An Exploration of Virtual Auditory Shape Perception

Footnotes

¹ Actually, at least six dimensions would be more accurate, as the perception of motion via audition is probably superior to static position sensing. See Waugh, 1979.

² With the possible addition of time, although time is already implicitly convolved with frequency.

³ See Patterson & Green, p. 342.

⁴ As referenced in Wessel, 1979

⁵ From an unpublished lecture by David Wessel at the University of California, Berkeley.

⁶ Almost,but not quite exactly, that is! See Shepard, p. 349.

⁷ American Bureau of Standards, 1960 as quoted in Risset, 1982.

⁸ The number on a given dimension is about seven. See Miller, 1956.

⁹ There are many reviews of auditory localization: Blauert, 1983, Middlefield & Green, 1991, and Oldfield & Simon, 1984 to name a few.

¹⁰ As reported in Blauert, 1983.

¹¹ Oldfield & Parker, 1984; Wightman & Kistler, 1989b.

¹² One exception is Oldfield & Parker, who predominantly observed back to front reversals.

¹³ This was the Gehring Audio-Media/Focal-Point system.

¹⁴ Unless you are fortunate enough to have a surround sound system.

¹⁵ Wenzel, Wightman, & Kistler, 1991; Wenzel, et al., 1993.

¹⁶ Actually they only solved a class of these problems. The problem of room acoustics remains unsolved.

¹⁷ See also Wenzel, 1992, for a review of virtual sound.

¹⁸ See also Wenzel, et al., 1993.

¹⁹ These factors are increases over free-field performance.

²⁰ Although this is usually called just "volume" in the literature, I will use the term "tonal volume" in this paper in order to emphasize the distinction from the common synonym for loudness.

²¹ For those future readers, we are speaking of the 19th century.

²² Perrot et. al, were able to determine that the rate of expansion of the image was quite consistent even across frequencies (mean rate of .38in/sec SD=0.035).

²³ See Perrott & Buell, 1982.

²⁴ Actually they also attempted to examine a third dimension: depth, but were unable to obtain consistent results.

²⁵ For more on the precedence effect see Wallach,et al, 1949, Perrott, Strybel, & Manligas, 1987, and Freyman,et al., 1991.

²⁶ E.g. Yost & Soderquist, 1984,.

²⁷ From the subject SDO in Wightman & Kistler, 1989a,b.

²⁸ This is as compared to free-field listening.

²⁹ Wenzel, Wightman, & Kistler 1991 observed horizontal asymmetry but not vertical.

³⁰ Although this subject had a relatively low confusion rate, she had a high average error, and was therefore excluded.

³¹ I am using "chains" of stimuli, so in this context it does not make sense to consider higher dimensional structures such as regions or volumes.

³² The method of limits is detailed in Snodgrass, 1975.

³³ For example, see Bregman & Steiger, 1981.