## 4 Synthesis of the Repository of Binaural Audio Recordings
### HRTF Sets  
The procedure for generating binaural excerpts (explained in detail in the next section) was based on the convolution of the individual music track signals with the head-related transfer functions (HRTFs). Twelve sets of HRTFs were selected for this study from the publicly available repositories (see Table 1). The key requirement during the selection process was that the HRTFs must have contained the measurement points across a \"full sphere,\" in order to be able to synthesize 3D scenes with the ensembles located in the front, back, below, and above a listener. The first three HRTF sets adopted in this study were originally measured by Huawei Technologies, TU Berlin, Munich Research Centre, and Sennheiser Electronic (HUTUBS) [35]. The remaining nine HRTF sets were obtained at the University of York (SADIE) [36], TH Koln [37], and TU Berlin [38], respectively.  
All the selected HRTF sets were measured in the anechoic chambers. The HUTUBS HRTFs were measured using the normalized least mean squares (NLMS) method [35], whereas the remaining HRTFs adopted in this study (SADIE, TH Koln, and TU BERLIN) were acquired by means of the sine sweep techniques [36; 37; 38]. Since the measurements could not be performed reliably at low frequencies, the impulse responses were compensated using various signal post-processing algorithms. For HUTUBS and SADIE HRTFs, the impulse responses were compensated below 200 Hz [35; 36], whereas for TH Koln, they were compensated below 400 Hz [37].  
Figure 3 illustrates the spatial resolution of the four example HRTF sets. Black dots surrounding a listener represent a grid of the measured HRTFs. The highest spatial resolution, being equal to 2\({}^{\circ}\) both in azimuth and elevation, was exhibited by HRTF sets taken at TU Berlin. The HRTF sets measured at University of York (SADIE) had the lowest elevational  
resolution. While their azimuthal resolution was still relatively high, ranging from 0.4\({}^{\circ}\) to 5\({}^{\circ}\), their elevational resolution was low, as it varied from 2.5\({}^{\circ}\) up to 15\({}^{\circ}\). Nevertheless, it was deemed adequate for our purposes.  
In order to ensure the generalizability property of the developed model, the selected HRTFs were diverse in terms of the heads used to undertake the measurements. As it is presented in Table 1, the HRTF sets were obtained using human heads as well as artificial ones (KU 100 and FABIAN). The measurement radius varied between 0.75 and 1.7 m. HRTF sets 7-9 were obtained using only the head (without a torso), whereas the remaining nine HRTF sets were measured using both the head and the torso. The lack of a torso could have had a detrimental effect on the synthesis of ensembles located below and above the listener (this experimental factor is examined below in the results section).  
For the last two HRTF sets presented in Table 1, the artificial head was originally rotated in azimuth relative to the torso by 10\({}^{\circ}\) and \(-\)10\({}^{\circ}\), respectively. These rotations were compensated so that the heads in both cases were pointing forward. This was achieved by a counter-rotation of the two HRTF sets by \(-\)10\({}^{\circ}\) and 10\({}^{\circ}\) in azimuth, respectively. While such a procedure \"equalized\" the position of the head to a front-facing direction, it could have introduced some asymmetry to the ILD and ITD cues, due to the consequent torso rotations. However, since the magnitude of the torso rotations could be considered relatively small (\(\pm\)10\({}^{\circ}\)), these HRTF sets (after the head rotation compensation) were included in this study.