# Measurements of Acoustical Parameters in the Ancient Open-Air Theatre of Tymdaris (Sicily, Italy) +
## 5 Discussion  
### General Results and Comparison with Other Ancient Theatres  
A first analysis is conducted on the collected IRs structure. The sound field in ancient theatres is generally considered more similar to a free field than a diffuse one. As previously mentioned, there is a limited energetic contribution after the direct sound. This characteristic has consequences both on the extrapolation of the acoustical parameters and their analysis. In fact, all the parameters were calculated from the IRs through their integration in reverse time, strongly affected by the first reflections. Thus, before analysing the whole structure of the IRs, some conclusions are drawn focusing on the Early Decay Curve (EDC), calculated on the squared impulse response. Figure 9 shows a measured EDC of a typical IR from open-air theatres. The analysis was made with Dirac version 5. As an example, receiver position R6 with dodecahedral source in S1 was chosen as typical EDC. On the x-axis, the arrival time of the direct sound, after the so-called \"flight time\" starting with the emission of the signal from the source, is indicated. The corresponding IR (S1D-R6) is shown in the following Figure 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Source** & **A\({}_{\text{i}}\) (dB)** & **B\({}_{\text{i}}\) (dB)** & **R\({}^{2}\)** \\ \hline Free field & 20 & \(-\)20 & 1 \\ S1D & 25.6 & \(-\)21.8 & 0.95 \\ S2D & 22.7 & \(-\)19.2 & 0.98 \\ S1F & 23.9 & \(-\)20.3 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Linear regression parameters for the Sound Strength decays in Figure 8 (Gmid = A\({}_{\text{i}}\) + B\({}_{\text{i}}\) log\({}_{\text{i}}\)0 d), and the related R\({}^{2}\) coefficient. Figure 8: G\({}_{\text{mid}}\) averaged 500-1 kHz measurement results for all the receivers and sources, expressed as a function of source-to-receiver distance. Figure 9: Measured EDC at 1 kHz for the S1–R6 measurement path with dodecahedral source. Considering the classification made by [PERSON] [46], this type of EDC is described as \"Cliff-type\" decay. In this case, either the direct sound or the early reflections are very strong and the direct sound itself could turn out to be not significant with measurements made beyond 10 m from the source, as in the case of this example. Consequently, [PERSON] reports that this type of EDC is usually leading to Early Decay Time (EDT) shorter than reverberation time such as \(T_{20}\) or \(T_{30}\), due to the difference between the slopes considered in the decay. EDT is determined from a best fit straight line to the first 10 dB of sound decays obtained the reverse-time integration of the squared impulse response curve, while for \(T_{20}\) the evaluation range of the slope is from \(-5\) dB to \(-25\) dB. In an open-air theatre, when the sound field substantially differs from a diffuse field, reverberation time is not in principle applicable, but despite this, it is largely used for the acoustic qualification of ancient theatres and for their comparison [2; 3; 10; 21; 47]. The main contributions to reverberation are few energetic reflections and the scattered sound energy coming from the steps in the cavea. Generally, reverberation time \(T_{20}\) or \(T_{30}\) show a limited variability in the theatre and for this reason they are used for comparison with other similar theatres. On the contrary, EDT shows a higher variability in the theatre as it is obtained from the very first part of the decay curve and its value is mostly affected by the arrival time and by the energy of the reflections after the direct sound. It is thus not used to obtain an overall qualification of the theatres that allows comparisons between different architectural typologies [7]. In this study, EDT resulted lower than reverberation time and is highly instable, thus in order to avoid the reader making misleading conclusions, it was decided not to show its values. Figure 10: Measured IRs in TYN for R6 position, all the source positions (S1 and S2) and typologies (D and F) considered.