Copyright © 2010
Created August 31, 2010. See Document History at end for details.
Musical View of Distortion
The basis for music is that frequencies which are related by simple
integer fractions sound good together. It would be reasonable to
say then that distortion products related in the same way are not
necessarily unmusical. Musical instruments themselves produce the
harmonic structure characteristic of their timbre by means of
distortion mechanisms inherent to their design and of the materials
from which they are made.
Consider how the functional and distortion mechanisms in musical
instruments create harmonics. Plucked or hammered stringed
instruments begin with a timbre consistent with that of a triangular
wave formed at the first moment of the musical impulse then decay as
materials would dictate. This is well documented in physics
textbooks. Upon release of the string, the initial triangle shape
divides into two half-size replicas and travel in opposite directions
along the string at a speed determined by the mass and tension of the
string. The fixed ends reflect and invert these decaying
triangles as they travel back and forth along the strings, the sum of
which add to produce the lateral vibration which drive the sound.
Distinct note percussion, as timpani, would operate similarly, except
in three dimensions. Bowed instruments, on the other hand,
initially produce a sawtooth wave instead. The bow tightly
controls the movement of the strings, first pulling the string smoothly
by the tack of the rosin on the bow. When the force exceeds the
tack of the bow the string snaps back to a baseline position.
This process continues repeatedly as the bow is pulled. Fourier
series analysis of these waveforms show a harmonic structure declining
with frequency even before considering that the construction materials
absorb higher frequencies more than lower. Then the strings would
drive the nonlinear soundboard (not unlike a nonlinear electronic
circuit), which would would further alter the timber of the
instrument. Wind instruments produce similar results by
somewhat different mechanisms.
We can infer at this point that harmonic distortion is linked to
instrument timbre. If sound reproduction equipment adds more
harmonic distortion of the same character, the sound will remain
musical, only it will be enhanced or altered. Whether the result
would be pleasing would be a matter of taste.
What about intermodulation distortion? Many hold IMD to the real
culprit behind bad distortion; is it? Musical instruments produce
IMD as well and sound good. All of the strings on a stringed
instrument drive the same soundboard. As long as the strings are
sounding notes in the same key, the IMD products remain in the same
harmonic structure that harmonic distortion produces. IMD ties
of the sounded notes together, the distortion products being audible
clues that the notes belong to the same instrument. IMD would
have its effect on the ability to distinguish one instrument from
another. Adding IMD in the sound reproduction chain would have
effect of blending all of the sounds together, attempting to make them
one. I have heard this effect in high distortion audio, all of
the sound meshed together, losing its distinctiveness. In small
amounts, even IMD would not be unmusical, only it would obscure some
details in the music.
All this would be well if all musical instruments were tuned to perfect
pitch, where all the notes played had perfect intervals. This is
not the case in Western music. In order to make all keys
playable, a compromise tuning system has been adopted. The
even-tempered scale is not integer based, but rather all notes are
separated by the same irrational ratio, the twelfth root of two.
As a result, what would be fractional integer intervals become somewhat
altered, approximate but not exact. In this context, the audible
effects of distortion are worsened because many harmonics that would
coincide do not fall to the same frequency.
I would seem that excellent reproduction would best served to make
distortion as low as possible but still musical or euphonic, unless
your tastes require otherwise
August 31, 2010 Created