Um… okay… What do we really have? It becomes clear, after some extensive listening, that using headphone EQ out to 10 kHz and beyond, is incorrect. The highest treble frequencies are being pushed far too much. An initial stab showed that I should probably limit my use of the InnerFidelity.com data to frequencies below 6 kHz.
And after pouring over numerous expert threads on headphone measurements, it is also clear that nobody has any real idea just how exactly to do meaningful headphone measurements.
And when I go back to my own “plate” measurements and look at them, they were actually pretty reasonable – within appropriate limits.
Here are my plate measurements for the Sennheiser HD650:
And here they are for the Beyerdynamic DT880:
The top graphs show my measurements at 48 kHz sample rate, with an arbitrary zero dB level. Ideally, a spectrally flat headphone would show a horizontal line across all frequencies. And these two headphones aren’t really that far off from being flat. Even their sub-bass response is less far from being flat, than they were from being along that -1 dB/octave slope.
The bottom graphs show the second derivative of these measurements with respect to log frequency – showing something about the sharpness of the curvature of my measurements in the top graphs.
I contend that sharp curvature in these measurements is caused by resonances in the ear cups / plate interface. And so we can eyeball the fact that we should probably ignore my measurements above about 3 kHz, where the 2nd derivatives are starting to come alive. I’m likely measuring less of the actual headphone and more of the internal cavity resonances.
Additional evidence of this comes from examining the phase response of the headphones. Those curves are very gentle, never showing anything related to an electromechanical resonance. You would expect to see a serpentine inflection near any actual resonance in the transducers. And we never see that.
So sharp peaks and dips in the amplitude response must be arising from cavity acoustic resonances. And when that happens you can’t really state anything meaningful about what the headphones themselves are producing.
I think the InnerFidelity.com data are similarly compromised above about 6 kHz. So the use of a Kemar dummy head helps us extend our measurements above 3 kHz, but only till 6 kHz. For all the expense, it seems like too little gain. These dummy heads are inordinately expensive, and the measurements remain suspect above 6 kHz.
And probably for good reason… my ear canals are very likely completely different from the canonical average ear canal planted in a Kemar head. Same with my pinnae and concha. And so any measurements from the Kemar dummy, even if you could assert their accuracy, would still likely have little to do with how I personally would hear the headphones at those frequencies.
What we can do is equalize the lower frequencies to make them fall along a reasonable profile. And I would submit that we should be aiming for spectrally flat response in the bass and midrange, up to around 3-6 kHz. If you want a non-flat listening profile, then dial in some coloring EQ ahead of Crescendo.
What happens up above 3-6 kHz is up to you and your headphones. It’s anybody’s guess what EQ really should be applied. And it would likely be different for every listener.
Crescendo assumes it is playing into flat transducers. If they aren’t flat, then the corrections will be slightly wrong.
Unfortunately, without being able to plant sensors inside our brains (even if we understood what they measured), we are forced into a situation where we have to anticipate what will be heard – open loop corrections.
For what it’s worth, if you really want a -1 dB/octave rolloff, you can get very very close to that by using a pair of low-shelf and high-shelf filters tuned as:
- low shelf: boost 5.1 dB at 183 Hz, Q = 0.174
- high shelf: cut 5.0 dB at 892 Hz, Q = 0.168
This will provide a near perfect -1 dB/octave slope from 20 Hz to 10 kHz, within 0.1 dB, and within 0.6 dB all the way to 20 kHz. Zero gain is around 440 Hz.
As with all coloring EQ, it should be performed ahead of Crescendo, so that Crescendo will know what you intend and can make appropriate hearing corrections.
But unlike all coloring EQ, if you try to flatten your headphone response with corrective EQ, that correction belongs after Crescendo. Crescendo already thinks it is playing into a flat transducer.
For my HD650’s I can correct by using a parametric EQ after Crescendo with the following filters:
- bell filter at 20 Hz, boost 4 dB, Q = 0.4
- bell filter at 340 Hz, cut 2 dB, Q = 1
- bell filter at 2250 Hz, boost 2.5 dB, Q = 2
These EQ filters are all less severe than when I tried to follow the -1 dB/octave rolloff with the InnerFidelity.com data. At 1 kHz this produces zero gain. The headphones are essentially flat with this EQ from 20 Hz to 3 kHz.
Beyond that, it feels right to add a bell boost of 3.5 dB at 8 kHz with Q = 2. But that one is purely speculative, and probably only applies for my hearing.