## 5 Results and Discussion
### Global Analysis  
Figure 9 represents the spatially averaged values versus frequency in octave bands and the standard deviations of these parameters. Reverberation, evaluated based on the values of \(T_{30}\) and EDT, even with the presence of the public, in all models over the centuries \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **125 Hz** & **250 Hz** & **500 Hz** & **1 kHz** & **2 kHz** & **4 kHz** \\ \hline Standing audience & 0.16 & 0.29 & 0.55 & 0.80 & 0.92 & 0.90 \\ (\(\text{Ip}/\text{m}^{2}\)) [30] & 0.10 & 0.10 & 0.10 & 0.10 & 0.10 & 0.10 \\ \hline Wooden occupied & 0.23 & 0.37 & 0.83 & 0.99 & 0.98 & 0.98 \\ bench [34] & 0.30 & 0.40 & 0.50 & 0.60 & 0.70 & 0.80 \\ \hline Wooden occupied chair & 0.24 & 0.40 & 0.78 & 0.98 & 0.96 & 0.87 \\ (\(\text{2 chairs}/\text{m}^{2}\)) [30] & 0.30 & 0.40 & 0.50 & 0.60 & 0.70 & 0.80 \\ \hline Stage: wooden & 0.18 & 0.12 & 0.10 & 0.09 & 0.08 & 0.07 \\ platform [30] & 0.10 & 0.10 & 0.10 & 0.10 & 0.10 & 0.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Modified materials, references, and absorption (up) and scattering (down) coefficients. Figure 8: Choir and upper tribune floor. Receivers located in stands for novices. is excessive, both for religious music and for speech. Only the values obtained for the 4000 Hz octave band fall within the optimum range [35]. The averaged values and their errors for \(T_{30}\) and EDT are very similar in each octave band, both in time and between both parameters. \(C_{80}\) and \(D_{50}\) follow the same behaviours and trends. The 21 st-century setting for theatre performances displays the best performance. The improvement experienced by the novices in the 18 th and 19 th centuries when the source is placed on the main alt  
Figure 9: \(T_{30}\), EDT, \(G\), \(C_{80}\), \(D_{50}\), \(J_{\rm LF}\) and IACC\({}_{\rm E}\) spatially averaged versus frequency octave band and error bars (standard error) for the different simulation hypotheses. is especially noteworthy. In the rest of the models, the behaviour is very similar, with significant differences only at low frequencies (125 Hz). In addition to the previous models, the figure showing the sensation of the width of the source (\(J_{\rm LF}\)) incorporates the analysis of the novices in the tribunes at the height of the choir and in the upper floor due to their different behaviour. This is not evident in the rest of the parameters. The differences between the two tribunes are revealed in the first temporary models (H1 and H2), with the source located in the main altar or choir, and with the best subjective sensations being obtained in the upper tribune due to the permanence of the sound late reflections in the dome lantern. Interestingly, when the source is placed in the main altar, the best source width is achieved in the upper tribune and the worst in the lower ones. For the audience located on the ground floor, the best sensation appears with the source located under the dome, followed by the models that locate the source in the main altar, and the worst results are obtained when the source is located in the choir. In this last case, the subjective sensation worsens in the 20 th century compared to the previous ones. The enveloping sensation of the listener, evaluated in the octave bands of interest (500-2000 Hz) is the most suitable for novices in the 18 th-19 th centuries, followed by the models where the source is placed in the choir. Next, are the models in which, throughout history, the sound source has been located in the main altar and, lastly, due to the location of the source, the 21 st century model for theatrical performances under the dome. Finally, the \(G\) values are high enough in all models to create an adequate subjective sound level. The highest values correspond to the 21 st-century model, with the source located under the dome. When it is located on the main altar, the sound level remains similar in its temporal evolution to a choir position, although there is a significant decrease compared to the main altar.