## 2 Methods  
### Room Model Setup  
The model of a variable acoustic concert hall, the _Espace de Projection_ at IRCAM in Paris (Figure 1), has been considered in this study. Figure 2 depicts the plan of the hall, which has a rectangular geometry (24 m \(\times\) 15.5 m \(\times\) 10 m), and a capacity of 350 seats [37; 38]. The geometry and the acoustical properties of the hall can be varied by controlling 172 independently rotating panels (2.3 m \(\times\) 2.3 m) named _periactes_. Each wall of the hall has four levels of panels. Each panel is made of three triangular prisms (Figure 1), which have three faces with different acoustic properties: reflective, diffusive, and absorptive. The absorptive scheme of all panels has been studied in order to have two different absorption coefficients for adjacent panels. Thus, the total number of panels is divided into two parts: the absorptive side of half of the prisms is filled with a material that absorbs low frequencies (type A), while the other part of the prism has a side that absorbs high frequencies (type B). These two typologies have been obtained by using perforated metal sheets with layers of glass-wood and aluminum sheets inside. The absorptive characteristics of the materials used in the hall are given in Table 1, namely type A and type B [37]. The acoustic characteristics of the walls and ceiling can be modified by changing the properties of the rotating prisms. Six different acoustic conditions of the panels, that is, absorptive, reflective, diffusive, absorptive/reflective, absorptive/diffusive, and diffusive/reflective, can be obtained for the rotating prisms in the second and upper levels, while the first level of the panels can only assume two different configurations: reflective and absorptive. The two hall configurations, whose in-field measurements results are analyzed and discussed in [PERSON] et al. [5], were chosen in this study so that one of the lateral walls was set at two different acoustic conditions: reflective and reflective/diffusive. The second condition is referred to as diffusive condition for easier understanding throughout the paper. Three CAD models have been created (Figure 1): the reflective condition (RF), which is modeled with flat surfaces, and the diffusive condition, which has diffusive surfaces modeled in two ways, flat (DF) or explicitly modeling the 3D triangular structure (DM). In the DF model, the prisms have been modeled as a flat surface to which a scattering coefficient equal to the scattering coefficient of the diffusive surface they represent (0.75 at 707 Hz) is assigned. This value was obtained by BEM-based simulations performed with prediction software named AFMG Reflex [39]. [PERSON] et al. [5] gives the results for the frequency-dependent scattering coefficient. Reflex is two-dimensional acoustics simulation software that models the reflection, diffusion, and scattering properties of a sound wave incident upon a defined geometrical structure. Some assumptions are made in these evaluations, namely that the geometry extends infinitely in the third dimension, i.e., into and out of the computer monitor screen. The surface of the sample is assumed to be perfectly rigid and does not absorb sound or allow sound to be transmitted through it. The calculation of the scattering coefficients is based on the ISO 17497-1 [26], while the directivities are evaluated based on the Cox and D'Antonio method [40]. In the DM model, the prisms are modeled as 3D geometries, and to each surface of the prisms a scattering coefficient equal to that of a flat surface (0.05 at 707 Hz) is assigned [41]. Figure 1: Photos of the two acoustic conditions in the hall: reflective (**a**) and diffusive (**b**). CAD model (RF) for the reflective condition, which is modeled with flat surfaces and s = 0.05. Two CAD models for the diffusive condition: DF (diffusive flat) the prisms have been modeled as a flat surface with s = 0.75, while in the DM (diffusive modeled) the triangular structure has been maintained and s = 0.05 is assigned to each small face.