(Note: The following article is adapted from Paradoxes of Muscial Pitch, by Diana Deutsch, Scientific American, August 1992, pg. 88. I think that this article has some interesting things to say about sound in general, and how human beings may not hear sounds exactly the same.)

Sound. Most of us take it for granted. A few of us (i.e. audiophiles) are more acutely aware of what we hear. But, what do we hear? Scientists around the world are trying to unlock the mechanisms of pitch and perception. Pythagoras took the first steps on the road to the modern definition of pitch vs frequency when he showed that the length of a plucked string is related to its pitch. The shorter the string, the higher the pitch. Other scientists, notably Galileo and the 17th century mathematician Marlin Mersenne, expanded upon Pythagoras' discoveries by proving that the pitch one hears is due to the frequency of vibration of the plucked string. Mersenne also discovered overtones, or harmonics. He demonstrated that a string vibrates at a frequency corresponding to the percieved pitch (known as the fundamental) and at whole number multiples of the fundamental (overtones or harmonics). So a string vibrating at 1000 Hz contains components at 2000 Hz, 3000 Hz, 4000 Hz, etc. Jan Schouten of Phillips showed that human beings use overtones to determine pitch. He was able to prove that human beings can perceive the pitch of a sound that corresponds to the fundamental frequency, even when the fundamental frequency itself is missing from the sound. In 1964, Roger N. Shepard of Bell Telephone Laboratories, using this information, was able to conduct a remarkable experiment. Using a computer program, written by a collegue, Mr. Shepard was able to construct a sound in which the pitch could be clearly identified (i.e. what note: C, G, F, etc.) but the octave containing the pitch (i.e. where the note is, 440 Hz vs 5280 Hz) could not. Basically, the sound contained only the harmonics that were octave multiples of the fundamental. In the absence of octave information, the brain still tries to organize tones so that it can judge relative pitch. Mr. Shepard found that a repeating series of these tones (A,B,C,D,E,F,G,A) were perceived as rising in pitch, ascending endlessly, even though they never moved beyond a certain octave.

Ms. Diana Deutsch, in 1992, started experimenting with a "tritone paradox". This is a pair of tones separated by half an octave. She found that when each of the 12 tritone paradox tones were played for test subjects, the tones were perceived as being centered around a certain pitch. Moreover, how this pitch was centered varied from location to location. People in the south of England centered the pitches differently (Figure 1) from people in California (Figure 2). After sophisticated analysis of speech patterns, Ms. Deutsch was able to establish a relationship between normal speaking tones and center tone as perceived in the tritone paradox tones. Simply put: your tone orientation is related to the pitch range of your speaking voice. This brings up a lot of interesting points for audiophiles. For example: Is this why loudspeakers from England, Japan, and the United States sound so different? As scientists continue to examine human auditory perception, answers to these and other questions will someday be discovered. Right now, it's still too early to draw any real conclusions. Yet, it is facinating to think that someday you'll be able to custom tune a stereo system for the country you were born in.

Last Updated: April 12, 1996

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