## 5 Conclusions  
In this contribution, an investigation was carried out into the influence of various beampatterns on the auditory distance. Two-dimensional simulation of a variable-directivity sound source at a single point in the room was shown to provide control of the auditory distance. Different beampattern designs were proposed that cause pronounced and graduated distance impressions. Additionally, the influence of the auralized room, source-listener distance, signal, and single-channel reverberation was studied.  
The mapping of beampatterns \(A_{1...7}\) and \(B_{1...7}\) to auditory distance curves is sigmoid-shaped. It resembles the compressive power functions described in [5], characterizing the relation between physical and auditory distance. Moreover, agreeing with [20; 21], signals with an increased relative amount of high-frequency energy appeared to be closer in the study.  
Figure 14: Medians and corresponding 95% confidence intervals for beampattern designs of assessed width for signal \(S_{1}\) with use of the IKO.  
Both decreasing the auralized room and increasing the source-listener distance yield a more compressed curve, which is slightly offset in case of the increased source-listener distance. Despite this, the range of discriminability is persistent.  
The use of single-channel reverberation is effective at increasing the auditory distance, however, it narrows the directivity-controllable range of distinguishable distance impressions.  
Successful modeling of the experimental results was presented and all models yield curves that are highly correlated with the experimental data. Interestingly, spatial measures used to quantify the ASW provide very accurate predictions.  
In addition to the findings obtained by loudspeaker-based auralization in the anechoic chamber, we could also present an evaluation of the designs synthesized by a variable-directivity sound source in a room. A listening experiment could show that in real environments the distance perception is biased due to visual cues leading to less pronounced distance impressions. In addition to the auditory distance the apparent source width was evaluated and we could show that in contrast to the natural environments of the study [31], the width highly correlates with distance impressions caused by the directivity of the sound source. This finding explains the performance of spatial measures in the first experiment and enhances the robustness of this new effect in real environments.  
Possible directions of further research are to investigate whether and to which extend larger performance venues (e.g., Ligeti Hall) affect the mapping to perceived distance to answer the question if this effect is preserved for a larger audience.  
The authors thank all listeners for their participation in the listening experiment. This work was funded by the Austrian Science Fund (FWF) project nr. AR 328-G21, Orchestrating Space by Icosahedral Loudspeaker. The paper is an extended version of [9].  
[PERSON], [PERSON], [PERSON], and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON], [PERSON], [PERSON], and [PERSON] analyzed the data; [PERSON] wrote the paper with periodic contributions by the other authors.  
The authors declare no conflict of interest.