Headphone Measurement Procedures - Frequency Response

Measuring Frequency Response
I could write a book about what a headphone frequency response measurement means --- and over a bit of time I will right here :) --- but for the moment we’re going to talk mostly about how the measurement is made, with just a few basics thrown in to help us follow along.

Headphone acoustics are significantly different than room acoustics because you are using an acoustic coupler as opposed to propagating the sound through free-space --- technically called the “free field” in audio terminology, and defined as three-dimensional space where there are no reflecting surfaces. When measuring speakers, you measure the sound out in the free field with a reference microphone and assume if the sound measures flat, you’ll hear it as flat if you put your head where the microphone was --- which is true. But with headphones, there is no free field in which to measure the sound. Due to reflections and modal oscillations within the enclosed volume between the headphones and your ear, the sound at any particular point within that space may be different than the sound at another point. As a result, the only legitimate place to measure the sound from headphones is at the eardrum.

That’s a problem because if the sound is flat out in the free field and you stick your head in it, the sound is no longer flat by the time it hits your eardrum. This difference between flat sound in the free field, and the EQ of the sound you hear at the eardrum when you stick your head in the sound in the free field, is called the Head Related Transfer Function.

Figure 1 shows the independent of direction Head Related Transfer Function of the Head Acoustics HMSII.3 head acoustics simulator.

Multiple things come into play that effect the EQ of the sound reaching your eardrum:

  • Your chest and head volume provide some acoustic gain at mid-frequencies.
  • Between 2000Hz and 5000Hz the concha (the little cup in your outer ear around the entrance to your ear canal) acts as a focusing dish to get sound into your ear canals, and as a result provides some significant gain to the signal at these frequencies.
  • The length of the ear canal provides opportunity for modal artifacts; typically peaks at 3kHz, 9kHz, and 15kHz roughly, depending on the exact size and shape of the ear.
  • Flat sound in the free field is not flat by the time it gets to your eardrum.

The other problem is that the earphone coupler has internal dimensions that allow modal artifacts to appear. These are like the room modes you try to damp with acoustic treatments in your listening room, but occur at much higher frequencies due to the small size of the chamber. These artifacts will move around as the size and shape of the enclosed volume changes with the position of the headphones on the ear. Therefore it is important to carefully measure the headphones in a number of different positions to get a true idea of the acoustic energy being emitted from the drivers. This is called spatial averaging.

Headphones must be measured in multiple positions to more accurately reflect the acoustic energy in the system.

Now that we know these two facts (that there is a HRTF we have to compensate for, and the headphones need to be measured in multiple positions) we can get down to the process of how a headphones frequency response can be measured.

Positioning the Headphones
Rough positioning of the headphones is done by eye; the ears on the head have indexing marks around the edge of the rubber insert that allow me to visually see if the headphone is roughly centered on the ear. Then using a 30Hz square wave playing through the headphones, I monitor the signal from the head on the oscilloscope to more finely position the cans on the dummy head.

By observing the signal carefully, I can tell whether the headphones are sealing properly, and I can tell how the quality of the signal changes with position. Once satisfied that the headphones are optimally positioned, I move them slightly forward for the first of five measurements. The amount I move them forward (and later back, up down, and centered) is small, and somewhat dependent on the headphone. Some headphones have large earpieces and I might move the headphones five millimeters in each direction away from center. Some on-ear headphones are so sensitive to movement due to the difficulty of achieving a seal that I can move them only a millimeter or two before the seal breaks. Basically, I try to move the headphones within the range that average competent user would experience in the real world, and within a range that the headphone appears to be delivering good performance.

Gathering the Data
Once the headphone is in position, I close the chamber and push the button to start the frequency response sweep. A 500Hz test tone is played, and the system regulates the tone to be 90dB SPL the eardrum of the head. This sets the amplitude of the signal generator for the test. I use 90dB SPL because I take it to be a loud listening level that headphones should be able to comfortably achieve. The IEC spec calls out 94dB, but I feel this level puts undue stress on headphones and would result in measurements that do not reflect the sound heard by most users. Because the purpose of the database I’m building is to give users characteristic information about the sound of headphones during normal listening I think this is a legitimate level. During the Total Harmonic Distortion tests, however, I measure both at the 90dB level and the 100dB level. If one were to listen to music at 90dB average, peaks in the materials could easily achieve 100dB. Therefore, I think it is important to see what distortions are encountered at a level somewhat higher than the IEC specified 94dB.

Screenshot of the Audio Precision panel set-up during frequency response measurements.

Once the reference level is set, the generator is set to sweep from 10Hz to 22kHz in 511 logarithmically equal steps. The AP analyzer measures the amplitude at each step and plots it as the raw frequency response for that headphone position. It then beeps letting me know that I need to move the headphones to the next position. I repeat the process positioning the headphones a total of five times (forward, back, up, down, centered), and the system spits all the data out into a spreadsheet.

Once in the spreadsheet, the data for all five measurements for each channel (left and right) are added together and divided by five. This provides the spatial averaging needed to reduce modal artifacts, and get a truer idea of the amount of acoustic energy available to be coupled into the ear.

Once a spatially averaged data set is created for the raw frequency response, the HRTF curve is subtracted. This is the step that compensates for the differences in EQ between the sound in the free field and the sound heard at the eardrum. The exact nature of this EQ curve is quite complicated, as I mentioned above, and there are three HRTF curves that come with the head as it’s calibration curves.

Free Field – The HRTF when a sound is emitted from a source directly in front of the head in an anechoic environment.

Diffuse Field – The HRTF when sound is coming at the head from all directions simultaneously.

Independent of Direction – A rather recently developed HRTF to measure real world sounds in less abstract and highly conditional situations than the two cases above.

I would prefer to have an HRTF calibration curve for the special conditions of two speakers placed 30 degree off axis as that is what the headphones are trying to simulate, but no such calibration exists. After lengthy discussion with the applications engineers at Head Acoustics, the Independent of Direction HRTF was picked as the most applicable for my purposes. In the end, it doesn’t matter too much as none of them are perfect, and since all headphones have the same HRTF applied, measurements are legitimate for comparative purposes. It is important to remember though, that even if there were such a thing as the perfect headphone, its frequency response as measured would not be flat due to these complexities.

A finished set of frequency response curves.

In the final product frequency response graphs here at InnerFidelity, you see the ten raw frequency response measurements (five left and five right)at the bottom of the chart. The spatially averaged and HRTF compensated frequency response for the headphones is at the top of the chart.

How close is this to the truth? Well ... it was the truth on that day, with that head, with those ears, in those positions. Will it sound like that to you? No ... but pretty close ... as close as it gets when it comes to objective measurements anyway --- this is pretty good gear. Here's the important thing: a lot of variables are accounted for, and the measurements I take today and next year will be useful and valid comparisons. The database will get pretty big over time. In producing a database of headphone measurements, InnerFidelity will bring you a whole big chunk of truth. That tickles me pink.

Will it be everything you need to know? No, it may help guide you quite a bit, but you'll still have to wrap the cans around your head to know what they sound like to you.

Ain't that nice.

Happy listening!

LFF's picture

Once again, an awesome post Tyll!

It was great to finally see exactly how you get those measurements. I also think it's very interesting how only the Head Acoustic heads use the IOD EQ while all the other brands lack this new, and for many people, better EQ. HRTF's fascinate me as they change with age, gender, size of the head, shoulders and ears. So many variables!

On another note, it's nice to see my beloved HF-1's in good hands. I hope you enjoy them and I can't tell you how happy it makes me to know that you own them. :-)

maverickronin's picture

So that's the HRTF you're using.

Do you have any more information on it, or is it proprietary and something that can't be shared?

Tyll Hertsens's picture
... there's a brochure here: http://www.head-acoustics.de/downloads/eng/application_notes/Equalization_brochure.pdf

And a paper here: http://www.head-acoustics.de/downloads/publications/binaural_technology/SFA92_Standardization_of_binaural_measurement_technique.pdf

maverickronin's picture

Thank you!

dalethorn's picture

I know you probably mentioned this, but what's the significance of the big dips around 10 khz, and do we really hear (not hear) a big suckout of the sound that's on our recordings in that frequency range?

johnjen's picture

Cool beans. It's always neat to catch how those subtle aspects made during setup effect the resultant consequences that impact the measurements themselves.

The devil's in the details, so to speak.

I also like those stray factoids of note, such as 2Ω output impedance of the BUDA…

And speaking of the BUDA I may have stumbled upon another significant operating improvement modality. Just say'n

ps where are those nifty smilies we have come to depend upon? ;-)

gregaria's picture

I think your article is truly riveting. Thanks!

branm's picture

Came across this page randomly, and I'm wondering if you can point me in the right direction. I don't have a lot of experience or expertise in headphones, but I'm working on a noise cancellation project for school and need a setup.

I do have access to an anaerobic chamber and an AP at work, but no head model. Someone told me they did a similar project with a flat piece of MDF wood and PVC. Obviously, not realistic. Comments? Have you come across this at all? Where b/c I can't seem to find any articles or appl. sheets describing this setup? Anything else you can suggest as an alternative?

Tyll Hertsens's picture
Don't know exactly what you're trying to accomplish, so don't have too much to say. No need for a head unless you are needing to model how flat the sound is. MDF would br fine if you are just going to see the relative differences of the thing on and off. Good luck.
200's picture

How would an ideal headphone measure with your system?

From what I can tell, it definitely ain't a straight line.

Tyll Hertsens's picture
Take a look at the LCD-3 graphs from the measurement download page, then smooth out any wigles in the highs. That's about as close as you'll get.
200's picture

Thanks, I'll take a look when they go up.

Unless you meant the LCD-2?

13mh13's picture

Finally got 'round to this article. V. well done, T. Keep 'em comin'. Gracias!

7Hz's picture

I don`t get why there is a compensation applied to resulting freq. Ideally headphone should be invisible (flat) and the music should be mixed appropriate.

Tyll Hertsens's picture
It's because my measurement system measures at the eardrum. By the time flat sound in free-space reaches the ear drum, it is colored by the shape and structures of the ears, head, and torso. So these colorations need to be removed to determine what the sound would be like in free space.
7Hz's picture

I am not the scientist at all :) just giving my thought. I have a thought that it shouldn`t matter what kind of a field it is, acoustic energy from transducer should be emitted equally in all frequencies which is ideally flat. I think HRTFs vary a lot and resonances or deadspots also vary. These variables is not possible to treat adequately equal and therefore I think the compensations is useless in a way compared to possibility to have ideally flat response. The dead spots or resonances impact would be dependant of physical architecture of the ear cups and other important construction of the headphone and not depending on frequency response compensations. These are just few thoughts of mine on the compensation curves and where they come from, how correct they are.

tcarson's picture

I can measure the 30deg HRTF for a HMS III if you like.

Can you explain why you believe it is better to show the free space FRF vs the colored FRF? When you play back a recording through the HEAD PEQV it removes the EQ and plays back at the LIN (colored) setting.


ultrabike's picture

I just got around to read this. Very nice article. Learned something. My understanding is that the brain adjusts (calibrates itself) to sound changes due to our own physical changes and characteristics. These changes maybe relatively fast because positional changes of the HP relative to the head seem to have significant impact on the sound characteristics, but I can't really say I hear that much difference when I put my HP a millimeter off optimal location. Only explanation I have is that my brain adapted quickly to these changes.

That is not to say that I can't tell differences at all. I mean if I put my hands on my DT990 or KSC75 sound WILL change (mostly for the worse)...

I can only imagine how speakers (reference grade, and Walmart cheapo dealo) will measure in a typical room (not an-echoic) at the ear cannal, and compare that to say a $12-$19 KSC75 :) Brain may have to do one hell of an adjustment there :)

I once told a co-worker of mine how much cleaner the dialog of a movie was though my lowly HD202s vs my mirage nanosats. He told me his entry level AKGs pretty much destroyed his Polk powered reference towers... No visceral sub-sonic stuff, and sound-stage is not the same, but HP do clarity, detail, articulation, speed, etc... so much better IMHO, and you don't have to wake up the neighbors...

sszorin's picture

Not entirely clear. What audio signal or signals do you use to measure the cumulative frequency response of a given headphones to make a resulting graph ? Are they sine waves / tones at progressing frequencies, one at a time or is it an audio recording of a music ?

Tyll Hertsens's picture
It's a swept sine wave from 10Hz to 22kHz in 512 log steps.
donunus's picture

Tyll, did you figure out the raw curve that you wanted (calibrated speakers in a 30 degree listening angle in a good room)? Do you have a link of what that curve might look like measured near the eardrums? That may be the curve Paul S. Barton is using for his headphone designs.

Tyll Hertsens's picture

Both Paul Barton and Sean Olive at Harman are working on it, and are far more qualified than I to come up with a curve. I'll just wait patiently for their results and then incorporate it when it seems solid.

donunus's picture

I think that will be a very cool curve for our cans to mimic. It would really be great if they showed the final raw curve in the eardrums coming from calibrated planar speakers vs calibrated dynamics for example since those have different dispersion characteristics and will surely sound very different in the ears if their flat calibrated measurements made at 1 meter during calibration were measured at 2 to 3 meters during final measurement in the eardrums.

It would also be nice if there were nearfield measurements (from around 1 meter) to a more typical home environment sweet spot of around 3 meters from the speakers at their typical listening equilateral triangles.

I can't wait to see these posted in the future and am very excited with what new headphone designs will sound like because of this information. I can only imagine the new monitor cans to be following the nearfield curve while audiophile designs using the slightly farther more laidback measurements.

Tyll Hertsens's picture

It seems to me that folks like PSB and Harman have their own thoughts on what a reference speaker system performance looks like, and it's from that understanding of what the ideal speaker system delivers that the resulting headphone curve derives. 

In the end we certainly may end up with a handful of compensation curves that comes from different people's idea of what ideal means on speakers.  It's going to be an interesting next ten years as these curves get developed and compete with each other. In the end it would be nice to have just one standard, but not sure if that's really going to happen.

donunus's picture

Let's at least hope that the new curves will spawn some fantastic sounding cans.

Tyll Hertsens's picture

...yes there is.  :)

tarsonis's picture

So Tyll. I don't get the explaintion and the point out for the LCD3 as the most ideal response on a headphone. In a studio environment we try to get a really flat response with room threatment. But actually the flat esponse in a ideal studio enviroment would look like the HRTF curve when the signal reaches our eardrum. I couldn't find a explaination why headphones have then a downfall slope above 1KHz. Every can that is called as a flat headphone in the communtiy have this downward slope. I don't see the logic why headphones shouldn't actually measure flat on the axis after such a HRTF curve is applied when its a goal in room? I was reading about the Welti curve and haram research but it didn't answer my question. Is it because the hp driver is so close to the ear? Would be great if you could clear this up or give out a hint where I could read about this.

tm's picture

This might be due to using a less than ideal anti-HRTF curve to compensate for the Head Acoustics dummy head with headphones on it. Tyll's desire for a custom curve to compensate for headphones is right on the money. But, even if you had a proper HRTF curve, the ear canal resonances would probably change with different headphones. AND, even if they didn't vary with different headphones, your resonances won't match those of the dummy head, so even if a particular headphone looked flat on Tyll's measurements, it probably would't be flat for you.

This is the reason I'm a big fan of EQing my headphones flat. There are several ways to do this, but it's subjective and requires some effort to learn how to do it. Personally, I use a combination of a keyboard synthesizer generating a sine wave and frequency sweeps to check the final result. Use a stereo parametric EQ and adjust it to sound even across the sweep. The synthesizer allows you to quickly locate dips or peaks and compare them to other areas of the spectrum.

The other possibility is that the designers of the LCD3 built a bit of a House Curve into its response so that it is "perceived" as flat. For a good explanation of this go to http://www.hometheatershack.com/forums/rew-forum/96-house-curve-what-why.... Like Bigfoot and UFOs, the whole House Curve subject is a bit controversial.

bang.hs's picture

Great work Tyll, I appreciate all your efforts for the audio community. I second this method of compensating the frequency response. Its much easier than getting your own personal HRTF which of course very few would be able to afford.
The omni HRTF graph that you've provided shows the response relative to 90 dB at 1 KHz.. many people with amps do listen at a higher level though.. what about 100 or 110 dB? Quite some phones can do a 120 clean at full rated power.. in this case.. the HRTF would change, right?
Is there any way you could provide the HRTFs for these levels? I'm sure almost everyone would be interested to see this!