Sensation of Sound Intensity and Perception of Loudness

  • Albrecht Schneider
Part of the Springer Handbooks book series (SHB)


This chapter is on sensation of sound intensity and perception of loudness. Since some of the relevant matter (on scaling concepts of loudness) has been presented in Chap.  30, and because a considerable portion of research on loudness is done outside musical contexts (namely, in industrial and environmental noise control as well as in audiology), this chapter condenses facts and models more than the previous two on pitch and timbre respectively. Section 33.1 of this chapter offers the physical and physiological basis of sound intensity sensation while Sect. 33.2 discusses features of some models of loudness sensation that have been established in psychoacoustics over the past decades. Since these models were originally designed for stationary sound signals and levels, and have been tested mostly in lab situations, they cannot adequately cover a range of real-world sound types found in natural or technical environments. In music genres such as techno presented in discos, or heavy metal performed in live music venues or at open air festivals to audiences at very high sound pressure levels, sound is heavily processed in regard to dynamics and spectral energy, which calls for appropriate measurement and assessment of sensory effects. Different from perception of pitch (where samples of subjects respond more or less in similar ways to certain types of sound signals), perception of loudness shows a high degree of variability even within groups of musically trained subjects reflecting their musical background and preferences (Sect. 33.3). Recent empirical evidence demonstrates that subjects judge loudness for various musical genres on a category scale (from very soft to very loud), however, the center (relative to loudness level and loudness scales) and the range of each category differ considerably, for individual subjects.

Finally, there is a concluding section (Sect. 33.4) in which some of the major topics and issues discussed in Chaps.  30–33 of Part D are summed up. In addition, a tentative model of the interrelationship of pitch, timbre and loudness perception is sketched.


auditory filter


amplitude modulation


auditory nerve


auditory pathway


Baseler Befindlichkeits-Skala


basilar membrane


critical band


characteristic frequency


corpus geniculatum mediale/medial geniculate body


equivalent rectangular bandwidth


frequency modulation


functional magnetic resonance imaging


Fourier time transformation


inferior colliculus


inner hair cell


outer hair cell


peristimulus compound action potential


standard deviation


superior olivary complex


sound pressure level


short-term Fourier transform/short-time Fourier transform


short-term memory


  1. 33.1
    E. Shaw, M. Vaillancourt: Transformation of sound pressure level from the free field to the eardrum in numerical form, J. Acoust. Soc. Am. 78, 1120–1123 (1985)CrossRefGoogle Scholar
  2. 33.2
    D. Keefe, J. Bulen, K. Hoberg Arehart, E. Burns: Ear-canal impedance and reflection coefficient in human infants and adults, J. Acoust. Soc. Am. 94, 2617–2638 (1993)CrossRefGoogle Scholar
  3. 33.3
    S. Voss, J. Allen: Measurement of acoustic impedance and reflectance in the human ear canal, J. Acoust. Soc. Am. 95, 372–384 (1994)CrossRefGoogle Scholar
  4. 33.4
    R. Aibara, J. Welch, S. Puria, R. Goode: Human middle-ear transfer function and cochlear input impedance, Hearing Res. 152, 100–109 (2001)CrossRefGoogle Scholar
  5. 33.5
    J. Rosowski: The effects of external and middle-ear filtering on auditory threshold and noise-induced hearing loss, J. Acoust. Soc. Am. 90, 124–135 (1991)CrossRefGoogle Scholar
  6. 33.6
    H. Fletcher, W. Munson: Loudness, its definition, measurement and calculation, J. Acoust. Soc. Am. 5, 82–108 (1933)CrossRefGoogle Scholar
  7. 33.7
    W. Rhode, A. Recio: Study of mechanical motions in the basal region of the chinchilla cochlea, J. Acoust. Soc. Am. 107, 3317–3332 (2000)CrossRefGoogle Scholar
  8. 33.8
    I. Russell, K. Nielsen: The location of the cochlear amplifier: Spatial representation of a single tone on the guinea pig basilar membrane, Proc. Nat. Acad. Sci. 94, 2660–2664 (1997)CrossRefGoogle Scholar
  9. 33.9
    M. Ruggero, N. Rich, A. Recio, S. Narayan, L. Robles: Basilar-membrane responses to tones at the base of the chinchilla cochlea, J. Acoust. Soc. Am. 101, 2151–2163 (1997)CrossRefGoogle Scholar
  10. 33.10
    C. Shera: Intensity-invariance of fine time structure in basilar-membrane click responses: Implications for cochlear mechanics, J. Acoust. Soc. Am. 110, 332–348 (2001)CrossRefGoogle Scholar
  11. 33.11
    S. Gelfand: Hearing. An Introduction to Psychological and Physiological Acoustics, 4th edn. (Dekker, New York 2004)Google Scholar
  12. 33.12
    E. Zwicker, H. Fastl: Psychoacoustics, Facts and Models, 2nd edn. (Springer, Berlin 1999)CrossRefGoogle Scholar
  13. 33.13
    G. Yates, I. Winter, D. Robertson: Basilar membrane nonlinearity determines auditory nerve rate-intensity functions and cochlear dynamic range, Hearing Res. 45, 203–219 (1990)CrossRefGoogle Scholar
  14. 33.14
    B. Moore: Frequency analysis and masking. In: Hearing, ed. by B. Moore (Academic, San Diego 1995) pp. 161–205CrossRefGoogle Scholar
  15. 33.15
    E. Relkin, J. Doucet: Is loudness simply proportional to the auditory nerve spike count?, J. Acoust. Soc. Am. 101, 2735–2740 (1997)CrossRefGoogle Scholar
  16. 33.16
    J. Doucet, E. Relkin: Neural contributions to the peristimulus compound action potential: Implications for measuring the growth of the auditory nerve spike count as a function of stimulus intensity, J. Acoust. Soc. Am. 101, 2720–2734 (1997)CrossRefGoogle Scholar
  17. 33.17
    J.O. Pickles: Introduction to the Physiology of Hearing, 3rd edn. (Emerald, Binkley 2008)Google Scholar
  18. 33.18
    Chr Plack, R. Carlyon: Loudness perception and intensity coding. In: Hearing, ed. by B. Moore (Academic, San Diego 1995) pp. 123–160CrossRefGoogle Scholar
  19. 33.19
    St Uppenkamp, M. Röhl: Human auditory neuroimaging of intensity and loudness, Hearing Res. 307, 65–73 (2014)CrossRefGoogle Scholar
  20. 33.20
    N. Durlach, L. Braida: Intensity perception. I. Preliminary theory of intensity resolution, J. Acoust. Soc. Am. 46, 372–383 (1969)CrossRefGoogle Scholar
  21. 33.21
    R. Schlauch: Loudness. In: Ecological Psychoacoustics, ed. by J. Neuhoff (Elsevier, San Diego 2004) pp. 317–345Google Scholar
  22. 33.22
    L. Marks: Binaural summation of the loudness of pure tones, J. Acoust. Soc. Am. 64, 107–113 (1978)CrossRefGoogle Scholar
  23. 33.23
    V. Sivonen, W. Ellermeier: Binaural loudness. In: Loudness, ed. by M. Florentine (Springer, New York 2011) pp. 169–197CrossRefGoogle Scholar
  24. 33.24
    J. Marozeau, M. Epstein, M. Florentine, B. Daley: A test of the binaural equal-loudness-ratio hypothesis for tones, J. Acoust. Soc. Am. 120, 3870–3877 (2006)CrossRefGoogle Scholar
  25. 33.25
    M. Florentine, M. Epstein: To honour Stevens and to repeal his law. In: Fechner Day 2006. Proc. 22nd Annu. Meet. Int. Soc. Psychophys., ed. by D. Kornbrot, R. Msetfi, A. MacRae (Univ. of Hertfordshire Press, Hatfield 2006) pp. 37–41Google Scholar
  26. 33.26
    H. Fletcher: Loudness, masking and their relation to the hearing process and the problem of noise measurement, J. Acoust. Soc. Am. 9, 275–293 (1938)CrossRefGoogle Scholar
  27. 33.27
    H. Bauch: Die Bedeutung der Frequenzgruppe für die Lautheit von Tönen, Acustica 6, 40–45 (1956)Google Scholar
  28. 33.28
    E. Zwicker, G. Flottorp, S. Stevens: Critical bands with loudness summation, J. Acoust. Soc. Am. 29, 548–557 (1957)CrossRefGoogle Scholar
  29. 33.29
    E. Zwicker, B. Scharf: A Model of loudness summation, Psych. Rev. 72, 3–26 (1965)CrossRefGoogle Scholar
  30. 33.30
    W. Hartmann: Signals, Sound and Sensation (Springer, New York 1998)Google Scholar
  31. 33.31
    E. Zwicker, E. Terhardt: Analytical expressions for critical-band rate and critical bandwidth as a function of frequency, J. Acoust. Soc. Am. 68, 1523–1525 (1980)CrossRefGoogle Scholar
  32. 33.32
    B. Moore, B. Glasberg: Suggested formulae for calculating auditory-filter bandwidths and excitation patterns, J. Acoust. Soc. Am. 74, 750–753 (1983)CrossRefGoogle Scholar
  33. 33.33
    H. Fletcher: Auditory patterns, Rev. Mod. Phys. 12, 47–66 (1940)CrossRefGoogle Scholar
  34. 33.34
    A. Schneider, V. Tsatsishvili: Perception of intervals at very low frequencies: Some experimental findings. In: Systematic Musicology: Empirical and Theoretical Studies, ed. by A. Schneider, A. von Ruschkowski (Lang, Frankfurt 2011) pp. 99–125Google Scholar
  35. 33.35
    R. Meddis, M. Hewitt: Virtual pitch and phase sensitivity of a computer model of the auditory periphery. I: Pitch identification, J. Acoust. Soc. Am. 89, 2866–2882 (1991)CrossRefGoogle Scholar
  36. 33.36
    R. Meddis, M. Hewitt: Virtual pitch and phase sensitivity of a computer model of the auditory periphery. II: Phase sensitivity, J. Acoust. Soc. Am. 89, 2883–2894 (1991)CrossRefGoogle Scholar
  37. 33.37
    R. Patterson, K. Robinson, J. Holdsworth, D. McKeown, C. Zhang, M. Allerhand: Complex sounds and auditory images, Adv. Biosci. 83, 429–443 (1992)Google Scholar
  38. 33.38
    R. Patterson, M. Allerhand, C. Giguère: Time-domain modeling of peripheral auditory processing: A modular architecture and a software platform, J. Acoust. Soc. Am. 98, 1890–1894 (1995)CrossRefGoogle Scholar
  39. 33.39
    E. Terhardt: Akustische Kommunikation (Springer, Berlin 1998)CrossRefGoogle Scholar
  40. 33.40
    B. Glasberg, B. Moore: Derivation of auditory filter shapes from notched noise data, Hearing Res. 47, 103–113 (1990)CrossRefGoogle Scholar
  41. 33.41
    B. Moore: Basic psychophysics of human spectral processing. In: Auditory Spectral Processing, Intern. Rev. Neurobiol., Vol. 70, ed. by M. Malmierca, D. Irvine (Elsevier, Amsterdam 2005) pp. 49–86CrossRefGoogle Scholar
  42. 33.42
    M. Slaney: An efficient implementation of the Patterson–Holdsworth auditory filter bank, Apple Comput. Tech. Report 35 (1993)Google Scholar
  43. 33.43
    T. Lin, J. Guinan: Auditory nerve fiber responses to high-level clicks: Interference patterns indicate that excitation is due to the combination of multiple drives, J. Acoust. Soc. Am. 107, 2615–2630 (2000)CrossRefGoogle Scholar
  44. 33.44
    E. Zwicker: Psychoakustik (Springer, Berlin 1982)CrossRefGoogle Scholar
  45. 33.45
    T. Poulsen: Loudness of tone pulses in a free field, J. Acoust. Soc. Am. 69, 1786–1790 (1981)CrossRefGoogle Scholar
  46. 33.46
    B. Glasberg, B. Moore: A model of loudness applicable to time-varying sounds, J. Audio Eng. Soc. 50, 331–342 (2002)Google Scholar
  47. 33.47
    J. Chalupper, H. Fastl: Dynamic loudness model (DLM) for normal and hearing-impaired listeners, Acustica 88, 378–386 (2002)Google Scholar
  48. 33.48
    R. Sottek: A hearing model approach to time-varying loudness, Acustica 102, 725–744 (2016)CrossRefGoogle Scholar
  49. 33.49
    J. Hots, J. Rennies, J. Verhey: Modelling temporal integration of loudness, Acustica 100, 184–187 (2014)CrossRefGoogle Scholar
  50. 33.50
    J. Rennies, M. Wächtler, J. Hots, J. Verhey: Spectro-temporal characteristics affecting the loudness of technical sounds: Data and model predictions, Acustica 101, 114–1156 (2015)Google Scholar
  51. 33.51
    J. Rennies, J. Verhey, H. Fastl: Comparison of loudness models for time-varying sounds, Acustica 96, 383–396 (2010)CrossRefGoogle Scholar
  52. 33.52
    B. Moore, B. Glasberg: Modeling binaural loudness, J. Acoust. Soc. Am. 121, 1604–1612 (2007)CrossRefGoogle Scholar
  53. 33.53
    A. Schneider, A. von Ruschkowski: Techno, decibels, and politics: An empirical study of modern dance music productions, sound pressure levels, and loudness perception. In: Systematic Musicology: Empirical and Theoretical Studies, ed. by A. Schneider, A. von Ruschkowski (Lang, Frankfurt/M. 2011) pp. 13–62Google Scholar
  54. 33.54
    A. von Ruschkowski, A. Schneider: Schallstruktur und potentielle Risiken für das Gehör: Eine empirische Studie in einer Hamburger Diskothek, Z. Audiol. 51, 115–121 (2012)Google Scholar
  55. 33.55
    M. Florentine (Ed.): Loudness (Springer, New York 2011)Google Scholar
  56. 33.56
    G. Grimm, V. Hohmann, J. Verhey: Loudness of fluctuating sounds, Acta Acust. united with Acust. 88, 359–368 (2002)Google Scholar
  57. 33.57
    H. Gockel, B. Moore, R. Patterson: Influence of component phase on the loudness of complex tones, Acustica 88, 369–377 (2002)Google Scholar
  58. 33.58
    N. Todd, F. Cody: Vestibular responses to loud dance music: A physiological basis of the ‘‘rock’n’roll threshold’’?, J. Acoust. Soc. Am. 107, 496–500 (2000)CrossRefGoogle Scholar
  59. 33.59
    N. Todd: Evidence for a behavioural significance of saccular arousal sensitivity in humans, J. Acoust. Soc. Am. 110, 380–390 (2001)CrossRefGoogle Scholar
  60. 33.60
    W. Babisch, B. Bohn: Schallpegel in Diskotheken und bei Musikveranstaltungen. Part II (Umweltbundesamt, Berlin 2000)Google Scholar
  61. 33.61
    W. Babisch, B. Bohn: Schallpegel in Diskotheken und bei Musikveranstaltungen. Part III (Umweltbundesamt, Berlin 2000)Google Scholar
  62. 33.62
    A. von Ruschkowski: Lautheit von Musik. Eine empirische Untersuchung zum Einfluss von Organismusvariablen auf die Lautstärkewahrnehmung von Musik, Ph.D. Thesis (Univ. of Hamburg, Systematic Musicology, Hamburg 2013), Google Scholar
  63. 33.63
    L. Braida, J. Lim, J. Berliner, N. Durlach, W. Rabinowitz, S. Purks: Intensity perception. XIII. Perceptual anchor model of context coding, J. Acoust. Soc. Am. 76, 722–731 (1984)CrossRefGoogle Scholar
  64. 33.64
    R.M. Warren: Subjective loudness and its physical correlate, Acustica 37, 334–346 (1977)Google Scholar
  65. 33.65
    R. Warren: Auditory Perception. An Analysis and Synthesis, 3rd edn. (Cambridge Univ. Press, Cambridge 2008)CrossRefGoogle Scholar
  66. 33.66
    H. von Helmholtz: Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Vieweg, Braunschweig 1863), 3rd edn. 1870, 6th edn. 1913zbMATHGoogle Scholar
  67. 33.67
    C. Stumpf: Tonpsychologie, Vol. 1 (Barth, Leipzig 1883)Google Scholar
  68. 33.68
    C. Stumpf: Tonpsychologie, Vol. 2 (Barth, Leipzig 1890)Google Scholar
  69. 33.69
    C. Stumpf: Die Sprachlaute (Springer, Berlin 1926)CrossRefGoogle Scholar
  70. 33.70
    R. Shepard: Circularity in judgements of relative pitch, J. Acoust. Soc. Am. 36, 2346–2353 (1964)CrossRefGoogle Scholar
  71. 33.71
    R. Shepard: Demonstrations of circular components of pitch, J. Audio Eng. Soc. 31, 641–649 (1983)Google Scholar
  72. 33.72
    J.-C. Risset: Computer, synthesis, perception, paradoxes, Hamburger Jahrb. Musikwiss. 11, 245–258 (1991)Google Scholar
  73. 33.73
    B. Repp: The tritone paradox and the pitch range of the speaking voice: A dubious connection, Music Percept. 12, 227–255 (1994)CrossRefGoogle Scholar
  74. 33.74
    D. Deutsch: The tritone paradox and the pitch range of the speaking voice: Reply to Repp, Music Percept. 12, 257–263 (1994)CrossRefGoogle Scholar
  75. 33.75
    B. Repp: Spectral envelope and context effects in the tritone paradox, Perception 26, 645–665 (1997)CrossRefGoogle Scholar
  76. 33.76
    C. Friedrich: Die Ambivalenz der Tonhöhenwahrnehmung des Tritonus. Eine empirische Studie basierend auf der Zweikomponenten-Theorie der Tonhöhe, MA Thesis (Univ. Hamburg, Hamburg 2006)Google Scholar
  77. 33.77
    D. Howard, J. Angus: Acoustics and Psychoacoustics, 2nd edn. (Focal, Oxford 2001)Google Scholar
  78. 33.78
    A. Schneider: Klanganalyse als Methodik der Popularmusikforschung, Hamburger Jahrb. Musikwiss. 19, 107–129 (2002)Google Scholar
  79. 33.79
    A. Schneider: Komposition und Produktion von ‘‘U-Musik’’ unter dem Einfluss technischer Medien. In: Handbuch Musik und Medien, ed. by H. Schramm (UVK Verlagsgesellschaft, Konstanz 2009) pp. 495–530Google Scholar
  80. 33.80
    D. Huber, R. Runstein: Modern Recording Techniques, 8th edn. (Focal, Oxford 2013)Google Scholar
  81. 33.81
    H.P. Hesse: Die Wahrnehmung von Tonhöhe und Klangfarbe als Probleme der Hörtheorie (Gerig, Köln 1972)Google Scholar
  82. 33.82
    W. Thies: Grundlagen einer Typologie der Klänge (Wagner, Hamburg 1982)Google Scholar
  83. 33.83
    G. Goley, W. Song, J. Kim: Kurtosis-corrected sound pressure level as a noise metric for risk assessment of occupational noises, J. Acoust. Soc. Am. 129, 1475–1481 (2011)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2018

Authors and Affiliations

  • Albrecht Schneider
    • 1
  1. 1.Institute of Systematic MusicologyUniversity of HamburgHamburgGermany

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