## 2 Methods
### Test Stimuli  
The experiment used five natural sound sources of conga, oboe, quartet, speech, and guitar, all of which were anechoic recording excerpts that were taken from [20]. They were chosen due to their varied spectral and temporal characteristics, as shown in Figure 2.  
The following eight experimental conditions were applied to the sources to create test stimuli. For the VLT cases, the attenuation was only applied to the direct sound in the height layer, with the ICTDs of 0 and 1 ms.  
1. Full band VLT (FB): octave-band-dependent attenuation is applied to the height layer. 2. VLTs for 1 kHz band and above (1 + B): octave-band-dependent attenuation is only applied to the 1 kHz band and above. 3. 4 kHz band VLT (4B): only the band centred at 4 kHz is attenuated. 4. 8 kHz band VLT (8B): only the band centred at 8 kHz is attenuated. 5. Blanket VLT: attenuation is applied to the height layer as a whole. 6. Main layer only: only the main layer is presented. 7. Height layer only: only the height layer is presented. 8. Vertically oriented phantom image with 0 dB ICLD: no level attenuation was applied, thus creating a vertical phantom centre image between the two loudspeaker layers. The rationales for the 4B and 8B conditions are as follows. Previous work by the present authors [9] suggest that there might be some perceptual dominance of the 7-9 kHz region in determining the VLTs for complex sources. Furthermore, in the literature it has been reported that the primary cues for elevation perception lie in the 4-10 kHz range [21; 22]. More specifically, 8 kHz is related to 'above' perception, according to [PERSON]'s directional band theory [14], and therefore it is hypothesised that the band that is centred at this frequency would have a major influence on the perception of image elevation. The 4 kHz band is mapped to 'front' localisation by [PERSON]. However, in a phantom image condition, which is the case in the present study, [PERSON] [23] showed that, with a pair of loudspeakers elevated at 30\({}^{\circ}\) from the listener's ear position, a 4 kHz octave band noise was perceived to be elevated at the same height as the loudspeakers, due to the phantom image elevation effect [24; 25]. Therefore, by reducing the energy of this band in the height layer, the perceived elevation of a phantom image that results from the vertical quadraphonic reproduction might be reduced. The 1 + B condition was created  
Figure 2: Long term average spectra and waveforms of test stimuli used for Experiment One. while considering a potential benefit of maintaining the original low frequency energy in the height layer signals captured using omni-directional microphones, whilst reducing all of the high frequencies that are potentially problematic for accurate localisation. In addition, the main and height layer only conditions as well as the blanket and 0 dB ICLD conditions were included to serve as references. Table 1 presents a summary of the VLTs that were used for each band in the current study This is based on the results from a previous study by the authors [8; 9]. For band attenuation, the VLTs that were applied to the speech, oboe, guitar, and quartet sources were the median results obtained for the continuous octave-band noise stimuli in [8]. On the other hand, band reduction for the conga used the VLT obtained for the octave-band noise burst stimuli used in the same study due to its transient nature. It should be noted that, in [8], the thresholds for both the continuous 8 kHz band and the burst 4 kHz band had a significant dependency on the ICTDs, whereas the other octave bands did not, regardless of the transient nature of the sound source. For this reason, in the current study, different thresholds were applied to those two bands, depending on the ICTD and source type. For blanket reduction, the median thresholds that were derived in [9] were used (i.e., \(-\)9.5 dB for 0 ms and \(-\)7 dB for 1 ms).