“Aerophones in flatland: interactive wave simulation of wind instruments” by Allen and Raghuvanshi

We present the first real-time technique to synthesize full-bandwidth sounds for 2D virtual wind instruments. A novel interactive wave solver is proposed that synthesizes audio at 128,000Hz on commodity graphics cards. Simulating the wave equation captures the resonant and radiative properties of the instrument body automatically. We show that a variety of existing non-linear excitation mechanisms such as reed or lips can be successfully coupled to the instrument’s 2D wave field. Virtual musical performances can be created by mapping user inputs to control geometric features of the instrument body, such as tone holes, and modifying parameters of the excitation model, such as blowing pressure. Field visualizations are also produced. Our technique promotes experimentation by providing instant audio-visual feedback from interactive virtual designs. To allow artifact-free audio despite dynamic geometric modification, we present a novel time-varying Perfectly Matched Layer formulation that yields smooth, natural-sounding transitions between notes. We find that visco-thermal wall losses are crucial for musical sound in 2D simulations and propose a practical approximation. Weak non-linearity at high amplitudes is incorporated to improve the sound quality of brass instruments.

1. Abel, J., Smyth, T., and Smith, J. O. 2003. A simple, accurate wall loss filter for acoustic tubes. DAFX 2003 Proceedings, 53–57.Google Scholar
2. Adachi, S., and Sato, M. 1996. Trumpet sound simulation using a two-dimensional lip vibration model. The Journal of the Acoustical Society of America 99, 2 (Feb.), 1200–1209.Google ScholarCross Ref
3. Bader, R. 2013. Damping in turbulent Navier-Stokes finite element model simulations of wind instruments. The Journal of the Acoustical Society of America 134, 5 (Nov.), 4219.Google ScholarCross Ref
4. Baines, A. 1967. Woodwind Instruments and Their History, third ed. Faber & Faber, London.Google Scholar
5. Bilbao, S., and Chick, J. 2013. Finite difference time domain simulation for the brass instrument bore. The Journal of the Acoustical Society of America 134, 5 (Nov.), 3860–3871.Google ScholarCross Ref
6. Bilbao, S., Hamilton, B., Torin, A., Webb, C., Graham, P., Gray, A., Kavoussanakis, K., and Perry, J. 2013. Large scale physical modeling sound synthesis. In Proc. Stockholm Music Acoustics Conference. 593–600.Google Scholar
7. Bilbao, S. 2009. Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics, 1 ed. Wiley, Dec. Google ScholarDigital Library
8. Bossart, R., Joly, N., and Bruneau, M. 2003. Hybrid numerical and analytical solutions for acoustic boundary problems in thermo-viscous fluids. Journal of Sound and Vibration 263, 1 (May), 69–84.Google ScholarCross Ref
9. Campbell, M. 2004. Brass Instruments As We Know Them Today. Acta Acustica united with Acustica 90, 600–610.Google Scholar
10. Chadwick, J. N., and James, D. L. 2011. Animating Fire with Sound. ACM Trans. Graph. 30, 4 (July). Google ScholarDigital Library
11. Chadwick, J. N., An, S. S., and James, D. L. 2009. Harmonic shells: a practical nonlinear sound model for near-rigid thin shells. ACM Trans. Graph. 28 (Dec.). Google ScholarDigital Library
12. Chadwick, J. N., Zheng, C., and James, D. L. 2012. Precomputed Acceleration Noise for Improved Rigid-body Sound. ACM Trans. Graph. 31, 4 (July). Google ScholarDigital Library
13. Chandak, A., Lauterbach, C., Taylor, M., Ren, Z., and Manocha, D. 2008. AD-Frustum: Adaptive Frustum Tracing for Interactive Sound Propagation. IEEE Transactions on Visualization and Computer Graphics 14, 6, 1707–1722. Google ScholarDigital Library
14. Cook, P. R. 2002. Real Sound Synthesis for Interactive Applications (Book & CD-ROM), 1st ed. AK Peters, Ltd. Google ScholarDigital Library
15. Cooper, C. M., and Abel, J. S. 2010. Digital simulation of “brassiness” and amplitude-dependent propagation speed in wind instruments. In Proc. 13th Int. Conf. on Digital Audio Effects (DAFx-10), 1–6.Google Scholar
16. Copley, D. C., and Strong, W. J. 1996. A stroboscopic study of lip vibrations in a trombone. The Journal of the Acoustical Society of America 99, 2 (Feb.), 1219–1226.Google ScholarCross Ref
17. Dalmont, J.-P., Gilbert, J., and Ollivier, S. 2003. Nonlinear characteristics of single-reed instruments: Quasistatic volume flow and reed opening measurements. The Journal of the Acoustical Society of America 114, 4 (Oct.), 2253–2262.Google ScholarCross Ref
18. de La Cuadra, P. 2006. The sound of oscillating air jets: Physics, modeling and simulation in flute-like instruments. PhD thesis, Stanford University.Google Scholar
19. Fabre, B., Gilbert, J., Hirschberg, A., and Pelorson, X. 2012. Aeroacoustics of Musical Instruments. Annual Review of Fluid Mechanics 44, 1, 1–25.Google ScholarCross Ref
20. Fletcher, N. H., and Rossing, T. 1998. The Physics of Musical Instruments, 2nd ed. corr. 5th printing ed. Springer, Dec.Google Scholar
21. Funkhouser, T., Carlbom, I., Elko, G., Pingali, G., Sondhi, M., and West, J. 1998. A Beam Tracing Approach to Acoustic Modeling for Interactive Virtual Environments. In Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, ACM, New York, NY, USA, SIGGRAPH ’98, 21–32. Google ScholarDigital Library
22. Gedney, S. D. 1996. An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices. Antennas and Propagation, IEEE Transactions on 44, 12 (Dec.), 1630–1639.Google ScholarCross Ref
23. Giordano, N. 2014. Simulation studies of a recorder in three dimensions. The Journal of the Acoustical Society of America 135, 2 (Feb.), 906–916.Google ScholarCross Ref
24. Hamilton, B., and Webb, C. J. 2013. Room acoustics modelling using GPU-accelerated finite difference and finite volume methods on a face-centered cubic grid. Proc. Digital Audio Effects (DAFx), Maynooth, Ireland.Google Scholar
25. Harrison, R., and Chick, J. 2014. A Single Valve Brass Instrument Model using Finite-Difference Time-Domain Methods. In International Symposium on Musical Acoustics.Google Scholar
26. Helmholtz, H. 1885. On the Sensations of Tone, second ed. Longmans, Berlin.Google Scholar
27. Hsu, B., and Pérez, M. S. 2013. Realtime GPU Audio. Queue 11, 4 (Apr.). Google ScholarDigital Library
28. Huopaniemi, J., Karjalainen, M., Vaelimaeki, V., and Huotilainen, T. 1994. Virtual instruments in virtual rooms – a real-time binaural room simulation environment for physical models of musical instruments. In Proceedings of the International Computer Music Conference, 455.Google Scholar
29. James, D. L., Barbic, J., and Pai, D. K. 2006. Precomputed acoustic transfer: output-sensitive, accurate sound generation for geometrically complex vibration sources. ACM Transactions on Graphics 25, 3 (July), 987–995. Google ScholarDigital Library
30. Keefe, D. H. 1984. Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions. The Journal of the Acoustical Society of America 75, 1, 58–62.Google ScholarCross Ref
31. Langlois, T. R., An, S. S., Jin, K. K., and James, D. L. 2014. Eigenmode Compression for Modal Sound Models. ACM Trans. Graph. 33, 4 (July). Google ScholarDigital Library
32. Lefebvre, A., and Scavone, G. P. 2012. Characterization of woodwind instrument toneholes with the finite element method. The Journal of the Acoustical Society of America 131, 4 (Apr.), 3153–3163.Google ScholarCross Ref
33. Macaluso, C. A., and Dalmont, J.-P. 2011. Trumpet with near-perfect harmonicity: Design and acoustic results. The Journal of the Acoustical Society of America 129, 1 (Jan.), 404–414.Google ScholarCross Ref
34. McIntyre, M. E., Schumacher, R. T., and Woodhouse, J. 1983. On the oscillations of musical instruments. The Journal of the Acoustical Society of America 74, 5 (Nov.), 1325–1345.Google ScholarCross Ref
35. Mehra, R., Raghuvanshi, N., Antani, L., Chandak, A., Curtis, S., and Manocha, D. 2013. Wave-based Sound Propagation in Large Open Scenes Using an Equivalent Source Formulation. ACM Trans. Graph. 32, 2 (Apr.). Google ScholarDigital Library
36. Myers, A., Pyle, R. W., Gilbert, J., Campbell, D. M., Chick, J. P., and Logie, S. 2012. Effects of nonlinear sound propagation on the characteristic timbres of brass instruments. The Journal of the Acoustical Society of America 131, 1 (Jan.), 678–688.Google ScholarCross Ref
37. Noreland, D., Kergomard, J., Laloe, F., Vergez, C., and Guillemain, P. 2013. The logical clarinet: numerical optimization of the geometry of woodwind instruments. Acta Acustica united with Acustica 99, 615–628.Google Scholar
38. O’Brien, J. F., Shen, C., and Gatchalian, C. M. 2002. Synthesizing sounds from rigid-body simulations. In SCA ’02: Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, ACM, New York, NY, USA, 175–181. Google ScholarDigital Library
39. Raghuvanshi, N., and Snyder, J. 2014. Parametric Wave Field Coding for Precomputed Sound Propagation. ACM Trans. Graph. 33, 4 (July). Google ScholarDigital Library
40. Ren, Z., Mehra, R., Coposky, J., and Lin, M. C. 2012. Tabletop Ensemble: Touch-enabled Virtual Percussion Instruments. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, ACM, New York, NY, USA, I3D ’12, 7–14. Google ScholarDigital Library
41. Ricardo, A., Scavone, G. P., and van Walstijn, M. 2007. Numerical simulations of fluid-structure interactions in single-reed mouthpieces. The Journal of the Acoustical Society of America 122, 3 (Sept.).Google Scholar
42. Rossing, T. D., Moore, F. R., and Wheeler, P. A. 2001. The Science of Sound, 3rd Edition, 3rd ed. Addison-Wesley, Dec.Google Scholar
43. Savioja, L., Manocha, D., and Lin, M. 2010. Use of GPUs in room acoustic modeling and auralization. In Proc. Int. Symp. Room Acoustics.Google Scholar
44. Savioja, L. 2010. Real-Time 3D Finite-Difference Time-Domain Simulation of Mid-Frequency Room Acoustics. In 13th International Conference on Digital Audio Effects (DAFx-10).Google Scholar
45. Scavone, G. P., and Smith, J. O. 1996. Digital waveguide modeling of woodwind toneholes. The Journal of the Acoustical Society of America 100, 4 (Oct.), 2812.Google ScholarCross Ref
46. Schissler, C., Mehra, R., and Manocha, D. 2014. High-order Diffraction and Diffuse Reflections for Interactive Sound Propagation in Large Environments. ACM Trans. Graph. 33, 4 (July). Google ScholarDigital Library
47. Smith, J. O. 1986. Efficient simulation of the reed-bore and bowstring mechanisms. In Proc. Int. Computer Music Conf., 275–280.Google Scholar
48. Smith, J. O. 1996. Physical Modeling Synthesis Update. Computer Music Journal 20, 2, 44–56.Google ScholarCross Ref
49. Smith, J. O. 2004. Virtual Acoustic Musical Instruments: Review and Update. Journal of New Music Research 33, 3, 283–304.Google ScholarCross Ref
50. Smith, J. O. 2010. Physical Audio Signal Processing. http://ccrma.stanford.edu/~jos/pasp/ (online book, accessed Jan 2014).Google Scholar
51. Tsingos, N., Jiang, W., and Williams, I. 2011. Using Programmable Graphics Hardware for Acoustics and Audio Rendering. J. Audio Eng. Soc 59, 9, 628–646.Google Scholar
52. Välimäki, V., Pakarinen, J., Erkut, C., and Karjalainen, M. 2006. Discrete-time modelling of musical instruments. Reports on Progress in Physics 69, 1 (Jan.), 1–78.Google ScholarCross Ref
53. van Walstijn, M., and Campbell, M. 2003. Discrete-time modeling of woodwind instrument bores using wave variables. The Journal of the Acoustical Society of America 113, 1 (Jan.), 575–585.Google ScholarCross Ref
54. van Walstijn, M. 2007. Wave-based Simulation of Wind Instrument Resonators. Signal Processing Magazine, IEEE 24, 2 (Mar.), 21–31.Google Scholar
55. Verge, M.-P. 1995. Aeroacoustics of confined jets: with applications to the physical modeling of recorder-like instruments. PhD thesis, Technische Universiteit Eindhoven.Google Scholar
56. Webb, C. J. 2014. Parallel computation techniques for virtual acoustics and physical modelling synthesis. PhD thesis, Acoustics and Audio Group, University of Edinburgh.Google Scholar
57. Zheng, C., and James, D. L. 2009. Harmonic Fluids. In ACM SIGGRAPH 2009 Papers, ACM, New York, NY, USA, SIGGRAPH ’09, 1–12. Google ScholarDigital Library