p 91 "In the piano the wire is struck with a hammer covered with soft felt. The felt prolongs the duration of the impact, so that, by the time that the hammer finally breaks its contact with the string, a substantial length of the string has already been set in motion. this reduces the energy which goes into the higher harmonics, and so avoids the harsh jangle of sound ... As we have seen that discord begins with the seventh harmonic, the hammer should be sufficiently felted to reduce the seventh and higher discordant harmonics (ninth, eleventh,etc) to small proportions."
Which is perhaps why harpsicords sound so "jangly."
It's also worth noting that the piano produces not just harmonic components, but also non-harmonic components, i.e. components which are not harmonically related to the fundamental, presumably due to the piano string also behaving like a rod, rather than just a string.
This is why the additive synthesis folks (such as Wendy Carlos of Switched On Bach fame) found it so difficult to replicate the sound of the piano. They'd always approached the problem by using harmonic components (additive synthesis involves creating the sound by building it up with pure tones forming the fundamental and harmonic components as opposed to subtractive synthesis where you start out with a harmonically rich waveform such as square, triangular and sawtooth, and apply filtering to change the harmonic content). Without the non-harmonic components, the results were disappointing.
So if one wants to replicate the sound of a piano, you have to think outside the harmonic box so to speak.
In any case, my point is still the same. If you want to relate amplifier distortion to the reproduction of music, it should be in the context of the sound produced by the various instruments (not just piano) rather than the music scale (and by the way, not all cultures use the western music scale that this discussion has centered around).
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