That is a conundrum. How are the tools used to measure calibrated? In analytical biochemistry we have some standards we use to make sure that a measurement taking by person A on day one is the same (within excepted variation) with the measurement taken by B on another. And depending on how critical the sample is- possibly across labs.
Is there a universal standard that all instruments use? If you take 5 such devices for measuring the usual suspects do they all give the same value? First order, second order, third order harmonic distortion at 1000 hz (obviously measuring the 2nd harmonic of 12 Khz is outside of audibility) . Intermodulation distortion? Group delay? What else? Even vs. Odd harmonics? Square wave response? Ringing?
Are we measuring everything that can affect the quality of sound?
Someone else commented that many of the "test instruments" used by audiophiles are indeed not necessarily reliable or accurate, but I would say that, at the commercial level, the opposite is true. (They are indeed correct when it comes to "affordable" test equipment, and sound cards, many of which simply don't meet spec.) However, if you take any Audio Precision test set (which is the industry standard), and run the same test, it will give you similar answers. (And, when you spend $50k on a piece of test equipment, you keep it in good repair and calibration - although I don't think the APs require much maintenance.) Likewise, if you look at a waveform to see what the ringing looks like, it will look the same on any AP printout, or on the output from any good quality oscilloscope. (You may get slight variations in what you rad or observe, but I don't think those variations have even been mentioned... nobody here is arguing a few percent either way.)
Someone else wondered what the smaller companies - who can't afford a $50k AP test set - use, and the answer there is that it varies anywhere between "lower cost but still reasonably accurate test equipment" and nothing at all. (There are several companies out there making expensive "audiophile USB cables" that don't work well at all, and don't even meet the minimum standards of a cheap data cable - presumably partly because the companies that make them don't own the equipment necessary to test them properly. Likewise, many boutique amplifier companies simply "play by ear" and don't actually test their designs or products at all. After all, the chef at your favorite restaurant probably doesn't send every new dish he creates out to a lab to be analyzed, right?) In the case of DACs, even an oscilloscope costing a few thousand dollars, and probably even a test run on a sound card, will usually allow you to see things like ringing. (Besides which, the chip manufacturers publish specs and oscilloscope images and, while people may question the scientific knowhow and ethics of an audio cable or DAC manufacturer, I don't think anybody is accusing Texas Instruments or Wolfson of publishing inaccurate or falsified data on the data sheets for their chips.)
Unlike with chemical processes, I also don't think lack of calibration standards, or equipment inaccuracies, are much of a factor at the level of these discussions. Most of the recent discussions are qualitative rather than quantitative. We're not arguing about whether 1 mS of ringing on a DAC sounds audibly different than 2 mS, or whether only the longer period is audible, we're arguing about whether it's audible
AT ALL. Likewise, nobody is disputing about how significant the difference is between speaker cables; the discussion is "Is there a difference, or is it all snake oil?"
Unfortunately, the audio industry has a long history of claims with no scientific basis at all, and claims based on downright false science, which has caused some people to get so frustrated that they automatically assume that everything for which they don't understand or agree with the science must be fraudulent. This is why you see reactions like:"Unless you can prove it's real, I don't even want to discuss it." (Note that, when I say history, I'm not suggesting that it is past... a significant percentage of products sold today make unrealistic or false claims - or claims that are based solely on "subjective opinions".) Also, unfortunately, as it is whenever the topic is very small differences in what humans perceive, psychological actors like the placebo effect have such a major effect on the results that they can sometimes be the ONLY actual cause of those results. (The huge market in snake oil is "powered" by the desire of people to hear what you can convince them they think they hear, or want to hear.)
A lot of the problem is also that many audiophiles simply don't have a good grasp of the science involved. This makes them easy to fool with pseudo-science, but it also renders them unable to understand legitimate science when it's presented to them.... as with ringing.
When you see ringing in the output of an amplifier, it is a sign of instability, and implies certain flaws in circuit design. (Ripples or tilts in the top of a square wave generally result from errors in frequency response, and can be used to detect them.) In an amplifier, ringing is strictly energy at audio frequencies that doesn't belong there, usually caused by an instability in the circuit itself, and will show up in distortion figures.
However, ringing in a DAC occurs for wholly different reasons, and has different implications. In a DAC, the ringing normally seen is a result of the oversampling filter, and consists of energy that
DOES belong there, but has been shifted to appear at the wrong times by the filter. This means that, if you take any sort of steady state distortion measurement, which sums and compares "the energy that belongs" and "the energy that doesn't belong" over some time interval, the energy the ringing contains doesn't count as an error (the energy sums correctly). This is how a DAC which shows very visible ringing can still measure with very low THD numbers; with a steady state signal the ringing won't be visible at all; with a transient signal, the ringing is part of the "legitimate signal" and in fact must be there for the total to sum correctly.
This being the case, for example, if you were to send a 5 mS burst of 1 kHz sine waves into a typical DAC, the output waveform would show something resembling your input signal, with ringing occurring both before and after it. If you were to test that DAC for THD, you would find that it measured very low - because that ringing is part of the signal that belongs there, so any test that sums the energy over time will not consider it to be distortion. However, if you were to instead measure the output at a whole series of instantaneous points in time before and after your input signal had stopped, you would find ringing present (and, if you considered that result "instantaneously", for those instants you would have 100% ringing and 0% "legitimate signal" - so, if you looked at it that way, at a point 1 mS after your impulse input was stopped, you would have 100% THD at the output.
Since the ringing in a DAC "really is" parts of the signal being "distorted" by being shifted in time, whether we can hear the ringing or not (or whether it sounds different if it happens before or after the impulse) becomes a matter partly of physiology and partly of psychoacoustics. (We have signal occurring at times where it shouldn't, quite near in time to when it should occur, so the question is whether the main signal masks us from hearing the signal that shouldn't be there or not. This masking could occur physically, in our ear, or psychoacoustically, in our brain.) Therefore, arguing that the steady state THD is so low it can't possibly be audible is a red herring. The real question is of whether the ringing is masked by the main signal, and if it is, whether it always is or only under some circumstances. (The proponents of "apodizing filters" are quite convinced that post-ringing is better masked than pre-ringing, and so that mathematically shifting some of the ringing from before the impulse to after it makes the signal "sound better" - at least with certain signals, and claim to have demonstrated this. I personally believe that I've heard differences that are consistent with this claim. Since the subject of masking is still not "thoroughly understood", I consider this to be something worth testing.)
(To me, since this is consistent with the science, I don't see it as especially unlikely to be true - and so it's clearly worth testing. Other folks here seem to find the science not to be credible, and so seem to require that time first be spent proving that there's something there worth testing - or even discussing.)