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 Figure 5. Screenshot from wave-based simulation of sound propagation in the Experimental Media and Performing Arts Center Concert Hall, Troy, NY.
 proximation for asymptotically high frequencies, when the wavelength of sound is much smaller than the dimensions of room surfaces but not for low frequencies or wave behav- iors such as diffusion and diffraction. Wave-based modeling requires approximating the solution to the wave equation, typically using finite volume, finite element, or boundary el- ement methods. These methods have existed for many years, but computational complexity has limited widespread use in concert hall acoustical design. Figure 5 shows a screenshot from a wave-based simulation, modeled as part of a research effort to highlight its potential utility in concert hall acous- tics (Hochgraf, 2015). By harnessing the computing power of parallelized finite-volume simulations over multiple cloud- based graphics-processing units (GPUs), wave-based mod- eling may become widely available and computationally ef- ficient very soon, allowing acousticians to test their designs with more accuracy and reliability (Hamilton and Bilbao, 2018).
An auralization will never replace the real experience of lis- tening to music in a concert hall because it does not enable direct, engaging communication between musicians and lis- teners. As a musician and frequent audience member myself, I look forward to more opportunities in the future to draw from these real listening experiences and to use auralization as a research and design tool to support innovative, “excel- lent” design.
Acknowledgments
I thank Alban Bassuet, Timothy Foulkes, Eckhard Kahle, Scott Pfeiffer, Rein Pirn, Paul Scarbrough, and Robert Wolff for sharing their candid thoughts in interviews on concert hall acoustical design. I am also especially grateful to Jonah Sacks and Ben Markham for their feedback and mentorship.
References
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Barron, M., and Marshall, H. (1981). Spatial impression due to early lateral reflections in concert halls: The derivation of a physical measure. Journal of Sound and Vibration 77(2), 211-232.
Bassuet, A. (2011). New acoustical parameters and visualization techniques to analyze the spatial distribution of sound in music spaces. Building Acous- tics 18(3-4), 329-347. https://doi.org/10.1260/1351-010X.18.3-4.329.
Beranek, L. L. (1962). Music, Acoustics, and Architecture. John Wiley & Sons, New York.
Beranek, L. L. (1996). Concert Halls and Opera Houses: How They Sound. American Institute of Physics for the Acoustical Society of America, Woodbury, NY.
Beranek, L. L. (2004). Concert Halls and Opera Houses: Music, Acoustics, and Architecture, 2nd ed. Springer-Verlag, New York.
Beranek, L. L. (2016). Concert hall acoustics: Recent findings. The Journal of the Acoustical Society of America 139, 1548-1556. https://doi.org/10.1121/1.4944787.
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Blauert, J. (2018). Assessing “quality of the acoustics” at large. Proceedings of the Institute of Acoustics: Auditorium Acoustics, Hamburg, Germany, Oc- tober 4-6, 2018.
Bregman, A. S. (1990). Auditory Scene Analysis. The MIT Press, Cambridge, MA.
Green, E., and Kahle, E. (2018). Dynamic spatial responsiveness in concert halls. Proceedings of the Institute of Acoustics: Auditorium Acoustics, Ham- burg, Germany, October 4-6, 2018.
Griesinger, D. (1997). The psychoacoustics of apparent source width, spa- ciousness and envelopment in performance spaces. Acta Acustica united with Acustica 83(4), 721-731.
Griesinger, D. (2011). The relationship between audience engagement and the ability to perceive pitch, timbre, azimuth and envelopment of multiple sources. Proceedings of the Institute of Acoustics: Auditorium Acoustics, Dublin, Ireland, May 20-22, 2011, vol. 33, pp. 53-62.
Haan, C., and Fricke, F. (1997). An evaluation of the importance of surface diffusivity in concert halls. Applied Acoustics 51(1), 53-69.
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