## 4 Experiment II: Directivity-Controlled Auditory Distance in a Real Room
### Experimental Setup  
In this experiment the effect is proven with a sound source able to vary its directivity namely the icosahedral loudspeaker (IKO, [[http://iko.sonible.com/](http://iko.sonible.com/)]([http://iko.sonible.com/](http://iko.sonible.com/))). This 20-sided, 20-channel playback device employs spherical beamforming as developed in [25; 26] and allows to steer beams up to third order into freely adjustable directions. The directivity of the IKO was controlled using the freely available ambiX plug-in suite [27] with Reaper as DAW. Firstly, auralized signals were encoded using the ambiX encoder, then converted using ambiX converter, and lastly filtered according to [10] using mcfx convolver. This yields twenty-channelaudio files used as conditions for the experiment. Audio playback was controlled by Pure Data on a standard PC with RME MADI audio interface to drive a Sonible d:24 power amplifier. The size controller of the ambiX encoder allows to vary the beam width from third to zeroth order (\(\textsc{size}=0\ldots 1\)). To create a beampattern design representing the design \(A\) of the first experiment, different settings of the size controller were used. By informal listening of the author, size values and orientations were determined, including a zeroth order beam and to opposed third order beams. Directivities \(A^{*}_{1\ldots 4}\) are facing to the listener with values of \(\textsc{size}=(0,0.27,0.47,1)\) and conditions \(A^{*}_{5\ldots 7}\) are rotated by \(180^{\circ}\) with \(\textsc{size}=(0.47,0.27,0)\). Thus, design \(A^{*}\) can be seen as modified version of \(A\), adjusted by the ear. Figure 10 shows calculated beampattern patterns \(A^{*}_{1\ldots 4}\) normalized to constant energy. Other designs evaluated in the experiment are known from the first experiment. While design \(B\) and \(C\) are identical (see Figure 1), design \(D\) is composed of directivities \(B_{1,3,4\ldots 7}\) and \(C_{4}\) in order to achieve the most distinct effect. A horizontal cross-section through measured frequency-dependent beampatterns of the IKO is shown in Figure 11.  
Figure 11: _Cont._  
Figure 10: Beampattern design \(A^{*}\). Room and positioning of the sound source corresponded to the condition \(R_{2}\), cf. Table 2. Similarly to the first experiment, listeners were asked to rate the distance of the auditory object on a graphical user interface. On a screen, the sketch of the setup was displayed and listeners had to adjust 7 randomly sorted markers to the auditory distance, where each marker represented a beampattern of the designs under test. Markers could either be moved directly (drag and drop) or, for fine adjustments, steered with a slider. Each condition could be repeated at will until listeners were satisfied with the match between marker placement and what they heard. To facilitate the task a fine grid indicating distances of \(0.5\,\mathrm{m}\) was displayed on the screen, cf. Figure 11(a). In the room microphone stands marked distances of \((1,2,4)\,\mathrm{m}\), cf. Figure 11(b). Listeners were asked to provide an honest report of what they actually perceived. This instruction had to do with the fact that there was no time limit to provide answers. It aimed specifically at asking listeners to avoid developing theories about which condition they were presented, as some listeners were aware of results from the first experiment. Figure 11: Horizontal cross-section through measured frequency-dependent beampatterns of the IKO normalized by the half-octave smoothed magnitude of the loudest direction in \(A_{1}^{*}\)=\(C_{1}\). Decibel values are color coded over frequency in Hertz and azimuth angle in degree. Figure 12: Conducting the listening experiment II. Additional to distance, the second experiment also examined the apparent source width (ASW) of auditory objects created by beampattern designs \(A^{*}\), \(B\), and \(C\) in a separate task.