How do we hear harmonics and how does it affect audio fidelity?

First and foremost, do we hear a sound wave as a sum of all the individual harmonics, at the fundamental frequency, or do we hear all the associated harmonics above the fundamental frequency and construct an overall sound wave from this?

If the second point is true, than surely a digital recording that cuts off frequencies above 20kHz (due to the 44kHz sampling rate) will produce a reduced waveform to an analogue recording, which surely will not have a "cut off" frequency, therefore the recorded sound wave will be closer to the original?

• Re, "...an analogue recording, which surely will not have a 'cut off' frequency." Actually, every analog technology that's ever been invented for audio recording has limited bandwidth. If the bandwidth isn't limited by anything else, it'll be limited by the physical size of the smallest feature (magnetic domain on a tape, wiggle in a groove, spot on a film strip, etc.) that the recording "head" can impress on the recording medium, in relation to the linear speed at which the head and the medium move past each other. Jan 7, 2019 at 19:49
• Note: That's one reason why the grooves of a constant-angular-velocity, vinyl, audio disk don't go all the way to the center: The bandwidth approaches zero as the track approaches the center. Jan 7, 2019 at 19:52
• Surely anolgue's continuous nature would see a curve tending to 0 as the frequency increases, up until the cut off you have mentioned in the actual design, therefore capturing a higher quantity of harmonics as oppose to digital? Jan 7, 2019 at 19:59
• OK, I see what you're saying: The frequency response of any analog filter never reaches zero in theory (and that includes the filter defined by the geometry of an analog recording head and speed of itsrecording media). But beyond a certain point, the amplitude of the recorded signal will be less than the amplitude of the noise that is present in every system. Jan 7, 2019 at 20:38
• @MattSmallwood It doesn't matter too much that there is a cutoff frequency, because the amount of energy in the high frequency components of most sound is very small anyway. But it is critically important that the digitizing process doesn't convert frequencies above the limit imposed by the sampling rate into frequencies below that limit, which interact with the "real" signal. That is one reason why professional quality recordings are often made with a frequency cutoff 48 or even 96 kHz not 20. The second step of filtering down to 20kHz then doesn't have to be done in real time. Jan 7, 2019 at 20:40