¿What is detail retrieval?

Yes. Measurements can be interpreted to fit a narrative. Generalising further, any scientific model, on which measurements are based from, is also just that…a model. It’s a pale representation of reality.

Honest minds know the limitations of theoretical science and empirical measurements, particularly in the field of audio engineering that largely rest on physiological aspects as well as human cognition, which in itself has not been comprehensively understood and modeled.

To this point, this is why I don’t see the hard delineation between audio devices in the signal chain as “production” or “reproduction” equipment. Any equipment in the sound chain adds/takes away something to/from the original sound. No equipment is 100% transparent. Any equipment/component introduces a finite non-zero time delay (phase shift), and nothing in nature is ever truly a linear system so every step of the chain adds harmonic distortions. People label these additions/reductions as “imperceptible”, which is true if taken on an individual basis. However, it is false to assume that cumulative effects are also imperceptible. Even EQ’ing a headphone colors the signal as it is not theoretically possible to alter a signal with zero time delay. The thing is that we care less about the “original” sound and more about what comes in our ear…the composite end product at the end of the signal chain. But of course, the SINAD-crazed people will disagree and fight to death that their expensive hi-fi equipment has faithfully reproduced an artist’s original sound that was perfectly captured in their flac recordings.

Btw, this is why I also love a tube amp. It shamelessly colors the sound and introduces consonant harmonics.

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Nor is it desirable to. Since headphones are minimum phase, EQing them to correct the FR is also correcting phase. Which is why minimum phase EQ filters are preferable for headphones. You want the phase shift.

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Well, in analog days it’s always minimum phase filters with the non-zero delays. The phase shifts generally introduce perceptible colouration that as you say improves the sound; it adds some sonic character, particularly with wide bandwidths and gentle boosts/cuts. But in some cases, like when using narrow bandwidth and steep pass filters, loss of resolution due to smearing could happen.

Now with digital audio…hmm, eliminating phase shifts with linear phase filters is probably desirable in the cases I mentioned above, like cutting out resonant frequencies. It improves/preserves resolution.

Anyway, I’m not going to argue. It’s all again subjective.

No I’m saying minimum phase EQ filters are objectively better. I can’t link to the Reddit comment I am quoting, but here is a better explanation from oratory1990:

We are not using EQ to shape the sound in a new way, we are using EQ as a remedy, to “repair” or “fix” inherent problems/idiosyncrasies of the headphone.
E.g. we’re using a filter at 5 kHz to combat a resonance of the headphone at 5 kHz.
The resonance of the headphone will not only affect the frequency response of the headphone but also the phase angle (as they are invariably linked in a minimum phase system)
By now calculating a minimum-phase filter to combat this specific resonance, we are combating the problem both in terms of magnitude frequency response as well as phase angle frequency response.

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Well, if what you hear after you’ve applied min phase is better than before, then that’s all that really matters.