The effect of sound incidence angle on loudness was investigated using real sound sources positioned in an anechoic chamber. Eight normal-hearing listeners produced loudness matches between a frontal reference location and seven sources placed at other directions, both in the horizontal and median planes. Matches were obtained via a two-interval, adaptive forced-choice (2AFC) procedure for three center frequencies (0.4, 1, and ) and two overall levels (45 and SPL). The results showed that loudness is not constant over sound incidence angles, with directional sensitivity varying over a range of up to , exhibiting considerable frequency dependence, but only minor effects of overall level. The pattern of results varied substantially between subjects, but was largely accounted for by variations in individual head-related transfer functions. Modeling of binaural loudness based on the at-ear signals favored a sound-power summation model, according to which the maximum binaural gain is only , over competing models based on larger gains, or on the summation of monaural loudness indices.
REFERENCES
1.
Bates
, D. M.
, and Watts
, D. G.
(1988
). Nonlinear Regression Analysis and Its Applications
(Wiley
, New York
).2.
3.
Blauert
, J.
(1997
). Spatial Hearing: The Psychophysics of Human Sound Localization
(MIT Press
, Cambridge, MA
).4.
Bodden
, M.
(1997
). “Instrumentation for sound quality evaluation
,” Acust. Acta Acust.
83
, 775
–783
.5.
Bronkhorst
, A. W.
(1995
). “Localization of real and virtual sound sources
,” J. Acoust. Soc. Am.
98
, 2542
–2553
.6.
Green
, D. M.
, and Swets
, J. A.
(1988
). Signal Detection Theory and Psychophysics
(Peninsula
, Los Altos, CA).7.
Hammershøi
, D.
, and Møller
, H.
(1996
). “Sound transmission to and within the human ear canal
,” J. Acoust. Soc. Am.
100
, 408
–427
.8.
Hellman
, R. P.
, and Zwislocki
, J.
(1963
). “Monaural loudness function at 1000 cps and interaural summation
,” J. Acoust. Soc. Am.
35
, 856
–865
.9.
ISO 226
(2003
). “Acoustics—Normal equal-loudness-level contours
,” (International Organization for Standardization, Geneva, Switzerland).10.
ISO 389-1
(1998
). “Acoustics—Reference zero for the calibration of audiometric equipment—Part 1: Reference equivalent threshold sound pressure levels for pure tones and supra-aural earphones
,” (International Organization for Standardization, Geneva, Switzerland).11.
ISO 389-7
(1996
). “Acoustics—Reference zero for the calibration of audiometic equipment—Part 7: Reference threshold of hearing under free-field and diffuse-field listening conditions
,” (International Organization for Standardization, Geneva, Switzerland).12.
ISO 532
(1975
). “Acoustics—Method for calculating loudness level
,” (International Organization for Standardization, Geneva, Switzerland).13.
Jesteadt
, W.
(1980
). “An adaptive procedure for subjective judgments
,” Percept. Psychophys.
28
, 85
–88
.14.
Jørgensen
, S. L.
(2002
). “MATLAB model for loudness perception—directional loudness
,” Unpublished masters thesis, Technical University of Denmark
(DTU), Copenhagen.15.
Kuhl
, W.
, and Westphal
, W.
(1959
). “Unterschiede der Lautstärken in der ebenen Welle und im diffusen Schallfeld
” (“Differences in loudness levels between a plane wave and a diffuse sound field
,”) Acustica
9
, 407
–408
.16.
Levelt
, W. J. M.
, Riemersma
, J. B.
, and Bunt
, A. A.
(1972
). “Binaural additivity of loudness
,” Br. J. Math. Stat. Psychol.
25
, 51
–68
.17.
Levitt
, H.
(1971
). “Transformed up–down methods in psychoacoustics
,” J. Acoust. Soc. Am.
49
, 467
–477
.18.
Marks
, L. E.
(1978
). “Binaural summation of the loudness of pure tones
,” J. Acoust. Soc. Am.
64
, 107
–113
.19.
Mohrmann
, K.
(1939
). “Lautheitskonstanz im Eutfernungswechsel
” (“Loudness constancy with changing distance
,”) Z. Psychol.
145
, 145
–199
.20.
Møller
, H.
, Sørensen
, M. F.
, Hammershøi
, D.
, and Jensen
, C. B.
(1995
). “Head-related transfer functions of human subjects
,” J. Audio Eng. Soc.
43
, 300
–321
.21.
Møller
, H.
, Sørensen
, M. F.
, Jensen
, C. B.
, and Hammershøi
, D.
(1996
). “Binaural technique: Do we need individual recordings?
,” J. Audio Eng. Soc.
44
, 451
–469
.22.
Moore
, B. C. J.
, Glasberg
, B. R.
, and Baer
, T.
(1997
). “A model for the prediction of thresholds, loudness, and partial loudness
,” J. Audio Eng. Soc.
45
, 224
–239
.23.
Olesen
, S. K.
, Plogsties
, J.
, Minnaar
, P.
, and Møller
, H.
(2000
). “An improved MLS measurement system for acquiring room impulse responses
,” in Proceedings of NORSIG 2000, IEEE Nordic Signal Processing Symposium
, Kolmården, Sweden
, 117
–120
.24.
Remmers
, H.
, and Prante
, H.
(1991
). “Untersuchung zur Richtungsabhängigkeit der Lautstärkeempfindung von breitbandigen Schallen
” (“Investigation of the directional dependence of the loudness of broadband sounds
”), Fortschritte der Akustik-Deutsche Arbeitsgemeinschaft für Akustik (DAGA), 537
–540
.25.
Reynolds
, G. S.
, and Stevens
, S. S.
(1960
). “Binaural summation of loudness
,” J. Acoust. Soc. Am.
32
, 1337
–1344
.26.
Robinson
, D. W.
, and Whittle
, L. S.
(1960
). “The loudness of directional sound fields
,” Acustica
10
, 74
–80
.27.
Robinson
, D. W.
, Whittle
, L. S.
, and Bowsher
, J. M.
(1961
). “The loudness of diffuse sound fields
,” Acustica
11
, 397
–404
.28.
Scharf
, B.
, and Fishken
, D.
(1970
). “Binaural summation of loudness: Reconsidered
,” J. Exp. Psychol.
86
, 374
–379
.29.
Schneider
, B. A.
, and Cohen
, A. J.
(1997
). “Binaural additivity of loudness in children and adults
,” Percept. Psychophys.
59
, 655
–664
.30.
Shaw
, E. A. G.
(1974
). “Transformation of sound pressure level from the free field to the eardrum in the horizontal plane
,” J. Acoust. Soc. Am.
56
, 1848
–1861
.31.
Shaw
, W. A.
, Newman
, E. B.
, and Hirsh
, I. J.
(1947
). “The difference between monaural and binaural thresholds
,” J. Exp. Psychol.
37
, 229
–242
.32.
Sivian
, L. J.
, and White
, S. D.
(1933
). “On minimum audible sound fields
,” J. Acoust. Soc. Am.
4
, 288
–321
.33.
Sivonen
, V. P.
, Minnaar
, P.
, and Ellermeier
, W.
(2005
). “Effect of direction on loudness in individual binaural synthesis
,” in Proceedings of the 118th Convention of the Audio Eng. Soc.
, Convention Paper No. 6512.34.
Wightman
, F. L.
, and Kistler
, D. J.
(1989a
). “Headphone simulation of free field listening. I. Stimulus synthesis
,” J. Acoust. Soc. Am.
85
, 858
–867
.35.
Wightman
, F. L.
, and Kistler
, D. J.
(1989b
). “Headphone simulation of free field listening. II. Psychophysical validation
,” J. Acoust. Soc. Am.
85
, 868
–878
.36.
Zacharov
, N.
, Tuomi
, O.
, and Lorho
, G.
(2001
). “Auditory periphery, HRTF’s and directional loudness perception
,” in Proceedings of the 110th Convention of the Audio Eng. Soc.
, Convention Paper No. 5315.37.
Zahorik
, P.
, and Wightman
, F. L.
(2001
). “Loudness constancy with varying sound source distance
,” Nat. Neurosci.
4
, 78
–83
.38.
Zwicker
, E.
, and Zwicker
, U. T.
(1991
). “Dependence of binaural loudness summation on interaural level differences, spectral distribution, and temporal distribution
,” J. Acoust. Soc. Am.
89
, 756
–764
.© 2006 Acoustical Society of America.
2006
Acoustical Society of America
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