# Echo Analysis in Iberian Bullfighting Arenas Through Objective Parameters and Acoustic Simulation 1
## 4 Results and Discussion
### Echo Criterion EK in the Study Cases
#### 4.2.5 Results in the Italica Amphitheatre  
In the Italica amphitheatre, of the 39 source-receiver combinations measured in the audience area, there is, in a first approximation, a risk of echo for speech in 11 combinations: S1-R6, S2-R2, S2-R3, and S2-R4; and in S3-R2, S3-R6, S3-R7, S3-R8, S3-R10 and S3-R11; see Table 11. However, the study of the energy-time curves of the impulse response in receiver R6 of source S1, and of combination S3-R2 shows that the signal providing the Dietsch-Kraak parameter value for speech is actually noise and not a real echo. Likewise, for combinations involving S2, the strong reflection is very close to or within the limit of 50 ms, which is not an echo but a reinforcement of the direct sound. In fact, in all these source-receiver combinations, the acoustic intelligibility parameters present good or excellent values. Only in the case of the S3 source and the receivers that are located in the cavea between 40 and almost 50 m from the source do they present a real echo, with a decrease in the acoustic parameters linked to the intelligibility of speech. Of the 10 source-receiver combinations measured with both the source and receiver in the arena, a risk of speech echo is present in 6 combinations: in S2-R1, and S2-R5; and in S3-R1, S3-R5, S3-R16, and S3-R17, see Table 12. After analysing the decay curves of the impulse responses of these receivers, it is concluded that in all the receivers in the arena associated with source S2, these are strong early reflections that reinforce the direct sound. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & **EK\({}_{\text{speech}}\)** & **EK\({}_{\text{music}}\)** & \(\mathbf{T_{\text{speech}}}\) & \(\mathbf{T_{\text{music}}}\) & \(\mathbf{d_{\text{s-r }}}\) (m) & \(\mathbf{D_{50m}}\) & **STI** & \(\mathbf{T_{\text{sm}}}\) (ms) & \\ \hline S1 Arena & & & & & & & & & & \\ North Zone & & & & & & & & & & \\ \hline R6 & 1.05 & 0.89 & 1399 & 1399 & 14.2 & 0.94 & Exc. & 0.84 & Exc. & 17 & Exc. \\ \hline S2 Arena & & & & & & & & & & \\ South Zone & & & & & & & & & & \\ R2 & 1.02 & 1.12 & 43 & 49 & 39.8 & 0.74 & Good & 0.65 & Good & 47 & Good \\ R3 & 1.03 & 1.06 & 52 & 55 & 45.2 & 0.77 & Good & 0.63 & Good & 40 & Good \\ R4 & 1 & 1 & 54 & 57 & 38.5 & 0.74 & Good & 0.58 & Good & 45 & Good \\ \hline S3 Arena & & & & & & & & & & \\ West Zone & & & & & & & & & & \\ R2 & 1.01 & 0.86 & 2842 & 2842 & 19.9 & 0.92 & Exc. & 0.76 & Exc. & 17 & Exc. \\ R6 & **1.01** & 1.35 & **95** & 94 & 40.0 & 0.62 & Good & 0.62 & Good & 49 & Good \\ R7 & **1.38** & 1.59 & **92** & 97 & 42.3 & 0.46 & Fair & 0.61 & Good & 59 & Good \\ R8 & **1.49** & 1.76 & **76** & 81 & 48.7 & 0.43 & Fair & 0.61 & Good & 62 & Good \\ R10 & **1.40** & 1.61 & **112** & 113 & 39.1 & 0.48 & Fair & 0.58 & Fair & 68 & Good \\ R11 & **1.32** & 1.62 & **115** & 120 & 43.7 & 0.51 & Fair & 0.60 & Good & 66 & Good \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Echo and other acoustic parameters in the Italica amphitheatre in the public area. In bold interpreted as an echo. The same applies to all the receivers associated with source S3 except receiver R17, where a delayed signal appears at 95 ms after the arrival of the direct sound, which reduces the values of the intelligibility parameters, especially \(D_{50}\). As a summary of Section 4.2 regarding the 347 impulse responses measured and processed to obtain the \(\text{EK}_{\text{speech}}\) and \(\text{EK}_{\text{music}}\) parameters in the bullrings and amphitheatre, Tables 5-12 of this section show the source-receiver combinations where \(\text{EK}_{\text{speech}}\geq 1\) and \(\text{EK}_{\text{music}}\geq 1.8\). Of the 307 RIRs recorded in the audience area (39 in RMCR; 75 in RMCS; 71 in Las Ventas; 83 in Campo Pequeno in the two configurations of the roof (59 with the roof closed and 24 with the roof partially open); 39 in the Italica amphitheatre) excluding the musical source positions, it can be concluded that there is a risk of echo for speech in only 11 positions in total.