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DIY universal IEM: From ER4s to F111 and beyond

post #1 of 12
Thread Starter 

I. Intro


I have had the the Etymotic ER4s for the longest time. Back then, it was considered insane to spend $300+ on headphones. It was before IEM were considered "cool", as most people didn't know what it was. And up till today, they were "good enough" for me. Good enough that I spend my DIY efforts on other things: converting Dynaco ST70s to triode configuration; pondering the virtues of SRPP vs. mu-follower; understanding the principles of screen driven pentodes; making my own tractrix horn expansion profiles for a mid-range horn; figuring out whether such a horn could be mated with a di-pole bass ... I dabbled a bit in headphone stuff, such as comparing a 6AS7G cathode follower vs. LT1010 buffer stage as a headphone amplifier (both sucked), or using buck brigade chips for a cross-feed circuit (never got past the design stage). In the end, the Sennheiser DSP pro that came bundled with the HD580 kept me happy for much longer.


An then, things changed. 


No, I didn't hear something way better. I still consider the ER4s "good enough", but


A. I was recommending IEMs to a relative of mine, reading through reviews to predict how it would sound, and most all, trying to see if a particular design really would incorporate all the technological claims into sonic gains. While my brain filled with all this knowledge, equal part started questioning how much of that is for real? It was time to try some of these concepts out for myself.


B. I discovered that BA transducers are now readily available and cheap enough. With all that is in place, it would be a quick foray into this subject, between the "bigger" projects that I am perpetually planning.


So, I decided it was time to try things out and heat up my soldering iron! I quickly defined the scope of the project:


1. According to JH's interview on google talk recently, he discovered the limitation of high frequency extension of a BA transducer to be the rising impedance/inductance of the driver. All drivers suffer from this problem, including loudspeakers, and there are plenty of cross-over solutions to alleviate that. JH's solution in essence is to parallel drivers to lower the inductance relative to the bass drivers. Strength in numbers, that it. But is this better than a properly executed cross-over?


2. Separately, one of JH Audio's CIEM reviews quoted JH saying that the lower distortion figures by using multiple drivers is not just a bonus, but a necessity in achieving good sound. Really? Single BA transducers don't play loud enough? I am curious to find out.


3. One of Etymotics simplicity is the deep insertion, which reduces the ear canal volume, thus raising the resonant frequencies so that is less intrusive. The downside is the discomfort, which is a serious compromise. So, can one design an IEM with shallow insertion such that it becomes a lot more comfortable? The answer is yes of course. But can a DIY effort succeed?


4. The popularity of the Fitear F111 echos the longevity of the single driver solution, and the success of the ER4s in terms of the Knowles ED29689 driver chosen. The variation on the theme by Fitear is the Titanium horn used. I understand the rudimentary issue of impedance matching at the throat and mouth of the horn in loudspeaker drivers, but how much of that translates to BA transducers? Given the limitations of geometry and space, can one really design a properly matched horn? Most horns used in hearing aids are a good 2cm long (such as the Libby horn), yet Fitear's is around 4mm. What gives?


5. Acoustic dampers have become the de facto way of tuning the response of an IEM. This is a brilliant solution and easily tweakable parameter in order to push a given design into the target response. But is there a sonic penalty? Is there a difference when an acoustic filter is used in order to match the impedance when the bore opening changes (suppressing resonant peaks) vs. when it is purely used as an acoustic filter to reduce the output at certain frequencies? 


I also made up my mind as to what I wasn't going to fiddle with:


1. Custom molds: this will be an universal insert IEM, there is too much of a learning curve for me to worry about mold casting and re-working the design if things don't pan out.


2. Multi-frequency drivers cross-overs: I am not a bass head, and I always admired the simplicity of a single full frequency drivers, starting with Lowthers, to the next step of co-axial/coincident drivers such as Tannoys and KEFs. Lowthers in the end had too many problems in order to be full frequency to me, but for BA transducers, it should be good enough, as the ER4s proves.


So, this is what's to look forward to in the following chapters:


II. The design
III. Construction notes
IV. How does it measure up? (How do you measure in the first place, without breaking the bank?)
V. Cut to the chase, how does it sound?
VI. Epilogue.


Warning! The material covered may be considered intermediate/advanced. I would like to apologize in advance if I loose some people by not providing enough background information. Neither is this meant to be a step by step instructable. Rather, it is to convey concepts and principles for correct implementation, to document what I found out to be important for a sound DIY design.

Edited by Aurally - 5/27/14 at 9:35pm
post #2 of 12
Thread Starter 

Current thread status: completed.

Edited by Aurally - 5/27/14 at 9:35pm
post #3 of 12
Thread Starter 

Reserved 2.

post #4 of 12

Be great if you can post your reference sources as you go along so folks can read up as they follow.

post #5 of 12
Thread Starter 

The Design

First, the components:

The drivers: I considered all possible drivers from the start. Sonion struck out because they are too hard to obtain stateside. Knowles has an excellent line of drivers, and initially I pondered if an integrated dual driver such as the GQ series was the way to go. In the end, I decided against it, mainly because the ED29689 used in the ER4s was good enough for me. My only twist on the subject was that I was going to use two ED29689s per channel. That would represent a easier load to drive, I would get twice the radiating surface. I could also play twice as loud with the same distortion levels, or get half the distortion at the same level as one driver. But mainly, it would prove out if multiple drivers offers any benefits.

The shell: Since this is was going to be something quick, I wasn't going to go it from scratch. I quickly found this ear bud:




It was an obvious choice. The package emphasized metal housing, which make it more durable for all the assembly and disassembly needed. It has a large bore size, making it easier to experiment with. Finally, the body is quite as big as well, so I wouldn't have to constantly worry if I had the space to stuff any components in it. Later I found that the shell is available at Lunashops.com, so I assume it is available under many other oem/generic brands.

The ear sleeves: The original sleeves that came with the earbud had poor isolation. The only other tips that fit came from my MEelectronics A151, and still I had to stretch the sleeve a bit to fit over this oversized bore. The tri-flange in the bunch became my favorite due to its length. 


Other sundries: acoustic filters, check, various plastic tubing, check. Electronic parts, whatever I had in my stash.


Early failures/eliminations:


The multi-driver concept is nice, and I could easily put two drivers in series and fit it in the shell. Of course it played louder, but there wasn't anything obvious gain in quality. In this context, multiple drivers gains little. If distortion is a concern, then it would make more sense in the context of multi-frequency drivers, where the frequency range with highest distortion is moved to one driver (usually the bass), thus reducing the total excursion in the high frequency drivers, allowing them to operate in a more linear region. This is totally analogous to speaker design.

Cross-over compensation should work, such as using a Zobel network to compensate for a rising series inductance. But I gave up on it for several reasons:

- I was too lazy to figure out the exact circuit in question. Is the impedance rise shown in all ER4s impedance plots due to purely inductive loads, or is it due to other mechanical compliances? 
- I didn't have enough surface mount components in my stash. This is not really a space concern, but simply that the leads in through hole components are too thick. Mechanically, once you solder them on the Knowles driver, the solder pad is easily torn apart when the through hole components is accidentally mishandled. Because of this, I lost two of the four drivers. This is also a second reason why I gave up on the multi-drivers per channel.

Well, that doesn't leave much else to explore, is there. There is still the horn aspect.

On the subject of horns, I found some references:


http://www.hearingreview.com/2009/09/earmolds-practical-considerations-to-improve-performance-in-hearing-aids/ had some discussion of horn vs. acoustic dampers. Good introduction, but these horns are quite long.


http://rinchoi.blogspot.com/2013/06/suyama-fit-ear-f111.html Rin Choi's analysis of the F111 gives a formula of the gain and cut-off for a given horn.


http://www.etymotic.com/publications/erl-0001-1981.pdf Etymotic's library of publication has this details explanation of how to shape the response of the ear tubes, including the effect of a horn. Again, these are long horns where the hearing aid is placed outside the ear, allowing for a long tapered tube.


While these formulae are good for back of the envelope estimation, they fall a bit short in real environments. Luckily, I was able to access some commercial finite element simulation software. The simulation software can calculate the eigenfrequencies of any irregular shaped chamber, and can also predict the response from a given input source. Note that the purpose of this excercise is not the design an IEM on paper, rather it is used to understand the effect of simple components in an ideal environment. 


For starters, let's consider the acoustic "space" of the ER4s vs. my DIY IEM with the extra large bore. The ER4s here is modeled as a thin tube terminated by an acoustic damper, feeding into a small space in the ear canal. The bare DIY IEM is shown as the transducer feeding into a larger and longer tube, as shown in the figures. In addition, each of the figures shows the acoustic pressure distribution at the main resonant frequencies. 





Since the ER4s feeds into a much smaller space, the resonant peak is pushed out beyond 10kHz. The bare DIY iem on the other hand, has the first quarter wave resonance at around 7kHz, as illustrated in the corresponding response plot.


Now, let's add some horn shaped transition in this bare DIY iem. Even to my surprise, not much changed. The resonant peaks are shifted upwards (probably the horn reduced the overall volume of the chamber), and the peaks are somewhat lower in amplitude, as the response plot shows.


Upon further contemplation, this actually makes sense. In a free space environment, a perfect horn can indeed kill any reverse traveling wave as there is no impedance mismatch anymore. But in this case, the finite ear canal volume forces the horn to operate within a resonant system. The horn itself cannot absorb the reflecting wave, merely diffuse it a bit, so the horn may change the effective length of the chamber, and kill higher order peaks due to impedance mismatches, but it does little to the fundamental quarter wave. Those who have dabbled in QWTP (quarter wave tapered pipes) or Voigt pipes know what I am talking about, despite the fact that the pipe is tapered, it's still a quarter wave pipe. The only way to kill the resonance is to dampen it with acoustic wool, which is equivalent to using acoustic dampers.


My solution to this is to add an additional cavity between the horn and the BA transducer. I first came upon this in a series of articles published in Speaker builder by Bruce Edgar, who noticed that some drivers were impossible to match to the mouth of his tractrix horn without severe resonant peaking/suckout. His solution was to introduce an airgap between the throat of the horn and the driver. The article where this is discussed can be found here: http://volvotreter.de/downloads/Edgar-Midrange-Horn.pdf




In this finite chamber, however, such an airgap is more akin to adding another resonant chamber. With the right dimension, this resonant peak "bridges" the two original peak, thus providing a better damped, wider bandwidth resonance. Comparing the final response plot of this system, one can see a 10dB boost compared to the ER4s in the 5-15kHz range that is relative flat ( within 7dBs).


I'm sure I am not the first to come up with this. If someone can tell me what this is known by, please enlighten me.


Coming up, it's time to find out if I am onto something! But I got to make it first.

post #6 of 12

Thanks for such an in depth posting. I did recall this place had a few already empty shells up ( they mod and sell earbuds also )  with other parts available also. Specifically the Shure 535 empty shells looked interesting, but there are others.

 This is from the thread in the IEM /Portable section for Dasetn earbuds




Looking forward to more posts

post #7 of 12
Thread Starter 

III. Construction Notes




The metal shell is merely glued together, no hinges that need to be popped. However, two forceful pliers are needed to separate the glue. The trick is finding the suitable ones that don't leave any scratches behind. The dynamic driver in the shell is also glued tight, I had to use a press to pop it out. Those without a press, I suppose the right nail and a hammer would do the trick. I kept the original wires that came with it as well. 


Fitting the new BA drivers


There is plenty of space inside, the main problem is filling up the extra space. The easy prototyping material is poster tack (also known as Blue tack in the audiophile community) that holds posters to the wall. Standard window caulking rope should also do the trick. Just wrap a wad around like one would do with chewing gum and stuff it inside. The following pictures show the early dual driver in the shell surrounded by tack material.





I suppose people who want more permanence can use any kind of epoxy.


Horn construction


Luckily, for this application, the exact horn expansion profile is less important that the overall dimension. Again, plastic is easiest to work with for me, so a couple nylon screws did the job.


 With the right combination of drill bits and files, just remove anything that doesn't belong there. I cut the inside diameter the same size to accept acoustic dampers, so I could try them out easily. As one can see, I didn't even bother filing out the screw threads.


Two final tips:


These metal files I got from a surplus store helped a lot (don't remember from where).



Stay away from any motorized contraption, such as a Dremel tool. The high speed melts the plastic, which makes it harder to get things right. Patience is key. With some practice, I could make one in 20 minutes. Here is the horn inserted in the shell.



That's it. 

post #8 of 12

Saw you mentioned possibly using window caulking. I used a grey putty meant for that once and the off gassing corroded the copper wiring, just a heads up.

post #9 of 12
Thread Starter 

IV. Measurements


At first, I was going to audition and make changes on the fly. I quickly realized while I can pick up the differences, I couldn't tell with enough certainty what I needed to change. I needed a way to measure the frequency response at the very least. But without some fancy expensive calibrated setup, what was one to do? The only measurement setup I have on hand is the U-mik from http://minidsp.com/products/acoustic-measurement/umik-1, coupled with REW (Room Eq. Wizard, an open source project from the people at hometheatershack http://www.roomeqwizard.com/). The software is meant for room acoustic correction, but it has the integrated setup to perform a sinusoidal sweep, and generate all the relevant plot from that. So, I taped on a 1/2in poly tube so that the IEM is in a sealed chamber. Crude? Yes, that's the point.



Of course, the chamber volume is uncalibrated, even if the U-mik comes with a calibration curve. But, for DIY purposes, it doesn't matter:

- I can run the ER4s as the baseline. Since this IEM response is well published, I know how far off the response curve is.
- For incremental changes, I'd just be comparing the response curve difference from one to the next.


In general, any microphone with decent freq. extension (such as the panasonic capsules) will do. Software is plentiful, REW for instance is totally adequate. Ten years ago, things were hard. Today, there is no excuse for any serious DIYer not to obtain the frequency response. 


So, let's start off comparing the ER4s (violet line) with my DIY iem bare (purple line), without the horn or any damping. The response is normalized at the low frequencies. I didn't plot anything below 200Hz, because I am not sure how well the seal is. Thus, I do not trust the data.


Below 5kHz, there are 3 major dips, which are from the non-ideal measurement setup, as they show up on both cases. The bare setup has more gain at 2-5kHz, but dips down at 7-8kHz compared to the Er4s, before another resonant peak provides some extra gain. 


Next, let's look what happens when a horn (but no cavity) is inserted (green line). The 7-8kHz region fills up, but the top end drops down by a good 10dBs. Also, the 9kHz resonant peak has been tamed. As the simulation showed in previous chapters, there is not a big change to expect.


Next, the cavity is added. With the 6mm horn, the cavity is about 1.5-2mm long. The horn is then filed down to make more room for the cavity. Here are the response of varying horn lengths. Some additional gain results at 4mm (top line). 


Now, compare the 4mm horn (with cavity) to the no cavity case, and one can see almost A 5dB gain from 7-15kHz. 


To complete the circle, the following graphs shows the ER4s (violet line) vs. the horn and cavity configuration (red line). There is a 5dB gain from 2- 11 kHz. It's still lower above 11kHz, but one needs to keep in mind the ER4s has a series resistance which boosts the top end, so the real comparison should be the diy IEM vs. the ER4p. 


Finally, the following response shows the horn+cavity setup with various dampers (680Ohm-red line and 2kOhms-green line shown) inserted, with the ER4s response as a baseline. One can see irrespective of the damper inserted, the 2-7kHz now matches the ER4s, yet there is varying degrees of attenuation from 7-11kHz.



Most reader will probably think "big deal" by now. All I got was I made the IEM brighter than the ER4s, but failed to even get the same top extension. For that, we need to correlate the change the response to subjective listening tests.

Edited by Aurally - 5/14/14 at 9:31pm
post #10 of 12

Nice! That's great for the 1st try. You might wanna check the polarity on those drivers again, looks like there's some cancellation due to drivers being out of phase going on resulting in those sharp dips.


May I ask what modelling software is that? Doesn't look like MatLab to me.

post #11 of 12
Thread Starter 

V. How does it sound?


The tangibles


Having seen the frequency response, many reader should be able to infer the tangible outcomes. This IEM is about 5dB hotter than the ER4s between 2-11kHz. As such, the presence region is a lot more emphasized. One could say that the signature now is much closer to the ER4B, and perhaps even brighter than that. With the acoustic dampers added, the 2-5kHz is very close to the ER4s, and they sound almost identical. One can detect the amount of "air" or high end extension is missing. 


Initially, I thought such as boost in the presence region would be really unatural. Indeed, for many "modern" recording, those mixed with digital consumption in mind, this boost pushes things over the top. Beyond a certain volume, things just become uncomfortable. One could lower the volume, at the expense of a bit reduced body in the midrange. However, for other recordings, especially those recorded in a real acoustic space ( as opposed to artificially added reverb), it becomes a totally different experience (more on that in the intangibles). What I have come to realize is that there is a much wider window of variation accepted in the presence region, i.e. a boost or depression of the frequency range doesn't really result in the tone of the music being "brighter" or "darker", but change in perspective. When I listen to most headphones without diffuse field equalization, the first thing my brain tells me is that I have heard this sound before, and it is usually in situations when the sound source is facing me dead on, or the music is playing in a very "dead" room. Yet, on any diffuse field equalized headphone (especially this one), my brain immediately places the instruments either to the left or right side of my ears. Either case, I don't hear it as the musician playing a different instrument with a different tonal character, but I am facing the musician differently, either facing with my nose, or in the diffuse field equalized case, facing with my ear. 


To put things in a different perspective, I am reminded by a recent study on the study of concert halls, that the Vienna Musikverein, and the Boston Symphony hall, both being long and narrow like a shoe box, present the most desired listening space. The reason given was that the close side wall allow more sound to bounce directly into the ears, thus creating a brighter presentation of the music.




The concert goer will not think that the orchestra is suddenly playing with differnt instruments than the other orchestras, but rather automatically adjust the "expectation" of the correct response to the current hall.


OK, so I like the bright sound. But is it for you? Some may think one could easily try this by changing the acoustic dampers, and thus creating a similar "boost" in the response curve. Unfortunately, I don't think that will work, which bring me to the other point: in order for the brightness to be bearable, it can't be coming from a underdamped resonant peak that is present on most IEMs. In this case, the damper does double duty: one to kill the resonances of the system, the other to shape the response towards the desired target. However, the resonances must be dampened to some "level" in order to be unobjectionable. For many IEM, the resulting response is one that is below the target response, not above. Therefore, lowering the damper value always presents a compromise. In my DIY IEM case, if I didn't include the cavity, the sound becomes more objectionable immediately, one could easily detect a shrillness that is gone with the cavity. So while the overall boost in the 2-11kHz is not universally desired by everyone, it does dampen the undesirable resonances to a more palatables levels. In other words, when something is "too bright", one must distinguish between a rising response curve vs. a resonant "peaky" response. The former may be perfectly acceptable, the latter not. That is why measuring the freq. response in my mind is an essential part of tweaking any IEM design. The purpose is not to figure out how close the response is to the target response, but to make sure there are not nasty hidden resonant peaks.


Finally, about the use of acoustic dampers in general. I have come to the conclusion that they are best avoided. While very effective in terms of what they do, they also "harm" the music too much. If there is a way to rid them, just do it.


The intangibles


I call this section intangible, because I feel less confident that I have a solid argument to justify my claims. I tried to measure what I heard, but I just couldn't. Nothing I say here can be supported with measurements, at least I couldn't. I'm sure there are people who would object to this line of argument.


For instance, the response tells me that my top extension is worse than the ER4S, yet this first thing I noticed when I started playing music is the background hiss. Initially, I thought something was defective, but with the dampers inserted, the background hiss went away. Maybe I am hearing the response boost at 7-11kHz? While nobody wants to hear more noise, it did reveal more detail as well. One test disk I frequently use is Dire Straits' "Love over Gold" album. In the second track "Private Investigations", the music starts off quiet. When the first couple of piano notes come in, one can hear a sudden increase in noise level (tape hiss), and then diminishes when these notes stop. Clearly, the mixing engineer had a noisier paino track, and tried to minimize it by adjusting the fader for that track. On any good headphone, one can pick this up provided you are playing it loud enough. On this DIY IEM, it seems I can pick up this effect at much lower volumes. But this is not limited to high frequency tape hiss. Another example would be Robbie Robertson's self titled solo album. At the start of the first track "Fallen Angel", the music starts with a couple low frequency rumbles with a long delay reverb. Again, if one turns up the volume high enough, one can hear the decay of each note suddenly and very artificially cut off between each "rumble". On this IEM, this "defect" is much easier to pick out. Mind you, this is low frequency rumble. My conclusion is that this has something to do with the absence of the acoustic dampers. Somehow, the acoustic dampers seem to "truncate" the sound at the lower levels. Some people describe this as an added "veil", other as the inability to go down to total silence. In any case, the effect is that the subtle cues that give hint to the acoustic environment are erased. For any recording that is done in a real acoustic environment, this DIY IEM allows the music to sound much "livier", not in the sense of just being brighter, but being able to make out where the "walls" of this soundscape are located. Some people may describe as an increased soundstage, but to me, better soundstaging implies the ability to place each instrument better, or wider separation of the instruments, which is not the effect I am hearing. It is simply being able to hear the acoustics of the room in which it is being recorded. The music still come from inside my head or just outside the ear, but I can feel the musicians playing in a real room as opposed to just in my head.


Another related effect I think I picked up is an increase in dynamics, typically associated with better phase coherence. I often read of people wanting bigger and tighter bass, but sometime wonder if they mean they desire more "impact", i.e. the punchiness that comes from a time-aligned system. In this case, the effect is supplied by the extra energy in the high frequency harmonics, rather than just having more bass. The real life analogy that comes to mind is the sound of real thunder close up and far away. People may think that each thunder sounds diffrently, but it's mostly because of the distance the listener is from the lightning. Close up, one hears a very loud and very sharp sound with lots of impact. As this sound travels further, two things happen: the high frequencies get attenuated, and the lower frequencies travel slightly slower than the high frequencies (loss pf phase coherence). Therefore, far away, one usually hears some light cracking noise (high frequencies getting ahead), then followed by a very long and indistinct low frequency rumble, very different from the high impact punch close by.


The closest sound samples I could find to illustrates this effect are here ( by no means a good A-B comparison):


Close by:


Far away:



Relating this back to music, the difference is of course much more subtle than the thunder example above. Suppose the drummer kicks that kick drum, if phase coherence is maintained, one would mostly hear a high impact "kick" that is higher in pitch. Because of all the higher frequency energy, the bass will actually sound lighter, like thunder close by. By comparison, a multi driver IEM with poor phase coherence and suppressed in the presence region "de-couples" the harmonics, thus making the bass sound with more "body" than "slam", very much like the sound of thunder being heard far away.


Now, I must emphasize that did not measure any visible phase difference in the response plots, but I'm quite certain I hear some difference as I described above. And again, the effect is much stronger without acoustic dampers. If you think what I hear is completely psychological and made up, I hear you. Having gone through this myself, I wish more people had the opportunity to hear an IEM without dampers that is at the same time not overly resonant. After personally hearing that, maybe you'll agree with me (or maybe not).

post #12 of 12
Thread Starter 



For the few people left who have been reading this thread, let me summarize a couple of points:


  • When I first started the project, I was looking to do a variation on the ER4s. Even if it sounded the same, but was more comfortable, it would have been a gain. Comfort wise, this IEM still requires that one inserts the sleeve as deep as possible. However, unlike the ER4s, this sleeve does not have the center stem, the IEM terminates halfway into the ear sleeve. Because of that, ti conforms better to the ears, and is comfortable. The current paradigm of having a small tube, terminated into a acoustic damper in order to match the ear canal impedance may be convenient to implement, it is not an ideal design solution.
  • While doing my own spin on the subject, one obvious path was to add a "horn" section, inspired by the Fitear F111. However, what I found is that there is no book written on this subject, at least not a short horn inside a quarter wave tube. However, as separate  subjects, there is plenty of literature on horns and quarter wave pipes. Combined, they will paint a decent enough picture to figure out what is going on, even without finite element simulation.
  • Measurements are a necessity. If anything, I hope this thread will show that measurement hardware and software is accessible and should not break the bank. 
  • Coupled with measurement, a lot more opportunities open up for the DIYer. For instance, acoustic dampers are nice because they offer a fixed, consistent, and repeatable damping. However, by packing cotton, wool, or any other acoustic wool, I can "roll' my own damper, since I will be able to measure the resulting response, and use it to determine how dense I need to pack it. The next DIYer may not be able to replicate my exact damper, but he/she can certainly achieve the same response if measurement are done.
  • Acoustic damping in general is a necessary evil. Provided that the same response can be achieved through other means, I believe most likely that option will sound better.


This design doesn't break any new grounds, but at the same time, it's not a straight copy of any existing design. Even though I have never examined the F111 in person, which might be considered the closest in design, the response of this IEM does not resemble the F111 response at all. The spirit of this design is still closer to the Etymotic than the Fitear.


Maybe one of those days, I will tackle a multi-driver design. 

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