## 2 Methods
### Subjective Investigation
In the experiment presented here, different triads (triangles) of the test signals have been prepared by convolving anechoic signals with the binaural impulse responses obtained in simulations at positions 1, 3, and 5 (highlighted in Figure 1). Each triad has been built for each anechoic signal and listening position. The triads included two identical signals and one different from the other two in the comparisons RF-DF and RF-DM. These signals have been presented to the listener in a randomized order: comparison of RF with DF (RF-DF-DF, DF-RF-DF, DF-DF-RF, DF-RF-RF, RF-DF-RF, and RF-RF-DF) and comparison of RF with DM (RF-DM-DM, DM-RF-DM, DM-DM-RF, DM-RF-RF, RF-DM-RF, and RF-RF-DM). Also the receiver position and the signal type have been presented in randomized order (Table 2). As in [5], the test has been presented to the subjects via high quality headphones (Sennheiser HD600) without any specific headphone equalization. As explained above, in order to build the psychometric curves, the percentage of correct answers is correlated to the stimulus intensity, which is decreased or increased by a constant step [58; 59]. In this study, the stimulus is represented by the difference between the reflective and the diffusive condition compared at each position. Since there is no method to quantify this stimulus intensity variation between the two conditions, the stimulus intensity variation is associated with the distance from the lateral wall, which increased constantly by 2.77 m (at 2.15 m, 4.92 m, and 7.69 m for position 1, 3, and 5, respectively). Music Samples and Test Subjects  
The music stimuli presented to the listeners were created by convolving the simulated binaural impulse responses with samples of anechoic music recordings (5-6 s). Three different anechoic music samples have been chosen based on different style, tempo, and spectral characteristics [5]: \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{Choral recording} \\ \cline{3-4}  & Motifs & \multicolumn{2}{c}{Piano solo} \\ \cline{3-4}  & & \multicolumn{2}{c}{Orchestra} \\ \cline{2-4} Randomized order & Listening positions & 1 & 3 & 5 \\ \cline{2-4}  & Signals & \multicolumn{2}{c}{RF-DF-DF, DF-RF-DF, DF-DF-RF,} \\  & & DF-RF-RF, RF-DF-RF, RF-RF-DF \\ \cline{3-4}  & & RF-DM-DM, DM-RF-DM, DM-DM-RF, \\  & & DM-RF-RF, RF-DM-RF, RF-RF-DM \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Listening test scheme. Three different music samples played for three listening positions. Samples “RF” are compared with samples “DF” and “DM”, which correspond to the reflective and diffusive condition of the lateral wall, respectively. The order of presentation of the samples has been fully randomized: motif and listening position. Six (3!) permutations of RF and DF or DM order could occur within one triad. * _choral recording_ (\"Alleluia\"--[PERSON], [PERSON], Anechoic Choral Recordings, Wenger),
* _piano solo_ (\"Etude Op. 10 no. 4\"--[PERSON], [PERSON], Digital Recording)
* _orchestra_ (\"Water Music Suite\"--[PERSON], Osaka Philarmonic Orchestra, Anechoic Orchestral Music Recordings, Denon)  
The subjects were chosen on a voluntary basis from professors, research assistants, and students at Politecnico di Torino (Italy). They declared their interest in acoustics and music, and all of them had experience in playing a musical instrument or singing in a choir. A total of 38 subjects participated in the listening tests. They were asked to perform an audiometric test by using an iPad-based application named uHear [60] and wearing the same headphones (Sennheiser HD600) subsequently used in the listening test. Only 31 subjects obtained results within the \"normal hearing level\" and have been considered suitable to perform the perceptual listening test. This sample consisted of subjects aged between 20 and 45 years.