# Optimization of Virtual Loudspeakers for Spatial Room Acoustics Reproduction with Headphones
## 4 Results
### Discrimination Criteria  
The discrimination criteria reported by subjects on a paper form were first encoded into electrical form. These answers were then interpreted and translated into English by using the wheel of concert hall acoustics [20], each answer translating into one or more terms. Then, the resulting attributes were sorted and accumulated so that the frequencies of all individual attributes could be reported for every sample pair separately. Only those attributes were included in the analysis whose corresponding discrimination was correct. The results of the analysis have been reported in order of frequency in Table 1. The most frequent perceptual discriminating factors between conditions were image shift, reverberance, and width. The small room had also reported differences in spectral balance, spatial impression and timbre. In the concert hall renderings, loudness differences were reported in addition to the attributes used also for the small room. Image shift was most frequently reported as the discriminating attribute in the small room. Uniform setup with 14 loudspeakers (U14) systematically collected the most reports, which reflects the high discrimination rate. In addition, the difference in reverberance made the discrimination of uniform setups (U14 vs. U22) even easier. Optimized setup with 14 loudspeakers (O14) had notable differences in spectral balance when compared with uniform setups. Most frequent reports on spatial impression concentrated in comparison of U22 to both O14 and U14. The elicited attributes in concert hall pairs were not as distinct as in the case of the small room. The most evident differences were width in O16 vs. U16 and spectral balance in U16 vs. U24. Otherwise \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline
**Space** & \multicolumn{6}{c}{**Small Room**} & \multicolumn{6}{c}{**Concert Hall**} \\ \hline Sample A & O14 & O14 & O14 & O22 & O22 & U14 & O16 & O16 & O24 & O24 & U16 \\ Sample B & O22 & U14 & U22 & U14 & U22 & U22 & O24 & U16 & U24 & U16 & U24 & U24 \\ \hline Subjects 4/4 correct & 2 & 13 & 7 & 10 & 7 & 14 & 3 & 0 & 1 & 3 & 2 & 4 \\
4/4 proportion (\%) & 13.3 & 86.7 & 46.7 & 66.7 & 93.3 & 20.0 & 0.0 & 6.7 & 20.0 & 13.3 & 26.7 \\ P\({}_{\text{adj}}\) (\%) & 7.6 & 85.8 & 43.1 & 64.4 & 43.1 & 92.9 & 14.7 & 0.0 & 0.4 & 14.7 & 7.6 & 21.8 \\ Cl. lower (\%) & - & 70.9 & 22.1 & 44.1 & 22.1 & 82.0 & - & - & - & - & - & - \\ Cl. upper (\%) & 18.8 & - & - & - & - & - & - & 29.7 & 0.0 & 3.3 & 29.7 & 18.8 & 39.3 \\ \hline
**Attribute** & \multicolumn{6}{c}{**Frequency of attributes elicited on the difference between samples A and B**} \\ \hline image shift & 4 & 15 & 9 & 13 & 9 & 12 & 4 & 2 & 6 & 2 & 3 & 2 \\ reverberance & - & 7 & 1 & 5 & 7 & 15 & 4 & 3 & 5 & 4 & 3 & 2 \\ width & - & 6 & 2 & 4 & 6 & 4 & 2 & 7 & 3 & 4 & 3 & 3 \\ spectral balance & 2 & 9 & 5 & 3 & 1 & 2 & 4 & 1 & 2 & - & 1 & 7 \\ timbre & 1 & 3 & 3 & 4 & 4 & 3 & - & 1 & 2 & 4 & 4 & 3 \\ spatial impression & 1 & 3 & 6 & 2 & 2 & 5 & 3 & 1 & - & - & 2 & 4 \\ envelopment & - & 4 & 3 & 5 & 1 & 3 & 2 & 2 & 3 & 1 & 2 & 3 \\ bass & 1 & 3 & 2 & 2 & 4 & 4 & 1 & 1 & 2 & - & - & 1 \\ loudness & 1 & 1 & - & - & 1 & - & 6 & 3 & 1 & 3 & 1 & 2 \\ brightness & 1 & 1 & - & 2 & - & 3 & 2 & 1 & - & 1 & 1 & - \\ distance & - & 1 & - & 2 & 1 & 1 & 1 & - & 1 & 1 & 2 & - \\ size of space & - & - & - & - & - & - & 4 & 1 & - & 1 & 1 & - \\ focus & 1 & - & - & 2 & 2 & - & - & - & - & - & - \\ warmth & - & - & - & 1 & - & 2 & - & - & - & - & - \\ openness & - & - & - & 1 & - & - & - & - & - & - & 2 & - \\ dynamic range & - & - & - & - & - & - & - & - & - & 1 & 1 & - \\ clarity & - & - & - & - & - & 1 & - & - & - & - & - & - \\ source presence & - & - & 1 & - & - & - & - & - & - & - & - & - \\ spatial balance & - & - & - & - & 1 & - & - & - & - & - & - & - \\ \hline Total & 12 & 53 & 32 & 44 & 39 & 57 & 33 & 23 & 25 & 22 & 26 & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of the listening test and the frequencies of the attributes elicited by 15 subjects for correctly rated pairs.