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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?

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  • $\begingroup$ 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. $\endgroup$
    – Solomon Slow
    Commented Jan 7, 2019 at 19:49
  • $\begingroup$ 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. $\endgroup$
    – Solomon Slow
    Commented Jan 7, 2019 at 19:52
  • $\begingroup$ 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? $\endgroup$
    – Matt Smallwood
    Commented Jan 7, 2019 at 19:59
  • $\begingroup$ 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. $\endgroup$
    – Solomon Slow
    Commented Jan 7, 2019 at 20:38
  • $\begingroup$ @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. $\endgroup$
    – alephzero
    Commented Jan 7, 2019 at 20:40

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Re the first paragraph, if you're asking about how the ear-brain system processes sound, the answer is that it's complicated and not entirely understood, and neither simple time-domain models or simple frequency-domain models can explain all the data.

I'm not as clear on what you're asking in the second paragraph. The cochlea can't respond to frequencies above about 20 kHz, so basically putting a low-pass filter there doesn't have any audible effect, except in the sense that there is no such thing as a low-pass filter that has a perfectly flat response below the cut-off.

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  • $\begingroup$ If harmonics summed together create the waveform that we hear, which will surely have elements of mainly the fundamental frequency and then the harmonics, then surely harmonics above 20 khz will affect the sum waveform, therefore a recording with "less" harmonic content will be less faithful? $\endgroup$
    – Matt Smallwood
    Commented Jan 7, 2019 at 19:53
  • $\begingroup$ @MattSmallwood, A recording with less harmonic content, but that doesn't mean a human ear can tell hear the difference. $\endgroup$
    – The Photon
    Commented Jan 7, 2019 at 21:01
  • $\begingroup$ @The Photon , so surely that means we hear sound waves almost as individual harmonics, by which our brain constructs the overall sound through "interference" by the harmonics. So a dog with a higher hearing range will literally hear a sound as a different tone due to the higher harmonics we could not hear, that add detail? $\endgroup$
    – Matt Smallwood
    Commented Jan 7, 2019 at 21:08
  • $\begingroup$ @MattSmallwood, yes, as I understand it, different structures in our ear respond to different frequency bands. No structure captures the time-domain waveform. But like this answer says, it's "complicated and not entirely understood" how our brain interprets the data from the ear to provide the perception of sound. $\endgroup$
    – The Photon
    Commented Jan 7, 2019 at 21:10

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