An Exploration of Virtual Auditory Shape Perception
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An Exploration of Virtual Auditory Shape Perception
I wanted to measure both the horizontal and vertical CMMA. Sine tones, as noted before, are particularly bad for vertical localization. White noise is generally used in vertical localization tasks, but can not be easily "tagged" such that one can distinguish two white noises. Perrott also performed experiments with concurrently presented white noise [1984b]. In this experiment nnhe made an unsuccessful attempt to measure the perceived vertical angular size of concurrent white noise stimuli. One of Perrott's subjects noted that the (horizontal) images of white noise appeared as a "surface composed of `dancing' parts" [Perrott, 1984b, p.1709]. My experiences with white noise in my "shaped ambiguity" experiment makes me wonder if somehow the reason for this is involved in the nature of a white noise stimulus. Perhaps it is somehow insufficiently "cohesive" to have extent on the vertical dimension. To avoid this possibility, in my experiment I employ stimuli consisting of harmonic complexes. These are somewhat better than sine tones for vertical localization, and yet can have clearly distinguishable pitches.
In these experiments I encountered an ill fitting duality. The atomic units that I can manipulate are treated functionally as point sources. I need these units to be distinct, and carry spatial information, but at the same time, in order to build forms, I want the parts to meld together. In the case of the Auditory vector display, the continuity comes from auditory apparent motion (as if there were speakers instead of lights on the theater marquee). In the auditory field display, I hoped to attain continuity by way of auditory extensity phenomena as discussed above.
The analysis of minimum perceivable feature size is qualitatively different depending on whether one thinks in terms of points or of lines. [31]I could imagine an auditory shape as a spatial arrangement of zero dimensional objects. In this case, the task would be to compare the relative positions of simultaneously presented elements. If, however, one were to think in terms of extended objects, some type of magnitude estimation paradigm would be appropriate.
Perrott used the former interpretation. He chose a method of constant stimuli wherein different spatial separations were presented at random, and the CMMA was set at a performance level. This method works best with extremely large numbers of trials. Since I would not be able to run hundreds or thousands of trials, I decided to use a modified version of the method of limits. This technique is more likely to give me good results with fewer data points, and allows for both zero and one dimensional interpretations as follows: Two sounds are set at a random (large) initial separation. The subject's task is to close the distance until they pass each other. The zero dimensional interpretation is that the sounds have exchanged places. The one dimensional interpretation is that the "image" gradually shrinks down to zero, and then begins to get larger again (only inverted). I offered both interpretations to the subjects, an they could use whichever made the most sense to them.
I employed a complete factorial design with unequal numbers of repetitions of different stimulus combinations (see table 8.1). The vertical and horizontal conditions were analyzed separately, so there was no issue of restriction of randomization.
Number of Repetitions of Stimulus Combinations
Azimuth Elevation Direction Repetitions -25deg. -25deg. Left or Above 2 -25deg. -25deg. Right or Below 2 -25deg. 0deg. Left or Above 4 -25deg. 0deg. Right or Below 4 -25deg. 25deg. Left or Above 2 -25deg. 25deg. Right or Below 2 0deg. -25deg. Left or Above 4 0deg. -25deg. Right or Below 4 0deg. 0deg. Left or Above 10 0deg. 0deg. Right or Below 10 0deg. 25deg. Left or Above 4 0deg. 25deg. Right or Below 4 25deg. -25deg. Left or Above 2 25deg. -25deg. Right or Below 2 25deg. 0deg. Left or Above 4 25deg. 0deg. Right or Below 4 25deg. 25deg. Left or Above 2 25deg. 25deg. Right or Below 2
Figure 8.1
Concurrent Minimum Audible Angle Experiment Interface
The initial configuration (i.e. on which side the lower pitched sound starts, and on which side the higher pitched sound starts) is shown in a drawing. When the subject clicks on the "Play Sounds" button the Convolvotron is set to a random initial separation (between 90deg. and 180deg.) and the software triggers sounds on the IIfx via MIDI codes. The "Play Sounds" button disappears, and is replaced by two buttons labeled: "Adjust" and "Passed" respectively. Each time the subject clicks on the "Adjust" button, the angle between the sounds is decreased by one unit according to the control function shown in figure 8.2 below. The subject clicks on the "Passed" button when she or he believes that the sources have passed each other.
Figure 8.2
Control Function In Concurrent Minimum Audible Angle Experiment
I suggested two models to the subjects. The first was that the sounds were independent objects, and the passing point was when one object passed the other. The second interpretation I suggested was that the sounds were two ends of the same object, and that the subjects should continue to adjust the size until they begin to hear the object getting larger again.
.
The adjustment process continues beyond this point until finally the subject
reports that S is "less than" R. This point is the lower difference limen,
.
The just noticeable difference is defined as:
.[32]
In my experiment, I neglected to measure
.
In effect, I assumed that
.
This is not necessarily a bad assumption, as the purpose in measuring
is to check for a constant error. I did not expect constant error to be a
problem because of the symmetry of the two simultaneous comparisons.
Unfortunately, the system may not have been as perceptually symmetric as I
expected: three of the seven subjects showed significant main effects for the
starting configuration of pitches. In other words, there was some kind of
localization bias for these subjects that is due to pitch. In the vertical
case, this is relatively easy to explain in terms of frequency characteristics
of the stimuli. Higher pitches are often perceived to have higher elevations[33]. The left-to-right effect is
harder to justify. The only hypothesis I have is that somehow, there was a
perceived loudness difference between the two pitches, which caused a perceived
directional shift.
The method of limits is intrinsically susceptible to two types of error: Habituation occurs when the subject overshoots the mark because they have gotten used to responding in a certain fashion: "Greater, greater, greater, greater, greater, greater, greater, greater, greater, greater... oops... equal, equal, equal..." The opposite type of error is expectation. In this case the subject has some expectation about when the change should occur, and reacts to that expectation instead of waiting for the actual perception to occur.
The non-linear control function that I used leaves this experiment open to habituation errors. Each time subjects press the button (after the objective crossing point is past), the step size, and hence the possible amount of overshoot, grows exponentially larger. Even without habituation errors this function would tend to cause systematic overshoot.
Correspondingly, the values I measured for the CMMA were ridiculously high. The horizontal CMMA values ranged from 20deg.-60deg. (see figure 8.3). Perrott's [1984a] values were in the 5deg.-10deg. range. A complete record of the off-center measurements, and of analyses of variance can be found in Appendix C.
Figure 8.3
Horizontal Concurrent Minimum Audible Angle at (0deg., 0deg.)
Vertical CMMAs were also all over the map. They ranged from less than 20deg.
to more than 80deg.. However, since there are no values in the literature with
which to compare them, they could be thought of as "upper-limits". It should
be noted that in the vertical analysis, several subjects had instances where
they reported the passing point before the stimuli crossed. These instances
were eliminated because negative separations would artificially decrease
the CMMA (in the case of subject KS to nearly zero). One subject (TM)
always reported the passing point before the objective crossing point.
I asked this subject about his criteria, and it turns out that he may have been
judging the equality point:
instead of
.
I took the absolute value of his data, and included it for comparison
purposes. TM's "CMMA" is extremely low compared to the other subjects (See
figure 8.4).
Figure 8.4
Horizontal Concurrent Minimum Audible Angle at (0deg., 0deg.)