List of Fourier coefficientes to simulate musical instruments
look up Additive Synthesis somewhere.  those Fourier coefficients are not constants.  the musical note is not normally a perfectly periodic function in time.  it is what i like to call "quasi-periodic".  so this is not exactly true (given some period $P$):

$$ x(t) = x(t+P) \quad \text{for all } t $$

but in the neighborhood of some given time $t_0$ this is approximately true

$$ x(t) \approx x(t+P(t_0)) \quad \text{for } t \approx t_0 $$

so the exact Fourier series for $x(t)$

$$ x(t) = \sum\limits_{n=-\infty}^{+\infty} c_n \ e^{j 2 \pi n f_0 t} \quad f_0 \triangleq \frac{1}{P} $$

is not precisely true, but more like

$$ x(t) = \sum\limits_{n=-\infty}^{+\infty} c_n(t) \ e^{j \theta_n(t)} $$

where 

$$ \theta_n(t) = \int\limits_{0}^{t} 2 \pi f_n(u) du + \theta_n(0) \quad f_n(t) \triangleq \frac{n}{P(t)} $$

so what you're looking for is a collection of envelopes, rather than a collection of constant coefficients, for some musical instrument.

in a previous life, living on an older computer (that might not power up now) and maybe even on some 3.5 inch floppy disks, i have some of that additive synth data.  actually, i am not sure where to get it all digested.  within the context of Wavetable Synthesis, i know how i would go about extracting it from "samples" of notes (like what you would get from a sample library like from Synthogy ).