## 4 Discussion  
### The Effectiveness of the Band-limited VLT Methods  
The data that were provided in the present experiment have shown that a shift in the perceived elevation of musical sources is apparent when a sufficient amount of direct sound is present in the height layer. In addition, using any of the band or blanket reduction methods that were tested can prevent this from happening. That both the blanket reduction and FB methods were successful was somewhat expected. For example, the blanket reduction thresholds had already been derived in a previous study [9] and so were reasonably expected to work. Additionally, it can be deduced from Table 1 that the influence of the height channel on the resultant amplitude of each source for the FB  
Figure 3: Median perceived elevation and associated notch edges (i.e., non-parametric 95% confidence interval) for each stimulus in the verification experiment. The dotted lines at 0\({}^{\circ}\) and 30\({}^{\circ}\) represent the positions of the main and height layers, respectively.  
method was low, with the average peak amplitude being equal to that for the main layer only condition. Therefore, it seems reasonable that the perceived location of the main channel signal would not be affected, as the audibility of the direct sound in the height layer was low with respect to that in the main layer. It was the main focus of the current study to investigate whether vertical localisation thresholds (VLTs) could be applied through the selective manipulation of frequency bands within the height layer, with the 1+B, 4B and 8B conditions all being effective.  
Consideration was first given to the discussions regarding the mechanisms that might determine the VLTs for complex sources in order to explain the effectiveness of the 1 + B, 4B and 8B methods. The difference in ear-input spectral energy of the height layer to the main layers the vertical quadraphonic condition was measured while using HRIRs that were obtained from the KEMAR dummy head database in order to gain further objective insights into this result [31]. The result is shown in Figure 4, in the range of frequencies covered by the 4 and 8 kHz octave bands (2840-11360 Hz). Any point where the difference is above 0 dB represents the dominance of the height layer over the main layer, and vice versa. From the figure, it can be observed that the height layer has considerably more energy in the 7-9 kHz region when compared to the main layer. Given that 8 kHz 1/3-octave band has an association with above localisation, according to [PERSON]'s directional band theory [14], it is reasonable to suggest that the large energy dominance in the 7-9 kHz region would result in the vertical phantom image condition being elevated with respect to main layer only presentation. By extension, this would also mean that providing sufficient attenuation of the phantom image in this range would result in the VLT being met, which seems to explain why the 8B and 1 + B methods were effective. In either case, the methods would necessitate the attenuation of the 8 kHz octave band by a minimum of 6 dB for transient sources and 10-13.5 dB for continuous sources, based on the listening test results (depending on the ICTD, see Table 1).  
With regard to the 4B method, it can be seen in Figure 4 that the difference in spectral energy between the main and height layers is much smaller for the 4 kHz octave band as compared to the 8 kHz octave band. However, as mentioned in Section 2.2, in [24] the phantom centre image of the 4 kHz octave band was found to be effectively elevated to the physical height of the height loudspeaker layer. This seems to suggest that the attenuation of this band that was tested in the present study was sufficient for suppressing the vertical localisation shift.  
Figure 4: Difference in ear-input spectral energy of the height layer to the main layer of a vertical quadraphonic configuration. The vertical dashed line separates the frequency range for the 4 kHz octave band (left) from that for the 8 kHz octave band (right).