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How to eliminate nulls in headphone designs

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As we know, headphones tend to incur frequency response nulls natural to our own ears. For example, below, you can see my in-ear, partially blocked canal entrance frequency response for the left driver of my Meze Elite, then the result from adding on the EQ from my personally measured HRTF as corresponds with a sound source of perfectly 90-degree incidence from the sagittal axis (the dotted phase response traces are inaccurate):

2023-11-15 - Meze Elite hybrid L unEQed.jpg

2023-11-15 - Meze Elite hybrid R 90 L.jpg


Here, it can be seen that the 6 kHz peak, 8.6 kHz null, and 14.1 kHz null are accentuated, suggesting that these features on the unEQed Meze Elite were consistent with my HRTF for sound sources of 90-degree incidence. I have measured these nulls as being similarly positioned on my other headphones. Angling the drivers by small amounts may only slightly alter the levels and positioning of these nulls.

For binaural head-tracking, the treble nulls would be constantly moving, whereby for true accuracy, you would have to first EQ up the headphones' default nulls (which is fortunately easy on my Meze Elite for which the nulls are fairly shallow and "round"). My ideal headphone for binaural head-tracking would be completely devoid of nulls in the treble, allowing the binaural renderer to apply your HRTF's nulls without other inaccurate nulls or inconsistent peaking filters present. Given this, what headphone design techniques are out there for eliminating these nulls? I'm thinking of damping, either increasing or decreasing reflections, else using differently angled drivers with calibrated phases.
 

Curvature

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Consider them artefacts. If you measure with a probe microphone very close to the eardrum, they no longer appear. At least if I understood papers correctly.

There is a compensation method developed by Etymotic for HF but it also requires probe measurements.
 
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Mr. Haelscheir
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Consider them artefacts. If you measure with a probe microphone very close to the eardrum, they no longer appear. At least if I understood papers correctly.

There is a compensation method developed by Etymotic for HF but it also requires probe measurements.
And what if that 6 kHz peak and at least the 8.6 kHz null were clearly audible when listening to sine sweeps with the in-ear microphones removed?

At least Figure 5.15 in https://www.researchgate.net/public...d_Modelling_Techniques_of_Ear_Canal_Acoustics showed smoothing of the nulls when measured at the "eardrum", but that was with an adjustable ear canal simulator much like a syringe.

Here is my smoothed (particularly impulse windowed from 1 kHz and up) canal entrance left-ear HRTF for a sound source panned 30 degrees to the left for comparison with the blocked and unblocked canal entrance measurements found in https://vbn.aau.dk/ws/portalfiles/portal/227875164/1995_M_ller_et_al_AES_Journal_c.pdf:

2023-11-02 - Meze Elite hybrid R 30 L EQ final.jpg


One thing that is for certain is that these nulls move in frequency depending on the direction of the sound source, though I haven't read up on whether those nulls are actually involved in sound localization, and I would suppose there was a reason to keep these nulls within the SOFA file.
 

Curvature

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And what if that 6 kHz peak and at least the 8.6 kHz null were clearly audible when listening to sine sweeps with the in-ear microphones removed?

At least Figure 5.15 in https://www.researchgate.net/public...d_Modelling_Techniques_of_Ear_Canal_Acoustics showed smoothing of the nulls when measured at the "eardrum", but that was with an adjustable ear canal simulator much like a syringe.

Here is my smoothed (particularly impulse windowed from 1 kHz and up) canal entrance left-ear HRTF for a sound source panned 30 degrees to the left for comparison with the blocked and unblocked canal entrance measurements found in https://vbn.aau.dk/ws/portalfiles/portal/227875164/1995_M_ller_et_al_AES_Journal_c.pdf:

View attachment 326447

One thing that is for certain is that these nulls move in frequency depending on the direction of the sound source, though I haven't read up on whether those nulls are actually involved in sound localization, and I would suppose there was a reason to keep these nulls within the SOFA file.
I would question how well you hear the peaks/nulls because the auditory filters/critical bands are broad in the kHz range. Frequency discrimination isn't very acute up there.

Oratory1990 measurements of the Meze Elite using the GRAS ear simulator/coupler and two different pads do not show HF nulls. So they have to be related to microphone vs. headphone driver position in your case.

The paper you posted says clearly that HRTFs show direction-dependent peaks/nulls (i.e., related to localization). It also is measuring sounds from various directions using speakers. With headphones on part of the HRTF is avoided. So do not read too much into your comparison given that the measurement conditions are different. Panning is not at all the same as a physically located source.
 
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Mr. Haelscheir
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I would question how well you hear the peaks/nulls because the auditory filters/critical bands are broad in the kHz range. Frequency discrimination isn't very acute up there.

Oratory1990 measurements of the Meze Elite using the GRAS ear simulator/coupler and two different pads do not show HF nulls. So they have to be related to microphone vs. headphone driver position in your case.

The paper you posted says clearly that HRTFs show direction-dependent peaks/nulls (i.e., related to localization). It also is measuring sounds from various directions using speakers. With headphones on part of the HRTF is avoided. So do not read too much into your comparison given that the measurement conditions are different. Panning is not at all the same as a physically located source.
Perhaps "null" is the wrong term here as opposed to "high-Q dip". I certainly don't want to be panned as a "null believer" or to be framed as measurably EQing down peaks that apparently aren't actually audible in sine sweeps nor pink noise, but I would still suggest you take a close listen to a slow logarithmic sine sweep through your own headphones, unless you have a pair that gives you a holy grail of smooth responses. Oh, and of course the sine sweep was showing me what frequency was being played ("Hearing Test HD" on YouTube for convenience); I'm not identifying the frequency "by heart" or through "perfect pitch". (For pink noise back when I would EQ by ear, I would first activate a peaking filter on Equalizer APO and play with the knob until I matched the frequency with the peak I was hearing through the pink noise, then EQ down accordingly. I am not an expert at choosing the perfect Q factor by ear mind immediately by eye, though.)

Have you not seen headphones.com's and Crinacle's GRAS 43AG measurements?

4850a0fe40059d310d46aca2b25b5091cf9ee97d.jpeg

Elite-Hybrid.jpg


Meze%20Elite%20(hybrid%20earpads).png

Is that not a null at 9.5 kHz (different ears, different frequency), or do we have a disagreement of terminology? Mind is there not a little 6 kHz or 6.5 kHz peak visible in each of these three graphs, consistent with my partially blocked canal entrance measurement (which mainly lacks the full canal gain, but probably introduces a 3 kHz dip from cancellations from the only partially blocked canal), or do we have yet another disagreement of terminology? Now, I do find it strange that the B&K 5128 measurements only have a 10.2 kHz null. Other than the lack of the canal resonance affecting the shape of the graph around 3 kHz, the features visible in my canal entrance measurements have generally correlated with what I hear through sine sweeps.

My personal HRTF was measured outdoors with a Genelec 8341A positioned 1.5 m away and in in-ear mics and a head-tracking IMU as provided by https://www.earfish.eu/:

20231013_171713.jpg


Though headphones bypass the body and most of the head, I would attribute the major stuff in the upper midrange and treble to the auricle. The point of the graphs in my OP was to demonstrate that the 90-degree left transfer function applied by SPARTA AmbiBIN in Reaper (as derived from measurements taken with the above setup) has nulls that line up with the same features seen in the unEQed graph, suggesting that headphones may indeed may be incurring some auricle-related features found in the 90-degree HRTF. Here is that transfer function in isolation (pre-processed with "diffuse-field EQ" to flatten the ear gain) as measured using my MOTU M2's loopback:

2023-11-16 - SPARTA Binauralizer NF R 90 L transfer function.jpg


But that depends on whether you believe those nulls also reach the eardrum.

https://www.head-fi.org/threads/mez...eadphone-official-thread.959445/post-17743506 (post #5,153) shows some other headphones of mine that exhibit these nulls (the ATH-M50xBT probably lacks the second null due to its partial compression of the pinna).

And by "pan", I meant using the SPARTA Binauraliser NF VST plugin which loads the corresponding HRTF (derived from the physically located source pictured above) for that relative virtual source angle. Here is the transfer function for a 30-degree "pan" left of center, with nulls clearly in different places corresponding with my raw in-ear measurements from a calibrated speaker as shown in post #3:

2023-11-16 - SPARTA Binauralizer NF R 30 L transfer function.jpg


As for headphone positioning, my measurements for various pad heights for the Meze Elite mainly showed changes in the depth of those nulls, the 8.9 kHz null (in that measurement session) progressing down toward 8.5 kHz between the highest and lowest positionings of the pads. If anything, there was nothing to suggest that the circular trace actually outputs more treble (or that its doing so has any significant influence on the in-ear frequency response within a properly sealed environment), though it can sound like it when moving the cups up and down while listening to pink noise, though that might be related to variations in seal while holding the cups.

Anyways, it seems like we are first debating whether there are any treble nulls to be gotten rid of in the first place when my measurements suggest that certain headphones do by default possess treble nulls corresponding with the localization cues for a perpendicularly positioned sound source (which headphones effectively are). If it is agreed/known that these nulls are objectively involved in localization, then I don't understand the objection to my in-ear microphones in fact being able to capture said audible nulls and for me indeed allowing convincing binaural head-tracking all around the virtual sphere.
 
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Curvature

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Perhaps "null" is the wrong term here as opposed to "high-Q dip". I certainly don't want to be panned as a "null believer" or to be framed as measurably EQing down peaks that apparently aren't actually audible in sine sweeps nor pink noise, but I would still suggest you take a close listen to a slow logarithmic sine sweep through your own headphones, unless you have a pair that gives you a holy grail of smooth responses. Oh, and of course the sine sweep was showing me what frequency was being played ("Hearing Test HD" on YouTube for convenience); I'm not identifying the frequency "by heart" or through "perfect pitch". (For pink noise back when I would EQ by ear, I would first activate a peaking filter on Equalizer APO and play with the knob until I matched the frequency with the peak I was hearing through the pink noise, then EQ down accordingly. I am not an expert at choosing the perfect Q factor by ear mind immediately by eye, though.)

Have you not seen headphones.com's and Crinacle's GRAS 43AG measurements?

4850a0fe40059d310d46aca2b25b5091cf9ee97d.jpeg

Elite-Hybrid.jpg


Meze%20Elite%20(hybrid%20earpads).png

Is that not a null at 9.5 kHz (different ears, different frequency), or do we have a disagreement of terminology? Mind is there not a little 6 kHz or 6.5 kHz peak visible in each of these three graphs, consistent with my partially blocked canal entrance measurement (which mainly lacks the full canal gain, but probably introduces a 3 kHz dip from cancellations from the only partially blocked canal), or do we have yet another disagreement of terminology? Now, I do find it strange that the B&K 5128 measurements only have a 10.2 kHz null. Other than the lack of the canal resonance affecting the shape of the graph around 3 kHz, the features visible in my canal entrance measurements have generally correlated with what I hear through sine sweeps.

My personal HRTF was measured outdoors with a Genelec 8341A positioned 1.5 m away and in in-ear mics and a head-tracking IMU as provided by https://www.earfish.eu/:

View attachment 326507

Though headphones bypass the body and most of the head, I would attribute the major stuff in the upper midrange and treble to the auricle. The point of the graphs in my OP was to demonstrate that the 90-degree left transfer function applied by SPARTA AmbiBIN in Reaper (as derived from measurements taken with the above setup) has nulls that line up with the same features seen in the unEQed graph, suggesting that headphones may indeed may be incurring some auricle-related features found in the 90-degree HRTF. Here is that transfer function in isolation (pre-processed with "diffuse-field EQ" to flatten the ear gain) as measured using my MOTU M2's loopback:

View attachment 326512

But that depends on whether you believe those nulls also reach the eardrum.

https://www.head-fi.org/threads/mez...eadphone-official-thread.959445/post-17743506 (post #5,153) shows some other headphones of mine that exhibit these nulls (the ATH-M50xBT probably lacks the second null due to its partial compression of the pinna).

And by "pan", I meant using the SPARTA Binauraliser NF VST plugin which loads the corresponding HRTF (derived from the physically located source pictured above) for that relative virtual source angle. Here is the transfer function for a 30-degree "pan" left of center, with nulls clearly in different places corresponding with my raw in-ear measurements from a calibrated speaker as shown in post #3:

View attachment 326517

As for headphone positioning, my measurements for various pad heights for the Meze Elite mainly showed changes in the depth of those nulls, the 8.9 kHz null (in that measurement session) progressing down toward 8.5 kHz between the highest and lowest positionings of the pads. If anything, there was nothing to suggest that the circular trace actually outputs more treble (or that its doing so has any significant influence on the in-ear frequency response within a properly sealed environment), though it can sound like it when moving the cups up and down while listening to pink noise, though that might be related to variations in seal while holding the cups.

Anyways, it seems like we are first debating whether there are any treble nulls to be gotten rid of in the first place when my measurements suggest that certain headphones do by default possess treble nulls corresponding with the localization cues for a perpendicularly positioned sound source (which headphones effectively are). If it is agreed/known that these nulls are objectively involved in localization, then I don't understand the objection to my in-ear microphones in fact being able to capture said audible nulls and for me indeed allowing convincing binaural head-tracking all around the virtual sphere.
I don't fully understand your goals

From your first post.
For binaural head-tracking, the treble nulls would be constantly moving, whereby for true accuracy, you would have to first EQ up the headphones' default nulls (which is fortunately easy on my Meze Elite for which the nulls are fairly shallow and "round"). My ideal headphone for binaural head-tracking would be completely devoid of nulls in the treble, allowing the binaural renderer to apply your HRTF's nulls without other inaccurate nulls or inconsistent peaking filters present. Given this, what headphone design techniques are out there for eliminating these nulls? I'm thinking of damping, either increasing or decreasing reflections, else using differently angled drivers with calibrated phases.
If the peaks/nulls are direction dependent and due to your ear shape, there is no problem and there is no cause to get rid of them. The "other inaccurate nulls" are the target, right? Looking at your in-ear results vs. coupler measurements, I don't see strong trends in the HF that, personally, having done in-ear measurements myself, I would EQ. Having said that, if, while listening, you find certain ranges objectionable, I would EQ to taste. That's more reliable for the HF.

By the way, all the measurements by Crinacle, oratory1990 and Amir on GRAS rigs show a dip around 10kHz, and above 10kHz measurements aren't considered reliable because of the impedance tolerances of the coupler.
1700144886251.png


The least resonant headphone I've seen in the HF is the DCA Stealth. So perhaps they have something going for them in the metamaterial absorbers they use that others don't, with their more standard techniques.
 
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Mr. Haelscheir
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I don't fully understand your goals

From your first post.

If the peaks/nulls are direction dependent and due to your ear shape, there is no problem and there is no cause to get rid of them. The "other inaccurate nulls" are the target, right? Looking at your in-ear results vs. coupler measurements, I don't see strong trends in the HF that, personally, having done in-ear measurements myself, I would EQ. Having said that, if, while listening, you find certain ranges objectionable, I would EQ to taste. That's more reliable for the HF.

By the way, all the measurements by Crinacle, oratory1990 and Amir on GRAS rigs show a dip around 10kHz, and above 10kHz measurements aren't considered reliable because of the impedance tolerances of the coupler.
View attachment 326612

The least resonant headphone I've seen in the HF is the DCA Stealth. So perhaps they have something going for them in the metamaterial absorbers they use that others don't, with their more standard techniques.
The "inaccurate" nulls I am referring to are those naturally induced by headphones which for my ears are partly consistent with those from a 90-degree free-field sound source. The "target" is to only have the nulls that are being applied by the binaural renderer and to not have any preexisting nulls interfere with them. That is, I am looking for how one would design a headphone that presents a perfect blank slate for dynamically EQing (binaural head-tracking) to the exact in-ear frequency response of perfectly neutral speakers in an anechoic chamber, and for that, only the nulls in the HRTF must appear. These nulls or peaks are not a matter of preference so much as matching one's headphones to the "exact truth" of said ideal studio monitors (approximated by subtracting the free-field microphone measurement from the in-ear measurement at around the same position and applying impulse windows where needed).
 

Curvature

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The "inaccurate" nulls I am referring to are those naturally induced by headphones which for my ears are partly consistent with those from a 90-degree free-field sound source. The "target" is to only have the nulls that are being applied by the binaural renderer and to not have any preexisting nulls interfere with them. That is, I am looking for how one would design a headphone that presents a perfect blank slate for dynamically EQing (binaural head-tracking) to the exact in-ear frequency response of perfectly neutral speakers in an anechoic chamber, and for that, only the nulls in the HRTF must appear. These nulls or peaks are not a matter of preference so much as matching one's headphones to the "exact truth" of said ideal studio monitors (approximated by subtracting the free-field microphone measurement from the in-ear measurement at around the same position and applying impulse windows where needed).
So it's really a general question about headphone design?

In that case, I couldn't tell you. The problem as I understand it is that headphone drivers are responsible for such a wide frequency range that HF commonly ends up showing breakup behaviour. Say you solve that, you still have seal problems for LF and standing waves for HF due to ear coupling, and other potential mechanical resonances in the housing. The drivers themselves—minus breakup, ear gain and standing waves—are more or less flat. There are no manufacturers to my knowledge who have solved the HF in headphones.

In speakers, you can reliably use a combo of tweeter, phase plug, waveguide and baffle shape to get very precise HF response. Not so in headphones, to my knowledge. No clear formula yet.
 
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