Abstract
In the last chapter, we learned about the last step in the trail from the source of sound to the brain via nerve signals from our ears. All these steps have been describable in what we refer to as physical terms and are objective. And yet we do not know in physical terms what it means when we say, “I hear a sound”. This last step has eluded explanation and clarification.
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Notes
- 1.
Such a situation exists in the regime of phenomena for which the specific nature of Quantum Theory is manifest. We have found, for example, that it is impossible to describe an atom in terms of images that we have amassed for describing the world at the macroscopic level. For further ideas into the issue of the nature of perception and what it means to think or feel, see the fascinating book by Daniel DennettConsciousness Explained, [Penguin Press, UK, 1992].
- 2.
The following Wikipedia website is a useful resource of links to many psychoacoustic phenomena: http://en.wikipedia.org/wiki/Psychoacoustics.
- 3.
The note is an A with a typical frequency of 440 Hz and a color patch with the color that the composer-pianist Alexandre Scriabin associated with the note A. For the reader who is interested in a more comprehensive discussion of psychoacoustics, I highly recommend the book by Juan Roederer, Introduction to the Physics and Psychophysics of Music – 4th ed. [Springer-Verlag, New York, 2008].
- 4.
There is a revised international standard (ISO 226 2003) to be found on the following website (1-22-2011): http://en.wikipedia.org/wiki/FletcherMunson_curves. I kept the older figure below because it includes the effect of aging. One reason for the difference are improved testing procedures.
- 5.
You can test your own hearing within the limitations of your level of training by using the applet on this website (1-22-2011): http://www.phys.unsw.edu.au/jw/hearing.html.
- 6.
The number 0.3 in the equation is actually an approximation for log 2 = 0. 3010….
- 7.
See the website (1-9-2011): http://home.tm.tue.nl/dhermes/lectures/SoundPerception/05Loudness.html.
- 8.
It is important to note that for small enough forces, the response of a real spring is essentially linear. That is, we can assume that the displacement of the spring is proportional to the force to a good approximation. Thus, the so-called ideal spring is an abstraction whose behavior is approached by a real spring for small forces. It is a remarkable fact that the bulk of physical theories and concepts are based on abstract models of the real world which assume linear response as an approximation, with deviations from linearity being second order effects which may or may not be essential to the phenomena of interest. Furthermore, the Principle of Superposition, which was discussed in Chap. 7, is dependent on a linear response of the system. Thus, to the extent that the response is nonlinear, this principle breaks down.
- 9.
This result is obtained from the trigonometric identity is \({\sin }^{2}\theta = 1/2 - (1/2)\cos 2\theta \).
- 10.
The result is based on the trigonometric identity: \(2\sin {\theta }_{1} \times \sin {\theta }_{2} = cos({\theta }_{2} - {\theta }_{1}) - cos({\theta }_{2} + {\theta }_{1}\)).
- 11.
If you look down into the sea, the light you see is scattered light. However, the effect of preferential scattering toward the blue is more than compensated for by the preferential absorption in the red.
- 12.
See Chap. 6 for a review of the connection between absorption and energy level differences.
- 13.
The expected curve is then τ ∝ 10 − b logf, where b is a constant. We can see the exponential behavior of the dotted curve.
- 14.
I have been greatly helped in my attempt to weed out the known understandings of fusion by two audio-psychologists: Alan Bregman of McGill University, Brian Roberts of Aston University (Birmingham, England) and Oliver Knill of Harvard University. Alan Bregman is the author of a book entitled Auditory Scene Analysis [MIT Press, Cambridge, 1994], in which he discusses how the brain processes and ensemble of sound inputs and organizes them according to sources. In particular, he explains how the brain is able to focus on one source of sound and ignore or become almost oblivious to other concurrent sources. As a result, we are able to hear one person speak in the midst of a dense crowd at a party.
- 15.
For a resource of introductory material and references on this subject see: (1-2-2011):http://jjensen.org/VirtualPitch.html#use. A more general concept than fusion of hamonics is the concept of virtual pitch. It takes into account the tendency of the brain to choose a pitch to be perceived even of frequency spectrum is not perfectly in a harmonic series and there is ambiguity. The concept of virtual pitch is attributed to Ernst Terhardt. See his publications: Pitch, consonance, and harmony, Journal of the Acoustical Society of America, 55 #5 1974. p.1061-1069, and Calculating Virtual Pitch, Hearing Research 1 1979. p.155-182. Below are references to fascinating illusory responses to sequences of complex sounds: (1) Shepard’s Staircase, wherein a sound seems to be ever decreasing in pitch but is actually cycling around like M.C. Escher’s staircase. For an incredibly hilarious representation of this illusion see (1-21-2011): http://www.flixxy.com/escher.htm. To listen to Shepard’s staircase see (1-21-2011):http://www.cycleback.com/sonicbarber.htmlReference: Shepard, R.N. (1964). Circularity in judgments of relative pitch, J. Acoust. Soc. Am., 36, 2346-2353. (2) Diana Deutsch (1-21-2011): http://www.philomel.com/musical_illusions/octave.phpIncluded are a number of sound files that allow you to listen to illusions.
- 16.
This website has sound bites that allow you to hear the change of pitch with increasing intensity. (1-21-2011):http://www.santafevisions.com/csf/demos/audio/412_dependence_pitch_intensity.htm.
- 17.
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Gunther, L. (2012). Psychoacoustics. In: The Physics of Music and Color. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0557-3_10
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