I can't represent or defend him, I'm not sure what's the source of his claims related to time domain. His standpoint is though (that I know, I specifically asked it) that you hear differently, say, a 10 kHz square waveform from a sinuus 10 kHz square waveform, Because of Fourier analysis related to harmonics consisting a waveform, that would imply we do hear frequencies beyond 20 kHz, through it's influence on waveforms within a hearing spectrum. I don't know whether scientific tests were performed on this. whether we hear a difference between different waveforms and a same frequency.
I'm not sure exactly what he's talking about, and I realise you're in the tough position of trying to relay arguments that deal with an area you're new to. Perhaps he's talking about intermodulation distortion, i.e. frequencies above the audible range intermodulating with frequencies in the audible range to create intermodulation harmonics also within the audible range. This is a real thing, but it is a form of distortion happens only when there is a flaw in the playback system.
Anyway, you can actually test your friend's claim for yourself, there's a
website that allows you to generate different kinds of waveforms at different frequencies and listen to them. Select say 10KHz or 15KHz and flick back and forth between a sine wave (pure tone) and a square wave.
But be warned, due to some weird quirk of the website, the squarewave is about 1dB louder than the sinewave (and the others are inexplicably quieter). You'll definitely be able to hear this level difference. But (and I know this is not strictly speaking fully possible), try to ignore the level difference and concentrate on trying to hear a tonal difference.
If you want to avoid the 1dB level difference and do the experiment in a properly controlled way, unfortunately you'll have to record the waveforms in something like Audacity, then use software to properly level match them, then play them back with Foobar and an ABX comparator plugin (under which circumstances you unfortunately won't be able to hear the difference at all unless you have hearing that extends higher than average in frequency).
But also, just think it through first. If you can't hear a fundamental tone at 22KHz, how could you hear a harmonic at the same frequency? What is your ear doing to the inaudible tone, just because there is now an audible tone present? But by all means try it if you don't believe me.
Also, if you do this, please make sure that your sample rate is set to at least 48KHz, but preferably higher. It needs to slightly more than double whatever the highest frequency is that you want it to reproduce.
Anyway, I'm strongly for double blind listening tests. There's no way objectivists can prove a certain set of measurements represents what we hear in a blind test unless it's actually confirmed in blind test. Without this it's still an interpretation and a theory without a final proof.
Nice
But... I think I disagree slightly again, if I've understood you correctly.
I think you're talking about the kind of double blind test where we just take one piece of equipment out of the chain and replace it with another, is that right?
IMO, these tests are of value only if we are trying to establish whether we can discern a difference between two devices, or doing market research.
If you want to validate a set of measurements, you can't do it by blind testing with the piece of gear measured, there are just too many variables being changed.
That's why audibility studies use the same equipment throughout the whole chain and change only one variable at a time (e.g. noise, distortion, phase, etc. etc.). This allows audibility thresholds to be determined (obviously with a margin of error, as in all science). These thresholds can then in turn be used to interpret the measurements of a specific device.
It's an imperfect process, but it's far, far more precise and valid than just blind testing a piece of gear and making assumptions about how the sound relates to its specific measurements. That's an interesting thing to do, but only slightly less of a stab in the dark than sighted testing.