## 6 Analysis of Results
### Comments on Simulated Results
This result indicates that the speech clarity is within optimal values when the _cavea_ does not have a roof over the stage and there is no porch crowning the seating area. Figure 7d,e show that the results are very similar and range from \(-\)2 dB to \(+\)1 dB, which is exactly in line with the criteria. This means that adding only the roof or only the upper porch improves the speech clarity in the theatre, so that it is within the optimal values. The addition of both architectural elements, as shown in Figure 7f, indicates that the C\({}_{50}\) values are between \(-\)3 dB and 0 dB, with some small areas at the top of the steps where the values are closer to \(-\)4 dB. This configuration is more advantageous for male singers than for female ones, but, in general, it is very close to the optimal values. Figure 7: Spatial distribution of speech clarity index (C\({}_{50}\)) at 1 kHz, with and without audience: scenario A1 (**a**), scenario A2 (**b**), scenario B (**c**), scenario C (**d**), scenario D (**e**), and scenario E (**f**). Similar to Figure 7, the plots in Figure 8 show the simulated results in terms of music clarity. In particular, Figure 8a,b show that the C\({}_{80}\) values are between 14 dB and 18 dB, with a negligible difference between occupied and unoccupied conditions. As for speech clarity, the C\({}_{80}\) results are far from the upper range limit. Figure 8: Spatial distribution of music clarity index (C\({}_{80}\)) at 1 kHz, with and without audience: scenario A1 (**a**), scenario A2 (**b**), scenario B (**c**), scenario C (**d**), scenario D (**e**), and scenario E (**f**). Figure 8c shows that the C\({}_{80}\) values, without a roof and upper porch, are better than those of scenarios A1 and A2, due to the presence of the scenic building at the steps of the _cavea_, with average values between 2 dB and 5 dB without an audience, and between 4 dB and 8 dB with an audience at 100% occupancy. This result is slightly higher than the upper limit established by the criteria (i.e., +2 dB), but acceptable for an open-air space. Scenarios D and E, shown in Figure 8d,e, have similar C\({}_{80}\) values, fluctuating between 4 dB and 5 dB on the steps near the orchestra and \(-\)1 dB or 0 dB in the last rows of seats. This means that the addition of a roof or an upper porch is useful to bring the music clarity values into the optimal range. A better situation is obtained when both architectural elements are added to the structure, as shown in Figure 8f. The plots summarised in Figure 9 show the simulated results of the strength at 1 kHz with respect to all the considered scenarios of the Roman theatre of Gubbio. Figure 9: _Cont_. Figure 9a,b show negative G values for the last rows of seats and for positions away from the orchestra. This reflects the definition of G, which should be equal to 0 dB at 10 m in a perfect anechoic environment; although the floor is reflective in the digital model, while all other vertical surfaces can be considered absorbent for both scenario A1 and A2, the minimum G values were found at about \(-4\) dB. Scenarios B and C, as shown in Figure 8c,d, have similar results, as the addition of the roof to the _cavea_ does not contribute to a visible increase in strength, with values ranging from \(-1\) dB to 8-9 dB. With the addition of the upper porch, as shown in Figure 8e, the G values are between 3 dB and 9 dB, which is appropriate for an open-air theatre. The addition of both architectural elements (i.e., roof and upper porch), as shown in Figure 8f, results in the G response of the theatre in Gubbio ranging between 4 dB (in the last rows of seats) and 10 dB (on the steps near the orchestra). Overall, the simulated results are comparable to those of other open-air theatres whose original reconstruction has been studied in previous research [4] and are in line with the expectations of this wok.