56 (1974) 653.
30. W. E. Worman: Self-sustained nonlinear oscillations of medium amplitude in clarinet-like systems. Dissertation. Case Western Reserve University, 1971. Ann Arbor University Microfilms (ref. 71-22869).
31. J. Saneyoshi, H. Teramura, S. Yoshikawa: Feedback oscillations in reed woodwind and brasswind instrumetns. Acustica 62 (1987) 194-210.
32. D. H. Keefe: Physical Modelling of Wind Instruments. Computer Music Journal 16 (1992) 57-73.
33. N. Grand, J. Gilbert, F. . Laloë: Oscillation threshold of woodwinds instruments. Acta Acustica (1996).
34. X. Rodet, C. Vergez: Physical models of trumpet-like instruments. Detailed behavior and model improvements. ICMC96 proceedings, Hong-Kong, 1996.
35. E. Hopf: Bifurcation of a periodic solution from a stationary solution of a system of differential equations. Ber. Verh. Sach. Akad. Wiss. Leipzig 95 (1942).
36. M. C. Crandall, P. H. Rabinowitz: The Hopf bifurcation theorem in infinite dimensions. Arch. Rat. Mech. Anal. 67 (1978).
37. D. J. Allwright: Harmonic balance and the Hopf bifurcation. Math. Proc. Camb. Phil. Soc. (1977) 453-467.
38. A. I. Mees, L. O. Chua: The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems. IEEE Trans. Circuits and Systems 26 (1979) 235-254.
39. O. Dieckmann, S. M. V. van Gils, S. A. and Lunel, H. O. Walther: Delay equations. functional, complex and nonlinear analysis. Applied mathematical sciences 110 (1995) Springer-Verlag.
40. P. Bergé, Y. Pomeau, C. Vidal: L'ordre dans la chaos. Hermann Editeur des Sciences et des Arts, 1995.
41. R. T. Schumacher: Ab initio calculations of the oscillations of a clarinet. Acustica 48 (1981) 71-85.
42. B. Gazengel, J. Gilbert, N. Amir: Time domain simulation of single reed wind instrument. From the measured input impedance to the synthesis signal. Where are the traps? Acta Acustica (1995).
43. J. Gilbert, J. F. Petiot: Nonlinearités dans les instruments de type cuivre: résultats expérimentaux. Actes de Colloque du quatrième Congrés Francais d'Acoustique, Marseille, 1996.
44. R. Msallam, S. Tassart: Physical model of the trombone including nonlinear propagation effects. ISMA'97 Proceedings, volume 2, University of Edimburgh. Institue of Acoustics, UK, 1997, 419-424.
45. V. Välimäki, T. Tolonen, M. Karjalainen: Signal-dependent nonlinearities for physical models using time-varying fractional delay filters. Proceedings ICMC98, Ann Arbor (Michigan USA), 1998, 264-267.
46. S. Tassart, R. Msallam, P. Depalle, S. Dequidt: A fractional delay application: time-varying propagation speed in waveguides. Proceedings of ICMC97, Thessalonike, 1997.
47. C. Vergez, X. Rodet: Bifurcation Sequence in a Physical Model of Trumpet-like Musical Instruments: From a Fixed Point to Chaos. Proceedings NOLTA'98, volume 2, CransMontana, Switzerland, 1998, 751-754. Research Theory of Nonlinear Theory and its Applications and IEICE, Presses Polytechniques et Universitaires Romandes.
48. Nafeyh: Applied nonlinear dynamics. Springer Verlag, 1991.
49. J. Gilbert, J. Kergomard, E. Ngoya: Calculation of the Steady-State Oscillations of a clarinet using the Harmonic Balance Technique. J. Acoust. Soc. Amer. 86 (1989) 35-41.