Description
Music received a maiden scientific consideration in the 6th century B.C.E. from the Greek mathematician Pythagoras. He established musical pitch intervals in terms of sub-lengths of a stretched string. Mersenne’s experiments (1627) highlighted the compensability of string length by the balanced-force exerted on the string and string density. It proved that string length was not invariant with pitch. However, rather than return to the string for the property that is invariant with pitch to serve as a foundation for scientific approach to music and auditory perception, physicists and mathematicians arrived at vibrational frequency as the stimulus to pitch through computations of ratios of a string’s mechanical quantities, and hearing research was engulfed in philosophy and mystical ratios in the effort to establish the harmony of the spheres in terms of musical intervals and harmony. Descartes (1641) contemplated those ‘sciences’ that borrowed from philosophy; he “judged that nothing which was solid could be built upon such unfound foundations.” This prediction haunts hearing research to this day. Today, we know that Ohm’s acoustical law (1843) is irredeemably flawed; and Helmholtz’s resonance (or place) theory (1877) is just as wrong. These eminent men had erected their theories on the Pythagorean string ratio theory. After 2,500 years since Pythagoras, pitch—the gateway to understanding music, speech and hearing—remains a defiant scientific mystery. A question arises: Was Pythagoras right? The Ecological Foundation of Hearing Sciences aims to bring the era of prehistoric physics of sound, mathematical reductionism, extrapolations, and philosophical speculations in hearing sciences to a close. The goal is attained through painstaking experiments to trace out the property of the sound source that maintains a direct, unchanging, and unchangeable relationship with pitch. The established invariance between a sound source property and the sensation pitch portrays sound the way the ear really sees it; it provides a solid foundation for future research in all aspects of auditory behaviour.
Music received a maiden scientific consideration in the 6th century B.C.E. from the Greek mathematician Pythagoras. He established musical pitch intervals in terms of sub-lengths of a stretched string. Mersenne’s experiments (1627) highlighted the compensability of string length by the balanced-force exerted on the string and string density. It proved that string length was not invariant with pitch. However, rather than return to the string for the property that is invariant with pitch to serve as a foundation for scientific approach to music and auditory perception, physicists and mathematicians arrived at vibrational frequency as the stimulus to pitch through computations of ratios of a string’s mechanical quantities, and hearing research was engulfed in philosophy and mystical ratios in the effort to establish the harmony of the spheres in terms of musical intervals and harmony.
Descartes (1641) contemplated those ‘sciences’ that borrowed from philosophy; he “judged that nothing which was solid could be built upon such unfound foundations.” This prediction haunts hearing research to this day. Today, we know that Ohm’s acoustical law (1843) is irredeemably flawed; and Helmholtz’s resonance (or place) theory (1877) is just as wrong. These eminent men had erected their theories on the Pythagorean string ratio theory. After 2,500 years since Pythagoras, pitch—the gateway to understanding music, speech and hearing—remains a defiant scientific mystery. A question arises: Was Pythagoras right?
The Ecological Foundation of Hearing Sciences aims to bring the era of prehistoric physics of sound, mathematical reductionism, extrapolations, and philosophical speculations in hearing sciences to a close. The goal is attained through painstaking experiments to trace out the property of the sound source that maintains a direct, unchanging, and unchangeable relationship with pitch. The established invariance between a sound source property and the sensation pitch portrays sound the way the ear really sees it; it provides a solid foundation for future research in all aspects of auditory behaviour.
