What (physically) causes the 7.5-8.5kHz peak in human hearing with IEMs and why it's important...

[Fraxo]

I'm sick of people saying "it's a resonance peak of the measurement rig" because it's not just that. I hear it clearly in every IEM with direct correlation to measurements and the peak's intensity. What varies of course is the exact position of the peak (7.5-9.5kHz range in 99% of cases excluding Etymotic).

Now, does that peak only occur in IEMs?
Does it only resonate in human ears while the driver itself might be measuring "peak-less" when measured outside the ear canal\simulator?

Read a lot about the human ear, pinna gain, but couldn't find any information about that peak, so I'd love some help with links or kind knowledge sharing. Thanks!

 

[half_dog]

This resonance comes from the interaction of hear canal and IEM structure(tips and protector screens). The exact value depends on the distance between eardrum and those structures, usually around 2cm. In this situation stationary waves are formed where their nodes are at the structure and the eardrum. The fundamental frequency f0 (harmonic) can be calculated by the formula Vs=(lambda/2)*frequency (for 36°C: Vs=348m/s, lambda = 0.04m). Hence we get freq~8700kHz. Because Etymotic has a deeper insertion, the f0 goes higher, so no 8.5kHz resonance.

 

[Fraxo]

This resonance comes from the interaction of hear canal and IEM structure(tips and protector screens). The exact value depends on the distance between eardrum and those structures, usually around 2cm. In this situation stationary waves are formed where their nodes are at the structure and the eardrum. The fundamental frequency f0 (harmonic) can be calculated by the formula Vs=(lambda/2)*frequency (for 36°C: Vs=348m/s, lambda = 0.04m). Hence we get freq~8700kHz. Because Etymotic has a deeper insertion, the f0 goes higher, so no 8.5kHz resonance.

@half_dog My man! That's such a fantastic answer... Thanks for sharing.

So to clarify further:

1. Is it true that no matter what you do (besides EQ or tuning down specifically) with shallow insertion IEMs - that peak will occur?
2. If you say this peak only occurs in IEMs due to their interaction with the ear canal, does it not mean that the peak is completely undesired? Since it doesn't exist in real world listening... Or perhaps I misunderstood something.
3. When some IEMs demonstrate much higher peaks that others - does it simply mean that their treble in general is higher around that region, or are there other factors in shape, angle or material choices that makes IEMs more prone to that peak?
4. Does the peak level also decreases with deeper insertion or simply shifts further?
5. Are there other frequency ranges enhancements\reductions that can be explained via human ear and IEM interaction other than the 7.5-9.5k peak and the pinna gain?

 

[half_dog]

You're welcome. Glad to help
About your questions, I won't have 100% of certainty over them but:

1. Although the peak "will" occur because of the environment it can be attenuated by EQ. It's similar to room nodes correction.

2. Not exactly undesired but needs to be addressed. And in real world there is others "peaks" of resonance as pina gain (which is "simulated" on some IEM - the hump at ~2 to 5kHz at Harman and DF)... The own ear canal has a natural resonance frequency but instead of a closed cylinder, we have an ear canal with only one side closed (by the eardrum). In this case the formula consider a 1/4 wavelength (for 2cm = lambda/4, we get 2175Hz - which might be sum for the simulated gain). It's like the designer needs add and subtract some frequencies to compensate how the IEM interacts with our ears.

3. Yes for both. It can either has a peak in this region caused by the driver tunning and its tips, filters, chamber shape can sum up for the peak. All these were supposed be considered during the IEM development, but...
Talking about materials shapes, a foam tip might attenuate the peak for example or a different shape like the spring tips, a inclined chamber adopted by Moondrop and other companies. All these has a considerable influence over the whole signature. The big problem about this is the design "expects" the user to be in a average group and hence the IEM might have the expected iteration with the user ear. Etymotic went further and tried to decrease this "dependency" with a deeper insertion.

4. It shifts to a higher frequency but as said before needs to be addressed. It's a physical phenomenon.

5. Yep, our body, as torso, head, mouth, organs etc can influence over how we perceive sound. That's so complicated when we open our mouths it is enough to change our ear canal impedance as an example. BTW I recommend some reading about HRTF, Harman target, Diffuse Field and Free Field.

Sorry my English

 

[Fraxo]

1. Although the peak "will" occur because of the environment it can be attenuated by EQ. It's similar to room nodes correction.

@half_dog I wonder how some high-end, shallow insertion models tone down that specific "8k" peak so well...
Do you reckon it's general tuning or specifically preventing the resonating factor in the ear canal by physical design?
I mean, is it even possible to prevent the resonance, or will it always have to be resolved by reducing the overall level of that frequency response to compensate for it?

 

[ADU]

You're welcome. Glad to help
About your questions, I won't have 100% of certainty over them but:

1. Although the peak "will" occur because of the environment it can be attenuated by EQ. It's similar to room nodes correction.

2. Not exactly undesired but needs to be addressed. And in real world there is others "peaks" of resonance as pina gain (which is "simulated" on some IEM - the hump at ~2 to 5kHz at Harman and DF)... The own ear canal has a natural resonance frequency but instead of a closed cylinder, we have an ear canal with only one side closed (by the eardrum). In this case the formula consider a 1/4 wavelength (for 2cm = lambda/4, we get 2175Hz - which might be sum for the simulated gain). It's like the designer needs add and subtract some frequencies to compensate how the IEM interacts with our ears.

3. Yes for both. It can either has a peak in this region caused by the driver tunning and its tips, filters, chamber shape can sum up for the peak. All these were supposed be considered during the IEM development, but...
Talking about materials shapes, a foam tip might attenuate the peak for example or a different shape like the spring tips, a inclined chamber adopted by Moondrop and other companies. All these has a considerable influence over the whole signature. The big problem about this is the design "expects" the user to be in a average group and hence the IEM might have the expected iteration with the user ear. Etymotic went further and tried to decrease this "dependency" with a deeper insertion.

4. It shifts to a higher frequency but as said before needs to be addressed. It's a physical phenomenon.

5. Yep, our body, as torso, head, mouth, organs etc can influence over how we perceive sound. That's so complicated when we open our mouths it is enough to change our ear canal impedance as an example. BTW I recommend some reading about HRTF, Harman target, Diffuse Field and Free Field.

Sorry my English

Just my 2c, but I think you're doin a great job of explaining this, half_dog! And I'm learnin alot.

 

[ADU]

@half_dog I wonder how some high-end, shallow insertion models tone down that specific "8k" peak so well...
Do you reckon it's general tuning or specifically preventing the resonating factor in the ear canal by physical design?
I mean, is it even possible to prevent the resonance, or will it always have to be resolved by reducing the overall level of that frequency response to compensate for it?

IEMs aren't my thing, so there's only so much I can offer on this topic. Most of half_dog's comments seem to be right on point though.

The ear canal is shaped essentially like a tube, or long funnel. So it follows more or less the acoustic and harmonic principles of a tube or cylinder as described here...

Acoustic resonance - Wikipedia

en.wikipedia.org

The precise resonant frequencies of a human ear canal are determined by its length. Which, in the case of an IEM, would also be effected by its insertion depth.

An unblocked ear canal of average length will resonate at harmonic frequencies of about 3k, 8-9k and 15k Hz, as shown below. And this resonant behavior is a major contributor to the peak or ear gain that occurs in the upper mids/lower treble when doing in-ear measurements of a headphone (or other sound source) at the ear drum reference point, or DRP...

The other major contributor to that ear gain region is the concha, which is the small bowl-shaped part of the pinna at the entrance to the ear canal...

The first, second and third harmonic resonances of the ear canal can sometimes be seen fairly distinctly in the raw in-ear measurements of better sounding headphones, made on measurement rigs that do a good job of simulating the acoustics of a typical human ear. Some recent examples of this made on the new HBK 5128 HATS rig...

You can even see the same three resonant peaks in the HBK 5128's measured response to a completely diffused external sound field (sans headphones), which is represented by the dashed purple curve on the Sennheiser HD-650 plot above.

So yes, these resonances are actually in the measurement rig! And are a perfectly normal part of its acoustic behavior, with certain kinds of sound sources... Even ones which are highly diffused. Go figure.

When you use an IEM though, most of this normal acoustic behavior of the ear goes out the door. Because there's no gain from the concha (or other areas of the pinna), and the normal harmonic resonances of the ear canal are changed, because the canal is blocked at both ends, and has been shortened in length by the IEM's insertion depth (as half_dog explained above). This means that you may lose some resonances that you want or need for normal sound reproduction inside the ear. And you may gain some others that are unwanted, which might unnaturally distort or color that normal sound.

It seems to me that an IEM manufacturer has basically two or three choices in this situation. If they want their earphones to have a neutral response that approximates a good pair of headphones or loudspeakers in a room, then they have to try tune their IEMs to match the measured response of those other sound sources at the ear drum, presumably by artificially boosting some frequencies and damping some others.

Another option is just to leave things as is, and give the user the flexibility to make those adjustments and tune the earphones how they want. Option number three would be some combination of the above.

 

[half_dog]

@ADU I really appreciate your (better and deeper) explanation. I was trying to answer Fraxo questions but I don't have enough knowledge for it. Thanks!

 

[SeshatCZ]

Thanks for sharing this Information. The IEMs are definitely an unique class of audio, with its special problems. It is very interesting to think about the Normal perception via an ear, and separately about the IEM-modified perception.

My question , maybe a bit of topic:

In Normal Perception, the resonances are circa odd multiples of 3 kHz (1× 3kHz, 3× 3kHz, and 5× 3kHz ). I don't know, if it is by chance, or it has some deeper physical meaning. However, what is a situation with these resonances with IEMs in ears?

Maybe it has been already answered, and I have not been able to comprehend it from previous posts, which are a bit too technical for me.

Thanks a lot for this discussion.

 

[ADU]

Thanks for sharing this Information. The IEMs are definitely an unique class of audio, with its special problems. It is very interesting to think about the Normal perception via an ear, and separately about the IEM-modified perception.

My question , maybe a bit of topic:

In Normal Perception, the resonances are circa odd multiples of 3 kHz (1× 3kHz, 3× 3kHz, and 5× 3kHz ). I don't know, if it is by chance, or it has some deeper physical meaning. However, what is a situation with these resonances with IEMs in ears?

Maybe it has been already answered, and I have not been able to comprehend it from previous posts, which are a bit too technical for me.

Thanks a lot for this discussion.

Sorry for the delay in responding to this, SeshatCZ.

The ear canal resonances are not really determined by chance. They are based on the length of the ear canal, and whether it is open or closed at one or both ends. And under normal listening conditions, I believe they would be roughly the equivalent of the first, third, and fifth harmonics, as you've described above. Here is the relevant passage from the Wikipedia article on tube acoustics that I think covers this...

------------------------------------------------------

"Closed at one end...

A closed tube will have approximate resonances of:

f = nv/4L

where "n" here is an odd number (1, 3, 5...). This type of tube produces only odd harmonics and has its fundamental frequency an octave lower than that of an open cylinder (that is, half the frequency). This equation comes from the boundary conditions for the pressure wave, which treats the closed end as pressure antinodes where the change in pressure Δp must have the maximal amplitude, or satisfy ∂(Δp)/∂x = 0 in the form of the Sturm–Liouville formulation. The intuition for this boundary condition ∂(Δp)/∂x = 0 at x = L is that the pressure of the closed end will follow that of the point next to it."

------------------------------------------------------

The resonances will, of course, vary somewhat by ear shape and canal length. And the final measured response at the ear drum will be a summary of the effects of the ear canal, the concha, other parts of the pinna, and also the size/shape of a person's head, neck and body, in the case of speakers in a room. In normal listening conditions, all of the above effect the sound before it reaches your ear drum. (And this is why you need a head, torso and ears to do accurate in-ear measurements of speakers in a room.)

I don't know what the precise resonances would be for an IEM. But there is also a section in the wiki article for cylinders blocked at both ends.

 

[SeshatCZ]

Thanks a lot ADU. It makes sense. Neverthless, I have thought, that IEM-manufactures know empirically some "sweet spots" frequencies to be able to compensate for changed conditions in ear canal with in-ears in. For me, the above frequencies in Normal conditions were unknown. Good to know it, to comprehend some design decisions for all audio products... It was a very informative Thread for me ...

 

[Chromatischism]

I don't know what the precise resonances would be for an IEM. But there is also a section in the wiki article for cylinders blocked at both ends.

There tends to be one at 7-8 kHz depending on insertion depth.

 

[ADU]

Thanks a lot ADU. It makes sense. Neverthless, I have thought, that IEM-manufactures know empirically some "sweet spots" frequencies to be able to compensate for changed conditions in ear canal with in-ears in. For me, the above frequencies in Normal conditions were unknown. Good to know it, to comprehend some design decisions for all audio products... It was a very informative Thread for me ...

Glad if any of it was helpful.

I should maybe also clarify that when I referred to an "unblocked" ear canal in a previous post, this meant open at one end, rather than both.

 

[Fraxo]

Glad if any of it was helpful.

I should maybe also clarify that when I referred to an "unblocked" ear canal in a previous post, this meant open at one end, rather than both.

@ADU @half_dog - It's been a while!

I've been searching extensively for the expected resonance peaks in an ear canal with an IEM inserted, which is closed at both ends. Can you help with relevant sources or the math behind it? After testing numerous IEMs, I consistently observe a sharp peak at 8kHz-10kHz, another at 12kHz-14kHz (deeper insertion - higher), and a broader elevation in the 2.5kHz-4.5kHz range.

Any insights you could provide would be greatly appreciated.

 

[ADU]

@ADU @half_dog - It's been a while!

I've been searching extensively for the expected resonance peaks in an ear canal with an IEM inserted, which is closed at both ends. Can you help with relevant sources or the math behind it? After testing numerous IEMs, I consistently observe a sharp peak at 8kHz-10kHz, another at 12kHz-14kHz (deeper insertion - higher), and a broader elevation in the 2.5kHz-4.5kHz range.

Any insights you could provide would be greatly appreciated.

Nuthin more really to add than what's been posted above. The first resonance should be in the 3k range. 2nd should be 3x that, or around 9k. 3rd should be 5x that, or around 15k, I believe. It depends to some extent on the measurement rig though. Some rigs have shorter simulated ear canals than others, which can effect the resonant frequencies.

The concha (bowl shape of ear before ear canal) can also produce notches in the same approximates ranges as the 2nd and 3rd canal resonances, potentially interfering with them. On the HBK 5128 rig, for example, it will often split the 2nd canal resonance into two (smaller?) resonances at about 8 and 10k.

 

[scolfaro]

Great thread