## 6 Analysis of Results
### Comments on Simulated Results  
Figure 5a shows that the simulated EDT results range from 1.5 s to 3.0 s, except for scenario A1 and A2, which represent the existing conditions, where the EDT is about 0.4 s, for the application of the two types of scattering coefficients. It can be seen that the addition of the roof makes the acoustic response slightly less reverberant than the scenario where only the porch is added. When both architectural elements are added to the seating area, the EDT results reach about 2.5 s over the entire frequency bandwidth, which is appropriate for an open-air theatre and meets the criteria for enclosed spaces, as indicated by [PERSON] [34]. Scenario E's results provide the best combination to support early reflections. For 100% occupancy, as shown in Figure 5b, the difference does not change for scenarios A1 and A2. For all other scenarios, the EDT values shift downward by about 0.5 s under occupied conditions. Previous research studies have demonstrated that the presence of an audience in open-air theatres does not significantly affect the acoustic response [40]. This result was found for scenario A, where the absence of a scenic building and porch made no difference regardless of whether the audience was present. Particular attention should be paid to the peak at 1 kHz, which is more pronounced in unoccupied conditions; this effect is due to the diffraction of the steps, as this is a typical phenomenon that occurs in other theatres. As for the reverberation time (T\({}_{20}\)), the reconstruction of the Roman theatre of Gubbio shows that the simulated results for all scenarios are between 1.8 s and 3.0 s, as indicated in Figure 5c, except for scenario A, where the T\({}_{20}\) is around 0.55 s. The room volume is of the utmost importance to determine the optimal range of reverberation time in a room. Assuming a room volume of approximately 6400 m\({}^{3}\), the acoustic response of the theatre associated with the reconstruction of the entire seating area (excluding the roof and porch) can be approximately compared to the acoustics of a concert hall suitable for light music, as indicated in Figure 6. With the addition of the audience, the results for the same scenario shift downward by 0.25 s, as indicated in Figure 5d, so that they are comparable to those of a concert studio with a similar room volume. For all other scenarios, the T\({}_{20}\) results shown in Figure 5c are up to 1.5 s higher than for scenario B, as discussed above, reaching 3.5 s when all the architectural elements are in place. The simulated results presented in Figure 5e indicate a difference of up to 0.2 (20%) between all scenarios, except for scenario A, for which the result is about 0.9 (90%), indicating that it is suitable for speech intelligibility. A very small change can be observed in Figure 5f when the _cavea_ is occupied by listeners. In Figure 5f, scenarios C and D have a similar response in terms of definition, while the results of scenario E with and without an audience are 0.38 and 0.40, respectively. Since clarity strongly depends on the considered position in the seating area, the spatial distribution of speech and music clarity can be more accurately represented with spatial acoustic maps, plotting the values referenced to 1 kHz, as shown in Figures 7 and 8. Figure 6: Optimal reverberation time T\({}_{20}\) at mid-frequency (500–2000 Hz) for the Roman theatre of Gubbio, as a function of volume size and building type [41]. Figure 7: _Cont._  
Figure 7a,b show that the C\({}_{50}\) results are 13-14 dB, with higher values for the seats closer to the stage. This is considered too clear for a speech performance, although it is typical and/or similar for other ancient open-air theatres that are damaged or ruined and missing several original structures. The simulations with two types of scattering coefficients make very little difference. Figure 7c shows that the C\({}_{50}\) results without an audience range from 0 dB to 3 dB, with levels shifted upward by about 2 dB with full occupancy.