A simple technical measure for the perceived source width Matthias Frank, Georgios Marentakis, Alois Sontacchi Institut f¨ ur Elektronische Musik und Akustik , Email: frank@iem.at Universit¨atf¨ ur Musik und darstellende Kunst Graz, Austria Introduction The inverse relation between the Auditory Source Width (ASW) and the Inter-aural Cross Correlation (IACC) has been used to explain the broadening of instrument sounds encountered when listening in concert halls. Reflections from walls and the ceiling that arrive later than the di- rect sound decrease the IACC and therefore increase the ASW in proportion to their laterality [1, 2, 3, 4]. Al- though spatialization systems exhibit big differences in the directions loudspeaker signals emerge from, a fact that may influence the ASW, this possibility has not been evaluated much yet. Measurements presented here are a part of a bigger study on the perception of the ASW in different amplitude panning methods. The loudspeaker spacing and the location of the source within the speaker array are varied. In this work, we investigate whether the magnitude of the so-called energy vector r E (see Equation 1) can be used to predict the ASW. The energy vector r E is computed analytically from the gains   and the position vectors   = {cos(  ), sin(  )} T of L loudspeakers: r E = ∑ L =1  2    ∑ L =1  2  , r w E = ∑ L =1 (  (  )) 2   ∑ L =1 (  (  )) 2 . (1) Its direction and magnitude relate to the direction and spread of the acoustic energy. A magnitude value of 1 would indicate all acoustic energy comes from a single direction, while one of 0 would correspond to energy distributed in all directions. It is found that a psycho-acoustically informed direction dependent weight (  ) of the gains   needs to be considered (as in r w E ). Below, r E and r w E denote the lengths ∣r E ∣ and ∣r w E ∣. We present correlation results between subjective ASW ratings and different objective measures: r E ,r w E (with different weightings) and IACC E3 obtained from binau- ral dummy head recordings (averaged over the first 80 ms at 500Hz, 1KHz and 2KHz octave bands [2]). Method ASW pairwise comparisons were done for all stimuli combinations from Table 1. Stimuli was 1.5s of pink noise presented at 65dB(A) in front of the listeners who were seated facing forward. Genelec 8020 loudspeakers were equidistantly placed at ear height on a circle with 2.5m radius in the IEM CUBE (11m × 11m × 5m, RT 60 = 470 ms, effective room critical distance 2.76m). After a short training phase, all comparisons were repeated four times. Subjects responded which of the two sounds in the pair (A or B) sounded wider by pressing a button on a keyboard. They could only listen to each sound in the pair once. The experiment and stimuli were generated in real-time using pure-data [5]. 16 subjects (10 male, 6 female) aged from 21 to 38 (median = 28) years participated in this test. All were members of a trained listening panel [6, 7]. The tested conditions correspond to realistic scenarios occurring in spatialization systems using amplitude panning. The following systems with two loudspeaker spacings (Δ  = 45 ∘ corresponding to 8 and Δ  = 22.5 ∘ corresponding to 16 equally spaced speakers) have been tested: 1. Vector Base Amplitude Panning (VBAP) where a phantom source was created within a speaker pair by manipulation of the loudspeaker gains [8] (1 or 2 active speakers), 2. Multi Directional Amplitude Panning (MDAP) where 10 virtual sources within a spread equal to the loudspeaker spacing around the desired source direction were defined [8] (2 or 3 active speakers), 3. 3rd and 7th order Ambisonics systems implemented on 8 and 16 speaker arrays respectively, with two different order weightings applied to each: max r E and basic [9] (2 or 8/16 active speakers). Table 1: Description of test conditions: used system, loud- speaker spacing and source position relative to the loudspeak- ers. *Note on conditions 1, 5 and 7: Each of these conditions represents several systems, in which the loudspeaker spacing and source position yield the same loudspeaker signals. Cond. System(s) Δ  position 1* real source,VBAP - on LS 2 MDAP 22.5 ∘ on LS 3 Ambi max rE 22.5 ∘ on LS 4 Ambi basic 22.5 ∘ on LS 5* VBAP,MDAP,Ambi max rE 22.5 ∘ half-way 6 Ambi basic 45 ∘ on LS 7* VBAP,MDAP,Ambi max rE 45 ∘ half-way 8 MDAP 45 ∘ on LS 9 Ambi max rE 45 ∘ on LS Results Within-subject repetitions were averaged and the pairwise comparison matrices were transformed into scale values, yielding 16 observations for each condi- tion (see Figure 1). Outliers were removed (one for conditions 1, 4 and 9) with Grubbs test ( =0.05). There was a significant main effect of speaker spacing ( (2, 45) = 155.35,< 0.001). The medians of the subjective data were regressed against: the IACC E3 (measured using B&K 4128C), the r E and the r w E with 3 different weightings. Results are presented in Table 2.