The Binaural Location of Pure Tones.

Hartley, R. V. L.; Fry, Thornton C.

doi:10.1103/physrev.18.431

Cited by 60 publications

(29 citation statements)

References 6 publications

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“…Function P n is a Legendre polynomial, and h 0 n is the derivative of a spherical Hankel function of the second kind with respect to its argument. The argument ka is the product of the wave number k (defined as 2p divided by the wavelength) and the head radius a, which is nominally 87.5 mm (Hartley and Fry, 1921;Algazi et al, 2001). The upper limit on the sum, N, must be infinite to obtain an exact solution, but because the sum converges, N is limited in practical computation.…”

Section: B Exact Diffraction Calculationmentioning

confidence: 99%

Testing, correcting, and extending the Woodworth model for interaural time difference

Aaronson

Hartmann

2014

The Journal of the Acoustical Society of America

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The Woodworth model and formula for interaural time difference is frequently used as a standard in physiological and psychoacoustical studies of binaural hearing for humans and other animals. It is a frequency-independent, ray-tracing model of a rigid spherical head that is expected to agree with the high-frequency limit of an exact diffraction model. The predictions by the Woodworth model for antipodal ears and for incident plane waves are here compared with the predictions of the exact model as a function of frequency to quantify the discrepancy when the frequency is not high. In a second calculation, the Woodworth model is extended to arbitrary ear angles, both for plane-wave incidence and for finite point-source distance. The extended Woodworth model leads to different formulas in six different regions defined by ear angle and source distance. It is noted that the characteristic cusp in Woodworth's well-known function comes from ignoring the longer of the two paths around the head in circumstances when the longer path is actually important. This error can be readily corrected.

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Section: B Exact Diffraction Calculationmentioning

confidence: 99%

Testing, correcting, and extending the Woodworth model for interaural time difference

Aaronson

Hartmann

2014

The Journal of the Acoustical Society of America

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“…These results indicate that the HRTF is roughly independent of distance when the source is more than 1 m away from the head. Despite the recognition by earlier researchers that the HRTF varies significantly with distance at distances less than 1 m (Stewart, 1911;Hartley k Frey, 1921;Firestone, 1930;Blauert, 1983), the dependence of the HRTF on distance remains largely unexplored. This paper examines the behavior of the head-related transfer function at distances less than 1 m. The first two sections provide background on HRTF measurements and the changes that occur in the HRTF as the source approaches the head.…”

Section: List Of Figuresmentioning

confidence: 94%

“…This approach to modeling near-field HRTFs is not new, and in fact was used to make manual calculations about near-field IIDs by Stewart (1911). Hartley and Frey (1921) manually tabulated interaural amplitudes and time delays at a variety of distances and directions using Stewart's derivation. The model described in this section was adapted from the work of Rabinowitz et al (1993), who examined the frequency scalability of head-related transfer functions for an enlarged head.…”

Section: Sphere Model Of the Headmentioning

confidence: 99%

Head-Related Transfer Functions in the Near Field

Brungart¹,

Rabinowitz²

1998

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“…First, they fit the more detailed empirical (Nordlund, 1962;Firestone, 1930)and theoretical (Steward, 1911;Hartley and Fry, 1921) data rather well, depicting the overall trends. Second, they are simple, single valued, and monotonic, making them suitable as parsimonious sensory processing algorithms and as realizable parameters for electronic modeling.…”

Section: The Plane Describes Z(r) For Various Values Of Each Of the Imentioning

confidence: 98%

“…Despite these discrepancies among trading-ratio values, acoustic diffraction theory (Stewart, 1911;Stewart, 1914;Hartley and Fry, 1921)and empirical microphone measurements (Firestone, 1930;Feddersen et al, 1957;Nordlund, 1962) Jeffress and Taylor (1961) acoustic images delivered via earphones in terms of external spatial referents. They used noise bursts containing the predicted ITD's as the stimuli and the selection of the appropriate lamp in a semicircular array around the subject as the response.…”

Section: Introductionmentioning

confidence: 98%

Psychophysical verification of predicted interaural differences in localizing distant sound sources

Molino

1974

The Journal of the Acoustical Society of America

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Subjects made forced choices to either side of a reference direction (0 ø, 30 ø, 60 ø, and 75 ø) to locate the image of pure tones presented through earphones. Various combinations of interaural intensity differences (liD's) and interaural time differences (ITD's) were used, including some combinations which do not occur in nature. Psychometric functions confirmed the expected apparent azimuth of ITD/IID combinations based on free-field diffraction theory and microphone measurements. The relative dominance of the intensive and temporal cues was examined at each frequency (500, 1000, and 8000 Hz). The shape of the psychometric plane for the bidimensional matrix at the 1000-Hz 30 ø condition showed possible nonlinearities in the trading relation. Data were also collected from the same subjects using the same signals presented by means of distant loudspeakers in an open field. When the free-field data were compared with the data from earphone-simulated sounds, they showed similar angular acuities, being approximately the size of those reported in the literature. The present study attempts to simulate with earphonesthe localization of distant sound sources. The simulation is achieved by inserting in the earphone channels various combinations of interaural time difference (ITD) and interaural intensity difference (IID)predicted for various azimuth positions. A more traditional approach to earphone experiments on auditory localization has centered around the determination of a trading ratio.The trading ratio is defined as that ITD/IID where the two interaural differences will just balance each other in determining the subjective location of the sound image. One group of experiments had subjects adjust one interaural difference (either the IID or ITD) in an acousti• "pointer" stimulus until the apparent direction of the "pointer" matched the apparent direction of another "reference" stimulus (Feddersen el al., 1957; Moushegian and Jeffress, 1959). Various combinations of either IID's or ITD's or both were inserted in the "reference" stimulus and the subjects made a single azimuth match from which a trading ratio could be computed. Whitworth and Jeffress (1961) largeIy repeated this procedure, but they succeeded in obtaining two localization responses and two trading ratios, one for each of two separate spatial images associated with the single "reference" stimulus. The use of auditory "pointer" stimuli in these and many similar investigations has provided a large body of information about relative discriminations among the apparent directions of various soundso This information is often difficult to relate, however, to measures of azimuth in real space expressed in degrees or radians, since the apparent direction of the "pointer" stimulus is not measured.In another group of investigations a somewhat different technique was chosen to determine the trading ratio. An example of this technique is a study by Harris (1960)o Harris's subjects introduced enough ITD in an acoustic stimulus to just counteract a given IID already ...

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The Binaural Location of Pure Tones.

Cited by 60 publications

References 6 publications

Testing, correcting, and extending the Woodworth model for interaural time difference

Testing, correcting, and extending the Woodworth model for interaural time difference

Head-Related Transfer Functions in the Near Field

Psychophysical verification of predicted interaural differences in localizing distant sound sources

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