Hmm I take it a different way from reading various books and papers.Disagree in theory here, the waveform shape each of these attacks and overtones and harmonics takes when they wiggle the microphone is, wait for it..."sinewave" ish... (not a textbook perfect sinewave, but damn near). No worries, it took me a while to grasp the concept and reading up on acoustics till my ears blead. ha ah ha.
Also, the amp can only be at one point at any one time, whether it is rising in output or dropping, and I do agree that a multi tone burst is better than just plodding in one constant frequency sinewave, and, any twin tone (that is a simple tone burst for sure) intermod test will reveal differences between amps, but it is still the level of these differences that are of concern....dang it be all, our ears really do have a limit to what they can do, despite what folks seem to believe to the contrary.....
...now what our brains can do, well ! ! !
Tom
If you look at a complex waveform in both time domain and frequency domain it does not look like a normal tone type sinewave, let alone using fourier analysis to provide snapshot of the fundamental and harmonics which will show how much different a single sinewave looks to a complex wave that must be derived from multiple sinewaves to be generate the original waveform.
In reality you would need a hell of a lot of sinewaves to make up a complex waveform such as an instrument playing a single note.
There are various papers on this subject discussing in terms of physics musical instruments and the waveform, including discussing sinewaves-tones-fourier with that of the instrument.
Using just the amplitude against time it may look that way, but it does not give the complete picture.
As an example here is microphone measurement of various instruments, using this not because it is more about energy above 20khz, but it shows just how complex a single note is,, especially when one considers how much it fluctuates from 20hz-20khz and also in the time domain due to attack-sustain-decay (which is not shown with this study):
The 2nd chart is interesting for the various amplitudes of the harmonics.
http://www.cco.caltech.edu/~boyk/spectra/spectra.htm
Which is an fft (single snapshot is the way I look at it) derived from a point in the amplitude-time graph.
That is a fair amount of sinewaves.
The problem is, there are not really that many well recorded-measured instruments out there that can be used as a reference.
To see what it really looks like you need to take the fundamental and all the harmonics, then correlate them to an envelope-spectral decay type graph where amplitude is vertical, frequency (which increases for each harmonic) is depth, and horizontal is the time.
I have only ever seen this done a few time, but it does show interesting characteristics when it is.
Appreciate we differ on this and as neither of us are experts agree either of us could be wrong or even both partially right
Cheers
Orb