What parameters should be measured to quantify differences between cable acoustic properties.

this should prove interesting

I have more trust in the human ear (my own) than electric measurement, but this may be interesting anyway.

For digital cables, jitter (at the DAC output). I don't know what amount is audible, but anyway, cables often cause no measurable jitter at the DAC output.

For interconnects, background noise (especially at 50/60 Hz), and frequency response (the amplifier output should be much better than a microphone. Measuring directly the cable output can affect strongly its background noise). I think that background noise at 50 Hz is not audible below -70 dB. Measurments give rather -85 to -115 dB.
Frequency response audibility is given by this chart : ABX Amplitude vs. Frequency Matching Criteria
Interconnects are way below this threshold. Their maximum deviation is around 0.02 dB.

For speaker cables, frequency response too (comparing the cable intput to the cable output). It depends strongly on the speaker. Actually, only electrostatic speakers with impedance falling down to 1 ohm cause audible frequency response problems from the cable.
Cables causing amplifier clipping are a problem on the amplifier's side.

In conclusion, there is no measurment that can be correlated with the sound of cables. However, you can notice that the audibility thresholds are defined with blind testing, while cables sound the same in blind testing.
So if you want to assess the "non blind" audibility of cables, you have to rely on the "non blind" audibility of technical parameters, then you end with the same mix-up between people that pretend to hear 0.000000001 % of THD as clear as night and day and people who pretend that 5 % is not audible in music, and all you have done is complicate the debate even more, adding another topic for endless discussions on top of cables : audibility of distorsion.

Sorry???? How do you know that?
At least you're asking the right question.
I've asked this question a few times, but never got an answer.
Nobody seems to know what parameters are relevant for our auditive perception (and how they affect it).

It depends on what you call auditive perception.

If it is blind listening tests, everything is well known : speakers and room make 98 % of the sound, through frequency response, reverberation and distorsion. Amplifier (if transistored, powerful enough and not clipping) and speaker cables make 1% through frequency response, and CD player 1 % through aliasing or some kind of distorsions or frequency response.

If it is normal listening, reduce all the above to 50%, and introduce 50% of psychology, which has no direct relation with the sound itself.

Oh, I forgot : add 50% more for the CD recording quality

That's a question nobody can answer. There's a cable-measuring test going on in the «cables» forum, with no significant result so far -- and I haven't seen a comparison which would show any kind of (universally accepted) significance. So the verdict is easy: Cables make no audible differences. At least to those who haven't heard them.

This thread could just as well be closed -- the question has been asked multiple times before, logically with no definitive answer, but a lot of personal attacks instead.

As much as I'm interested to see any data on the subject, I have more or less given up on it. It's not that cables don't show measuring differences, but they are tiny and don't provide a hint which of them could cause which audible characteristic. Nevertheless to me cables are a reliable tool for fine-tuning my system. I could just decide they don't do anything, the differences are imagined -- but what would I gain by doing so? The effects are absolutely persistent, so it's as good as if they were real.

Of course I'm joking a bit, because I still think they are real. No failed DBT would convince me of the opposite (I've passed a blind headphone-cable test). During my speaker-builder «career» I've done a lot of non-blinded comparisons between different crossover-network tuning variants. The measuring differences with the components were minuscule (some of them within less than 1‰ -- let's say 4.782 vs. 4.778 μF). It wouldn't have been practicable to do them blinded, let alone DBT -- imagine 20 or more different tunings within 1 hour. Anyway, according to the hegemonic objectivist philosophy they have been useless. Personally I don't think so. And I suppose that most speaker builders use the same tuning method -- with success.
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Good question, I've suggested something similar in the past. What I'd like to see is a setup where two recordings are made. One with an aftermarket cable and one with a control cable. Record the system being played with each, then lay the waveforms over each other.

I'm not an engineer by trade, but I find human perception utterly unreliable. Having been a criminal defense attorney, I learned that circumstantial evidence is best. That's against folk wisdom, but evidence bears it out. A fingerprint on a window doesn't forget, lie, change its mind, or become uncertain because it was drunk at the time. It doesn't tell you everything, but it is what it is without the human uncertainty.

There was an interesting episode when I took a class on evidence. During one session, a visitor briefly interrupted the class to ask where the library was. The professor told him and he wandered off. At the end of the class, the professor asked us to write down what the guy was wearing, then invited him back into the room. It had been a setup to teach us a lesson on perception and the value of eyewitnesses. There had been about 40 law students in the class, it was an unstressed environment, everyone was sober and rested, and everyone had a good look at the guy.

Not one of us remembered what the guy was wearing. He hadn't changed and came back in the room with the same outfit.

I know this isn't directly applicable to audio, but it illustrates just how unreliable humans are. Myself included - I got the outfit completely wrong, too. But something circumstantial, like a security video, would have been dead on.

It goes to show why we have to rely on measurements made with machines. That's counterintuitive and abhorrent to many, but that is the only reliable way to truly know something. If tests can be repeated by others, using different equipment, it lends more credibility.

This is why I want to see comparative recordings overlaid on each other. If something is truly going on, it will show up there. If nothing shows up, then Occam's Razor clearly points to human error.

Erik: Well, psychology teaches that humans have a better memory for shocking experiences. Not the devil's advocate, but just a thought.

There will always be significant differences between two recordings, even without changing the cable. 16 bits recordings can detect volume variations less than 1/100000, which surely occur when the components temperature drift. Electromagnetic noises from lights, computers, switches etc will also likely be recorded. And, way above all this, without atomic clocks for playback as well as recording, time drift will lead to very high level differences because the cancellation of the two recordings won't be properly synchronized.
Synchronizing the recordings require asynchronous sample rate conversion, which should affect the sound quality more than interconnects.

The influence of the cables will be very difficult to sort out.

And in the case of no significant differences (shown by statistical analysis over many recordings, for example), it shall always be blamed on the poor quality of the recording device. It is likely that people will hear the cable influence during playback, but not in the recording.

The most direct way to investigate is to compare blind and non-blind listening : if you hear a difference, try in a blind test. If you still hear it, fine. That would be an extremely interesting result.
If you fail the test, then, you can begin the most interesting investigation of all : to find why the test fails, comparing the listening conditions, and looking for the exact parameter in the test setup that make the difference disappear (if you don't hear it during the test), or change (you hear another one during the test, not correlated with the cable).
Narrowing the test conditions, you can proceed until there is only one alternative : the test succeeds reliably, or the knowledge of the cable is the only factor left that produces the audible différence, working even when you think the cable is on, while it isn't.