## 8 Outcomes and Simulated Results  
### Acoustic Parameters  
The analysis of the simulated results considers the optimal range of key acoustic parameters, with particular focus on speech. A graph has been created to represent the reverberation time. Spatial acoustic maps illustrate the distribution of speech clarity, as these values vary depending on the listener's position within the seating area.  
Figure 8 summarizes T20 values according to ISO 3382 [29], across frequency bands ranging from 125 Hz to 4 kHz. The graph presents the average results for all virtual microphones used in the models. Simulations were performed under both occupied and unoccupied conditions.  
Figure 8 shows that in Sisto V Hall, T20 values decrease from 4.8 s at mid frequencies to 1.7 s when the hall is not occupied. With full occupancy, T20 values drop by an additional 0.5 s, making the environment more suitable for speech understanding [51].  
In Aula Magna, T20 values decrease from 3.9 s at mid frequencies without treatment to 1.9 s in unoccupied conditions. When fully occupied, T20 values decrease by another 0.4 s, reaching approximately 1.5 s at mid frequencies.  
For speech clarity, C50 values are plotted as acoustic maps in Figure 9, while Equation (1) explains the relationship between the early sound energy within 50 ms and the late sound energy after 50 ms to the end of the impulse response [51]. This equation  
Figure 8: Simulated T20 results related to Sisto V Hall and Aula Magna.  
Figure 7: Disposition of the additional materials within the two halls: Sisto V (**a**) and Aula Magna (**b**).  
explains the importance of balance between early and late reflection and, therefore, the best value is considered 0 dB, with a little tolerance that goes from \(-2\) dB to \(+2\) dB [52]. When the early sound energy is dominant (positive values of C50), the listener is more in the case of direct field, meaning that no reflections from the room helps to support the sound content. In contrast, when the late sound energy is dominant (negative values of C50), the listener is in the reverberant field, meaning that the room is very reverberant, and the comprehension of sound content is poor.  
\[C50=10 Log[\frac{\int_{0}^{50\ ms}p^{2}(\tau)\cdot d\tau}{\int_{50\ ms}^{ \infty}p^{2}(\tau)\cdot d\tau}] \tag{1}\]  
Figure 9a shows that there is no significant difference in C50 values between occupied and unoccupied conditions in Sisto V Hall, as they are evenly distributed across the room. Under occupied conditions, C50 values increase by approximately 2 dB, ranging from 0 dB to \(+4\) dB for seats near the stage, and between \(-1\) dB and \(-2\) dB in the rest of the hall. A similar trend is observed in unoccupied conditions, but C50 values range from \(-1\) dB to \(+2\) near the stage and around \(-4\) dB in the rest of the hall. Overall, C50 values in Sisto V Hall with the acoustic treatment fall within or close to the optimal range for speech clarity (\(-2\) dB and \(+2\) dB) [32; 33].  
Figure 9b shows that in Aula Magna, C50 values are around 0 dB and \(+1\) dB near the stage under unoccupied conditions, while at the back of the hall, they drop to around \(-4\) dB. With full occupancy, C50 values increase by approximately 1 dB, reaching around \(+2\) dB near the stage and \(-2.5\) dB at the back. These values fall within the optimal range for speech clarity [47].  
Figure 9: Spatial distribution of speech clarity index (C50) at 1 kHz, with and without audience: Sisto V Hall (**a**), Aula Magna (**b**).