«Acoustic cues for perception “represent a narrow-minded
way of thinking which leads us into a blind alley when faced
with the problem of discovering the real nature of the
auditory mechanism.” [1].
The Pythagorean string ratio theory is the pivot around
which revolve all work in hearing [2; 3]. In this regard,
Stephen & Bates [4]: noted: “Pythagoras’ discovery, instead
of acting as a stimulus for further experiments became the
basis of fantastic philosophical and mathematical
speculations such as the famous “harmony of spheres”, and
so for another 2000 years, sound was mainly involved in a
semi-mystical arithmetic of music.” The situation has not
changed today. After all, Ohm’s Acoustical Law [5], and
Helmholtz’s Resonance/Place Theory [6], both reflecting
perception by ratios of stimulus magnitude, are the acoustical
and neurophysiological facets of the string ratio theory. The
difficulties encountered in the search for acoustic cues to
perception, whether in music or speech, have led many
investigators to label the objective “elusive” [7] or
“ambitious” [8]. The ecological approach is presumably
promising [9, 10, 11, 12]; and recent researchers, following
in the footsteps of Pythagoras, have conducted mechanically-
based investigations into pitch perception [13, 14, 15, 16,
17]. However, rather than seek out the invariant property of
the sound source that underlies subjective pitch, modern
investigators focus the effects of individual mechanical
parameters of the sound source on frequency of vibration, or
the relationship between the vibratory modes of the entire
sound source and pitch, all as though vibrational frequency
were invariant with pitch. »
Akpan J. Essien
The Mechanical Invariance Factor in Musical Acoustics and
Perception (Revisited)
This article adress is in my post above ...