# Echo Analysis in Iberian Bullfighting Arenas Through Objective Parameters and Acoustic Simulation 1
## 4 Results and Discussion
### Reverberation Times
In the Madrid bullring, the results show that the criteria established in the ISO standard are met in 87.2% of the combinations (71 source-receiver combinations for 6 octave bands). In no case are both criteria violated simultaneously at all frequencies. Of the 12.8% that fail to comply, 10.1% correspond to \(\xi\), violations, with the greatest contribution in the extreme bands of 125 and 4000 Hz. The most notable non-linearity occurs when the sound source is in position S2 at all frequencies for receivers R1 to R5, and for low and high frequencies in receivers R16 to R18 (all these receivers with the sound source on the same radial axis). For receivers R1 to R5, this is due to the proximity of the barrier, which decreases (compared to other sound-source positions) the number of early and late reflections. For receivers R16 to R18, it is due to late-energy focusing. In the Lisbon bullring, it is found that of the 642 recordings (18 reception points, 6 octave bands, 6 sound-source positions, in the two configurations of the bullring roof), 90.8% meet the linearity criterion \(C\) of 0-5% and \(\xi_{\rm T30}\) of 0-5%; 6.5% fall within the range of doubtful values \(C\) of 5-10% and \(\xi_{\rm T30}\) of 5-10%; and 2.7% fail to meet the linearity criterion \(C>10\%\) and \(\xi_{\rm T30}>10\%\). In the Roman amphitheatre of Italica, it is obtained that of the 294 recordings (16 reception points, 6 octave bands, 2 sound-source positions of S1 and S2, plus 17 reception points, 6 octave bands corresponding to S3), 71.6% fail to verify the linearity criterion \(C>10\%\) and \(\xi_{\rm T30}>10\%\); 5.3% are in the range of doubtful values \(C\) of 5-10% and \(\xi_{\rm T30}\) of 5-10%; and 23.1% verify the linearity criterion, \(C\) of 0-5% and \(\xi_{\rm T30}\) of 0-5%. This lack of linearity in Roman amphitheatres seems to be a common feature, since in the Roman performance spaces of Segobriga [7], while in the Roman theatre, all the curves verify the conditions of linearity, and in the amphitheatre of Segobriga, the linearity, although \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **RMCR** & **RMCS** & **Las Ventas** & \
\begin{tabular}{c} **Campo** \\ **Pequeno CO 1** \\ \end{tabular} &
\begin{tabular}{c} **Campo** \\ **Pequeno PO 1** \\ \end{tabular} & **Italica** \\ \hline S1 at 1000 Hz & 2.02 & 2.10 & 3.29 & 3.16 & 3.01 & 1.19 \\ S1 Mid freq. Average & 2.0 & 2.14 & 3.31 & 3.27 & 3.07 & 1.25 \\ All sound sources at 1000 Hz & 1.96 & 2.07 & 3.16 & 3.16 & 3.02 & 1.21 \\ All sound sources Mid freq. average & 1.98 & 2.13 & 3.21 & 3.24 & 3.06 & 1.24 \\ \hline \hline \end{tabular}  
* Closed oculus (CO), partially open oculus (PO).  
\end{table} 
Table 4: Reverberation time \(T_{30}\) (s) in the bullfighting arenas. scarce, depends on the position of the sound source presenting the best conditions when it is located in the centre of the conic. In the Italica amphitheatre, no improvement of the conditions of linearity is observed with the position of the sound source and it cannot be measured in the centre of the conic due to the _fossa bestiaria_.