All real signals can be constructed of a set of periodic functions. Let's remember that. So yes, one can calculate the spectrum of Beethoven's 9th, end to end, and then reconstruct it. Accurately, to numerical limits (with enough bits of mantissa, perfectly for a 24 bit input).
Now, using a variety of simple signals works much better than one or two tones. Various 'buzz tones' can isolate distortions via spectral analysis rather effectively, to say the least.
A signal with the frequency spectrum of the a fragment of the 9th can be obtained in two ways:
- From extracting a fragment of the 9th
- From synthesizing a continuous, periodic signal with exactly the same spectrum, which is easily feasible, but there will be no notes or melody at all
I can guarantee the same spectrum, but I can guarantee also that you won't recognize the 9th. My guess is that one will prefer the ninth, although it will measure the same.
It's sort of similar to the volkswagen measurements gate of diesel engines gas mileage. Measures well, performs bad.
My point is that we miss some meaningful measurement as to musical signal