Mastering legend Bernie Grundman explains why the measurement crowd has it all wrong!

“ I honestly have no idea what “accuracy of the music” means.

That’s one of the differences between you and Bernie.”

what? That he is fluent in gobbledygook and I am not? I guess it’s a job skill for folks working in the audio industry 

“Measurements aren't taken in the real world and the way the equipment is used, it's usually taken in isolation, not the system as a whole with music.”

what measurements are you looking at?

Music is not math or science.  It is art.

Music (art), math and science indeed may intersect, but they are not the same thing. They are all different things (again, it is true, especially math and music, that they often intersect).

If someone wants to listen to music after they've undertaken rigorous scientific and mathematical processes and/or determined they've achieved maximized fidelity by citing measurements on a page (irrespective of how the music actually makes them feel - of course, confirmation bias is always a hazard when one claims their music makes them 'feel better' because they've cited measurements on a page, but that's a whole other ball of wax), that is their prerogative. 

Music is not math or science. It is art.

You are right ...

I will only add more...

Music is mathematics + art, mind+heart = spiritual transformative healing experience and often more than a distraction ...

I discovered recently that it is not so much that music is mathematical but more it is mathematics which is in its core musical and rythmical ...

The heart and the spirit guide us all ...music is the audible manifestation of this guidance ... Mathematic is art  and contemplation of new concepts and new worlds  way more than  mere logic...It is why mathematics in his essence is musical ...

See Alain Connes " the music of shapes" on youtube ...

The answer to your question is in this paper :

https://www.temporalcoherence.nl/cms/en/pyra

« 4. Some remarks about the non-linear properties of human hearing.

Although it is outside the scope of this paper, it should be noted that human hearing is likely to
be neither linear nor time-invariant, which can explain the findings of refs. 6 and 7. Another
clear indication is that human hearing is able to circumvent the uncertainty relations (ref. 8).
(N.B. Note that the uncertainty relations are a direct consequence of the linear Fourier
Transformation). The findings of ref. 8 correspond to the findings of refs. 4 and 5. This could
be the gateway to understand the discrepancy between the results, based on linear theory and
the perceptual findings as described above. The often-remarkable properties of human hearing
are the subject of a paper by Kunchur (to be published).
The temporal resolution of human hearing is at least an order of magnitude better than derived
from its frequency response, so it is very likely that especially metal percussion instruments
show a clear difference between ‘live’ and recorded sound. Alas, most microphones and
tweeters are insufficiently at par with the temporal resolution of human hearing, so the
perceived reproduction is clearly inferior to the ‘live’ sound. The ‘high resolution audio’ does
improve the situation, but a major improvement of the microphones and tweeters is required
to bring this to full fruition. More information on this subject can be found in several papers,
which can be downloaded from www.temporalcoherence.nl
Although the Fourier theory has been well established since the second half of the 19th century,
it is surprising that so little attention is given nowadays to the conditions, required to apply the
linear theory. It has been applied unreluctantly to electronics and human hearing, even though
neither fulfil either of these requirements. Therefore, it should not come as a surprise that the
results are inconsistent with listening experiences. We have encountered that also in the paper
on Feedback Flaws

5. Consequences of non-compliance with the conditions of Fourier theory.

It should be clear that when the conditions of linearity and time-invariance are not fulfilled,
results, based on the Fourier theory, can be thrown straight into the wastepaper basket.
Regretfully, these conditions are rarely respected and without hesitation, the frequency
response, determined with continuous sinewaves, is interpreted as if it were from a linear and
time-invariant system. Which explains why the behaviour of the amplifier with dynamic signals
(like music) differs from the (expected) behaviour, based on results obtained with steady,
continuous signals. To reproduce complex and dynamic signals like music well, the amplifier
needs to be -next to a large number of other conditions- also as much as possible time-
invariant and all its amplification stages should be as linear as possible. If not, artefacts will
show up which manifest themselves mostly in the time domain and lead to a degradation of the sound stage and thus of the perceived quality. It is banging on an open door that the less
an amplifier (also internally!) fulfils the requirements for a linear and time invariant system, the
larger the contribution of artefacts to its output signal will be. As several of these cannot be
detected using continuous sine waves, these differences may not show up in the specifications.
This can explain why amplifiers with similar specifications give significant differences in the
perceived quality.

“Measurements aren’t taken in the real world and the way the equipment is used, it’s usually taken in isolation, not the system as a whole with music.”

what measurements are you looking at?