## 4 Digital 3D Models and Acoustic Similarities in the Two Vaulted Halls  
The digital models of the two case studies have been reproduced with AutoCAD 2024 software, by drawing the surfaces as 3D faces. The two halls are characterized by a single nave, covered by a barrel-vault ceiling, with windows positioned along one side of the longitudinal axis. Table 1 summarizes the architectural features of Sisto V Hall in comparison to the Aula Magna of Parma. Figures 2 and 3 show the plan and sections of the models for the selected vaulted spaces, created from drawings and site measurements. In both halls, the longitudinal axis is intersected perpendicularly by pointed-arched vaults. The primary difference between \begin{table}
\begin{tabular}{l l l} \hline
**Description** & **Sisto V Hall** & **Aula Magna Parma** \\ \hline Type of vault & Barreled & Barreled \\ Longitudinal axis (m) & 43.8 & 22.2 \\ Transversal axis (m) & 9.8 & 10.3 \\ Maximum height at the center of the vault (m) & 9.2 & 12 \\ Total volume approx. (m\({}^{3}\)) & 3672 & 2400 \\ \hline \end{tabular}
\end{table} 
Table 1: Architectural characteristics in the vaulted halls. the two spaces is their length, with Sisto V hall being nearly twice as long as Aula Magna. A common feature of both halls is the audience arrangement, which is divided into two areas by a central corridor. Regarding finish materials, the walls in both halls are made of plastered brick, with frescoes on the ceiling and tiled floors. Aula Magna is provided with a shallow podium in timber (20 cm high), used for conference chairs during student celebrations or congress settings. Sisto V Hall, instead, even if not provided with wooden podium, is used for conferences and classical music performances. In Aula Magna, the basement level is clad with timber boards reaching a height of 2.1 m, whereas in Sisto V Hall, the basement-level  
Figure 3: Drawings of the Aula Magna at the University of Parma. Figure 2: Drawings of the Sala Sisto V Hall, Museum of the Opera of San Lorenzo Maggiore in Naples. walls are entirely plastered. At the time of site measurements, the chairs in Sisto V hall were made of plastic, while those in Aula Magna were solid wood. After creating the models, the files were exported in DXF format to prepare them for acoustic simulations, which were carried out using Ramsete 3.13 software [26]. Like many other commercial acoustic software programs, Ramsete is based on ray-tracing computation using a pyramid with a triangular base (instead of conical) propagation, making it suitable for evaluating speech intelligibility within a room. The first step in the acoustic simulation process involved calibrating the absorption coefficients of the interior material. This calibration was based on on-site acoustic measurements, performed using the following equipment:  
For Sisto V Hall: firecrackers as the sound source [27] and a Brahma microphone [28]. For Aula Magna: an equalized omnidirectional loudspeaker (Look Line, Bergamini, Parma, Italy) and an omnidirectional microphone (Bruel & Kjaer 4165, Virum, Denmark). The Brahma microphone consists of a tetrahedral arrangement of four cardioid capsules that are capable of acquiring the necessary information to synthesize the harmonics of the 3D soundscape related to the first-order Ambisonics (IOA). The omnidirectional microphone, instead, does not allow the reconstruction of a 3D soundscape because it is composed of only one capsule that does not recognize the direction of arrival of a soundwave. In both spaces, acoustic measurements were undertaken by placing the sound source in two positions: one corresponding to the conference table and the other at the opposite end, representing the public entrance [29]. In Sisto V hall, the receiver was placed in 24 positions, organized in 12 parallel rows evenly distributed to cover all seating areas.