## 2 Experiment I: Directivity-Controlled Auditory Distance in Auralized Rooms
### Experimental Setup
To monitor potential influence of additional reverberation for some conditions, signals were reverberated before auralization. Two levels of reverberation were tested, of which level 1 corresponds to a room impulse response with a reverberation time of \(T_{60}=0.5\,\mathrm{s}\), level 2 to one of \(T_{60}=1\,\mathrm{s}\), and level 0 to the anechoic signal. \begin{table}
\begin{tabular}{c c l l l l} \hline \hline \multirow{3}{*}{room} & \(R_{1}\) & IEM CUBE, & \(10.3\,\mathrm{m}\times 12\,\mathrm{m}\times 4.8\,\mathrm{m}\), & \(T_{60}=700\,\mathrm{ms}\), & \(d_{1}=1.7\,\mathrm{m}\) \\  & \(R_{2}\) & IEM CUBE, & \(10.3\,\mathrm{m}\times 12\,\mathrm{m}\times 4.8\,\mathrm{m}\), & \(T_{60}=700\,\mathrm{ms}\), & \(d_{2}=2.9\,\mathrm{m}\) \\  & \(R_{3}\) & IEM Lecture Room, & \(7.6\,\mathrm{m}\times 6.8\,\mathrm{m}\times 3\,\mathrm{m}\), & \(T_{60}=570\,\mathrm{ms}\), & \(d_{3}=1.7\,\mathrm{m}\) \\ \hline \multirow{3}{*}{signal} & \(S_{1}\) & female speech taken from _Music for Archimedes_, CD Bang and Olufsen 101 (1992) sequence of irregular artificial bursts & \\  & \(S_{2}\) & speech-spectrum noise with increased kurtosis & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of tested rooms \(R\) and signals \(S\). Figure 3: Room and source configuration for \(R_{1}\), \(R_{2}\), and \(R_{3}\) together with loudspeaker ring used for auralization. \(R_{1}\) and \(R_{2}\) are based on the IEM CUBE differing in the source-listener distance and room \(R_{3}\) is based on the IEM Lecture Room. The listening experiment was carried out as a multi-stimulus test where listeners had to comparatively rate multiple conditions, denoted as sets. Their task was to indicate the distance of auditory objects on a graphical user interface displaying a continuous slider for each condition of a set along the ordinal scale _very close_ (vc), _close_ (c), _moderate_ (m), _distant_ (d), and _very distant_ (vd). The listeners were allowed to repeat each condition at will, and audio files were played back in loop. Fifteen listeners participated in the experiment (three female, twelve male; age 23-54). All of them were experienced listeners in 3D audio and experienced participants in psychophysical studies of hearing; all reported normal hearing acuity. Tested sets (set 1 to 12, see Table 3) comprise 7 conditions, each representing a beampattern, room, signal, and reverberation level. Under a varied beampattern design, e.g., \(A_{1\ldots 7}\), the influence of room (set 1, 10, 11), signal (set 1, 2, 3), and reverberation level (set 1, 12) was only examined separately, yielding responses \(x_{1\ldots 7}^{1}\) for each subject. These separate multi-stimulus sets do not yet permit cross comparison due to the absence of a common reference. As a solution, maintaining a limited testing time, the additional 9-stimulus comparison sets (13\(\ldots\)15) were tested with fewer beampatterns \(A_{1,A,7}\) and instead involving cross-comparisons with regard to signal (13), room (14), and reverberation level (15). They yield cross-comparison responses \(x_{1,4,7}^{1}\) that enable a comparison involving a fine-grained directivity variation in Figures 6-8. In these figures, responses \(x_{2,3}^{1}\) and \(x_{4,5}^{1}\) were re-mapped for each listener by linear scaling and shifting to match \(x_{1,4}^{1}\) with \(x_{1,A}^{1}\), and \(x_{4,7}^{1}\) with \(x_{4,7}^{1}\), respectively:  
\[x_{i}=\left\{ \begin{array}{ll}x_{i}^{1}&\text{for}\;i\in\{1,4,7\},\\ \frac{x_{4}^{1}-x_{1}^{1}}{x_{4}^{1}-x_{1}^{1}}(x_{i}^{1}-x_{1}^{1})+x_{1}^{1} &\text{for}\;i\in\{2,3\},\\ \frac{x_{7}^{1}-x_{4}^{1}}{x_{7}^{1}-x_{4}^{1}}(x_{i}^{1}-x_{4}^{1})+x_{4}^{1} &\text{for}\;i\in\{5,6\},\end{array} \right. \tag{2}\]  
i.e., a complete response set \(x_{1\ldots 7}\) per listener, signal, room, and reverberation level. During the listening session, the listeners were requested to face loudspeaker 1 (\(\phi=0^{\circ}\), cf. Figure 3), which corresponds to the direction of the auralized sound source.