Numerical simulations of Italian opera houses using geometrical andwave-based acoustics methods
Dario D’ORAZIO(1) , Giulia FRATONI(2) , Anna ROVIGATTI(3) , Brian HAMILTON(4)(1) University of Bologna - Department of Industrial Engineering, Italy, dario.dorazio@unibo.it(2) University of Bologna - Department of Industrial Engineering, Italy, giulia.fratoni2@unibo.it(3) University of Bologna - Interdepartmental Centre for Industrial Research, Italy, anna.rovigatti2@unibo.it(4) University of Edinburgh - Acoustics & Audio Group, UK, Brian.Hamilton@ed.ac.uk

AbstractThe acoustics of opera houses represents an interesting topic in scientific literature due to their architectural andmorphological characteristic traits (shape, materials, coupled volumes). A way to exploit the outstanding valueof Italian theatres acoustics is to perform different typologies of music while adding or removing acousticallysignificant elements on the stage. Numerical simulations may be used as useful tools for designing distinct
layouts and for optimising such performances. The present study investigates strengths and weaknesses of
two different room acoustics modelling approaches: geometrical acoustics (GA) and wave-based methods. The
commercial GA software ODEON and a hybrid ray-tracing and finite-difference time- domain (FDTD) approach
are applied in this work. Measurements carried out in a sample of Italian Opera houses provide reference datafor 3D virtual models calibration. Preliminary comparisons between room acoustical simulation methods areshown and discussed.
Keywords: opera house; acoustic simulation; ray-tracing; wave-based method; finite-difference timedomain.

1INTRODUCTION

The particular features of theatres designed for classical opera cause recurrent and precise acoustic effects thathave always raised a great interest in the scientific community [1, 2]. The present study describes a comparison
between two distinct simulation methods used on a sample of four historical Italian opera houses to investigate
advantages and disadvantages of each approach when applied to this kind of performance spaces [3]. Acoustic
data obtained with a series of physical measurements campaigns were considered as reference point during theassessment of the different performances.

2METHODThe opera houses taken under study represent an heterogeneous sample since they vary in the main hall shape,
the construction materials, the volumes and the reverberation conditions (see Fig. 1 and Tab. 1). Between
2014 and 2016 these theatres were surveyed through a massive acoustic measurement campaign carried out
according ISO 3382-1 [4, 5]. Objective room criteria were extracted from the impulse responses acquired using
the exponential sine sweep technique, with two sound source points on the stage and a mesh of receivers
spread throughout stalls, boxes and galleries. A simplified numerical model was created for each opera house
under study and was maintained for both the simulation methods adopted, on one hand a geometrical acoustics
algorithm and on the other hand a hybrid wave-based and ray-tracing method.
2.1 Geometrical acoustics
The ray-based software select in this work uses a hybrid algorithm that mixes the deterministic image source
method approach for the early reflections and the statistical ray-tracing for the reverberant tail. A frequency

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(a) BOL(b) BON(c) ALI(d) DUS

Figure 1. View of numerical 3D models employed in both the calibration processes.
Table 1. Main features of the sample of the opera houses surveyed.

BOLBON
ALI
DUS

ShapeVhall(m3 )Vflytower(m3 )N-Tiers of boxes/galleries-Prosc. ArchWxH

Year-T30,M(s)

Bell
Horse shoe
Horse shoe
Modern

5500
3130
3360
7400

19900
8900
5280
2820

1000
798
835
999

4 boxes + 1
4 boxes + 1
4 boxes + 1
2 galleries + balcones

15 x 1212 x 7.8
12.5 x 11.7
10.3 x 11.2

1763
1846
1852
1940

1.46
1.70
1.21
1.32

dependent series of absorption coefficient was assigned to the layers of numerical models as well as scattering values allowed to compensate the lack of modeled details and to consider wave phenomena as diffraction
effects [6, 7].
2.2 Wave-based method
The hybrid wave-based method uses a finite-difference time-domain procedure for low and medium frequencies
and ray-tracing for higher frequencies. In theatres like those surveyed in this work the threshold frequency wasapproximately 4 kHz, depending mainly on the volume and the available compute resources. Material properties
are expressed in terms of acoustic admittances assigned as boundary conditions to surfaces [8].

3PRELIMINARY RESULTS AND DISCUSSIONSIn order to compare the results between the simulations methods two different calibration processes were carriedout employing the same common geometries and achieving the match with measured room criteria (reverberation time, early decay time, sound clarity and centre time). Firstly the calibration of numerical models wasdeveloped using the geometrical acoustic software with absorption and scattering coefficients taken from previous scientific literature and then adjusted through an iterative procedure. The absorption values obtained at theend of the process were successively used as starting point for the choice of boundary conditions in the wavebased method. The final absorptive properties resulting from the two calibration approaches show the highest
difference in scattering elements as the seats in the stalls and the furniture within boxes and galleries.

REFERENCES[1] Beranek, L. Concert Halls and Opera Houses: Music, Acoustics, and Architecture. Springer, NY (USA),
2nd edition, 2004.

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[2] Prodi N., Pompoli R., Martellotta F., and Sato S., Acoustics of Italian Historical Opera Houses, J. Acoust.
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