The comparison of a 1hz beat to a 1hz sound should be absurd on its face: you need about 20-30hz to become audible, and it's a low rumble more felt than heard. Very low frequencies sound absolutely nothing like intermodulation beats.
You can look at your "A440 at a constant volume" example as a 0Hz(DC) signal getting louder and softer 440 times a second, but this is the only case in which your example holds. Amplitude modulation creates sum and difference frequencies, so the A that you hear is 440Hz + 0Hz. if you change that 0Hz to 1kHz, you get a signal thats the sum of a sinewave at 560Hz and a sinewave at 1.44kHz, neither of which are an A.
The distinction is that the 1Hz signal is modulating the audible signal, not adding to it, if you look at the spectrum of the sum of those frequencies there is no 1Hz component, whereas if you added a 1Hz signal you'd get something completely different. And in this case the amplitude of the signal is always changing faster than 1Hz.
Edit: another way of looking at it: You wouldn't say you can "hear DC" because you can hear an A440 played at a perfectly constant volume.
Counterintuitively, there is no frequency component generated at the beat frequency when you sum a 1kHz and 1.001kHz signal, its easy to test that out with matlab, octave, scipy/numpy/matplotlib, etc. Generate the two signals, add them together, and look at the Fourier transform, you'll see two components, one at 1kHz and one at 1.001kHz (assuming you take a long enough window to have that type of resolution) and no component at the beat frequency. A third sinewave doesn't just jump out of nowhere when you add two separate sinewaves together.
If you take the sum of those two signals and run them through an ideal brickwall highpass filter at 999Hz so there are no frequency components below 999Hz, you'll still "hear" the beat frequency because it isn't a separate spectral component, its just the two signals slowly going out of phase, cancelling eachother out, and then going back in phase and boosting the amplitude.
Even if it did produce some new frequencies through some non-linearity (which is negligible in most environments afaik), the recording equipment would capture the low frequency waves produced by those interactions. So the only question is whether there are significant non-linearities in our hearing system, and the overwhelming evidence is no again afaik.
Quoting xiphmont
> Once you're driving air so hard it becomes nonlinear, thus introducing intermodulation distortion in the air, that distortion produces actual audible-range distortion products. And because the distortion you're hearing is in the audible range, a recording will sample and reproduce it accurately.
> You're hearing the audible _result_ of IMD, you're not somehow listening to the distortion curve itself.
Have you been to a concert? There's no recording/playback technology that can reproduce anything close to the sound of a full orchestra. It's all lossy.
Have you read the article/quantization discussion on what is meant by lossy? If your recording equipment is good and your reproduction equipment is good, 16/44 is enough to reproduce the concert sound perfectly (as far as human hearing goes). What you do not experience is everything else but the sound -- the vibration of the super loud bass on your skin, the energy of the public, the beauty of the venue.