## 6 Discussion  
From these results, we present three key findings. The first is that there are significant differences in the attribute ratings given to particular HRTF sets by a general audience. The second is that there exists some correlation between these attributes, for example that of externalisation, richness and preference, but that this correlation is not high. The third is that individual measurements were not perceived by subjects to be of optimal performance. Overall, it is the HRTFs of the dummy mannequins that are most preferred. Surprisingly, it is the HRTFs of the head without shoulders (the KU100) that received the highest rating for preference. This is despite averaging similar or less favourable ratings than the measurements of KEMAR, H11, H20 and H7 with respect to all other attributes, according to general correlations shown in Figure 11. It is likely, therefore, that there exist other factors not identified in this study that have a stronger influence on overall preference. There are two major differences between the measurements of the dummy heads and the human participants: movement and microphones. Despite best efforts, some movement is inevitable with human subjects, the binaural heads on the other hand remain perfectly still. Larger in-built microphones were also utilised for the dummy heads. Significant differences between the preference ratings of human measurements (H20, H7, H9) and (H19), however, indicate that microphone selection alone cannot be the sole cause of preference. It is therefore proposed that the stillness with which a participant sits could impact the quality of measurement and hence the performance of the HRTFs. We see strongest relevant correlation between the attributes externalisation and preference with a Pearson's correlation coefficient value of 0.46. However, we note that this does not indicate a particularly strong correlation. A similar result is seen between richness and preference whilst brightness* appears to correlate relatively poorly with all other attributes. A slight preference for brighter timbres over darker timbres may be interpreted from Figure 11. This is confirmed by the positive correlation coefficient (\(\rho=0.23\), see Table 6) calculated between brightness and preference. These values indicate a slight correlation between the attributes tested in this study. However, it is in fact of more interest to note the lack of strong correlation. Such results show that HRTFs may be rated as highly preferable regardless of their timbral or spatial characteristics. Therefore, selection of an optimal HRTF remains a complex task and likely depends on the application. A key result is the randomness with which a participant rated their own measurements. [PERSON] (20) comments on the repeatability and hence reliability (or lack thereof) of HRTF ratings. They conclude that although, in general, HRTF rating is a difficult task, repeatability of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Brightness** & **Brightness* & **Richness** & **Externalisation** & **Preference** \\ \hline
**Brightness** & 1 & 0.86 & 0.15 & 0.17 & 0.23 \\
**Brightness* & (0.86) & 1 & 0.19 & 0.21 & 0.27 \\
**Richness** & (0.15) & (0.19) & 1 & 0.37 & 0.40 \\
**Externalisation** & (0.17) & (0.21) & (0.37) & 1 & 0.46 \\
**Preference** & (0.23) & (0.27) & (0.40) & (0.46) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Pearson’s correlation coefficient values calculated between attributes (excluding anchors and anomalies). results is significantly higher at the extreme ends of the response scales. This indicates that had individual measurements significantly out-performed non-individual measurements, as one might expect, we should have seen consistent results. However, this was not the case. We find that individual measurements may not necessarily be the optimal tool for binaural rendering, especially when considering the more general requirements of good spatial audio reproduction beyond localisation. Such claims are echoed throughout the literature [7; 8].