Sorry for the late response. I have been seriously tied up ever since I wrote that long post.
That's very impressive and really a smart question, and the answer is not easy, because as far as I can figure out, not everything is known about psychoacoustic properties of the ear and the brain. Again, this is a subject of research, although I feel, not a lot has been done, but I may be wrong because this is in a domain that is far away from my areas.
It has been proven beyond reasonable doubt that many instruments have harmonics far far above 20 kHz, and some too with significant fraction of the energy. For example, let us look
at a paper by James Boyk of the California Institute of Technology (CalTech):
There's life above 20 kilohertz! A survey of musical instrument spectra to 102.4 kHz . I am really impressed by the pains taken by him and his group of students to correctly determine the spectrum of a variety of instruments, taking into account all kinds of perceivable corrections. You can find out what these guys do at this link:
Caltech Music Lab Home Page
Obviously, the interesting question is: So what? Can we hear the harmonics above 20 kHz or whatever the personal upper limit?
In section X (Significance of the results) of James Boyk's article, this issue is discussed. Boyk is giving reference to other scientific work where people have claimed that higher harmonics do matter. I can also give a few references where similar proclamation has been made.
But somehow I have a feeling that a great deal of scientific work has not been done in this area.
With the above as background of what we know with some definiteness, let me elaborate on my previous post regarding this matter.
When I said in my previous post that every single musical note (for example the middle C of the piano) comprises of many waves each having frequencies which are integer multiple of the frequency of the wave with the lowest frequency (called the fundamental frequency), I agree, this to start with is a very confusing statement. A wave is a periodic pattern in time and space, and the periodic pattern corresponding to a sound (a single musical note in our case) is not the pattern of a sine (or a cosine) wave, rather it is distorted to a different shape by the presence of the harmonics. Theoretically, a periodic shape like that can be expressed as a classical superposition (addition) of the so-called normal modes, each normal mode is a sine wave and each having a different amplitude and frequency (fundamental and the higher harmonics). Experimentally also, a spectral analysis can be done, as done by Boyk and his group.
The shape of this wave (actually called a wavepacket) is responsible for the quality (timbre) of the sound produced. Unless human ear has a spectral analyzer in-built, there is no reason for the ear to split up the received sound into its component sine waves and then act as a filter so that components above 20 kHz does not pass through resulting in a change of the timbre. On the other hand, there are audio equipments like a DAC which presumably does this for an implementation of the recovery of the sampled data - because the sampling theorem works in the Fourier (frequency) space rather than in the time domain. I have to confess, I know very little about the ear and its actual functioning procedures, but it seems reasonable to me that it is not a ADC+DAC device and there is no reason for the ear to go into the Fourier domain.
However, there is a reason for the ear to have a cut-off of the fundamental frequency. The period in space of the wave-packet is basically the wavelength (wavelength of the wave packet is the same as the wavelength of the fundamental sine wave). It is well known that none of the body parts has infinitesimally small space resolution - hence there is a smallest wavelength of the incident wave packet that the ear can be expected to resolve. The frequency is proportional to the inverse of the wavelength - as a result
there is an upper limit on the fundamental frequency that is perceivable by the human ear.
Unless there is a reason for frequency domain to enter, a sound is completely described by the wavelength of the wave packet (or alternatively the fundamental frequency), the intensity and the shape of the wave packet (the so-called quality of the sound).
Regards.