A 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 the 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 all of the sounded notes together, the distortion products being audible clues that the notes belong to the same instrument. IMD would then have its effect on the ability to distinguish one instrument from another. Adding IMD in the sound reproduction chain would have the 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.

Document History
August 31, 2010 Created