Headphone Measurements Explained - Frequency Response Part One
Understanding the Problem
Headphone frequency response measurements are not only difficult to make, but also quite difficult to interpret. Headphones can't be measured with normal measurement microphones, they have to be measured like they are usedcoupled to a microphone that mimics the acoustic characteristics of the ear. Essentially, when we measure a headphone, we are taking a measurement of what the ear drum hears.
The problem is, by the time outside sound gets to your ear drum it's not flat any more. Our brain is used to hearing sound with this non-flat ear drum response. When we measure headphones we have to know very precisely what that non-flat ear drum response is so that it can be subtracted from headphone measurements to return them to a flat line for evaluation. In order to understand headphone measurements, you have to understand the various factors considered to develop this headphone target response compensation curve. You'll also have to understand that an industry-wide standardized curve currently doesn't exist (though one is in development), so there is no clear answer regarding "what flat is" with headphones. With this article I hope to provide you with a few helpful concepts and hints, but plenty of questions will remain at the end.
This article will be in two parts. This first part, will explore the target response curve and how to recognize it. The second article will look at specific types of artifacts seen in headphone frequency response measurements, and what they mean.
What our ear drum hears in front of a speaker.
At the top of the diagram above, we see a measurement microphone in front of a speaker. Let's assume it's a perfectly flat speaker being measured in an anechoic chamber (a room with no acoustic reflections). The microphone will have a very small interaction with the acoustic energy, but for the most part it is designed to measure very accurately the sound field present without disturbing it. In this case, if the speaker is "flat" (acoustically neutral), the output from the mic will also be flat.
Now, let's remove the mic and put a person in front of the same speaker and look at the signal at that person's ear drum. It will no longer be flat because of a number of acoustic interactions between various parts of the body with the incoming acoustic signal. The graph below shows the various acoustic gain contributors to the frequency shaping heard by a person positioned in front of a speaker.
The dotted black line (1) shows the boundary gain from your head. Assume for a moment your head is roughly a one foot sphere. At very low frequencies, with half wavelengths much longer than the dimension of your head, there will be little interaction between the acoustic wave and your head. But as you raise the frequency of the sound to the point where its half-wavelength is of similar dimension as the head, you begin impede the sound and create some gain at the boundary. In the case of a 12" head and the speed of sound at 1126 feet/sec, sound will start getting some gain at around 563Hz. As you can see, the plot of spherical head gain is at 0dB below 300Hz, and then slowly transitions to about +3dB at around 1200Hz. (To the best of my understanding, boundary gain at the side of the head should only be able to deliver 3dB of increase, while the chart shows around 6dB at 10kHz. Sorry, I can't explain why this is so.)
Likewise, your torso (shoulders, chest, belly) will provide some boundary gain. Your body is bigger than your head, so its effect will begin at lower frequencies. But because your ears are not directly attached to your body and are separated at a distance, as soon as the half-wavelength becomes equal to that distance you will begin to lose coupling and the effect will diminish. You can see that dashed line (2) in the chart above indicating the torso providing some gain at lower frequencies to about 1kHz. Between 1kHz and 2kHz this torso curve actually goes negative due to destructive interference between the direct sound at the ear and the sound being reflected off the torso. Above 2kHz there is no torso interaction capable of significantly shaping the sound heard.
Colored lines in the graph above represent acoustic gain contributions from various parts of the ear itself. The blue line represents the focusing effect of the concha bowl into the ear canal of sound in the mid-treble region (with a peak at about 5kHz). The green line represents contributions from the pinna flange, which are somewhat lower in frequency due to being farther from the ear canal opening than the concha, and lower in level due to the milder cup shape of this area of the ear. The ear canal and ear drum resonance is represented by the red line (5), and shows its first resonant peak at about 3kHz (1/4 wavelength of ~1" long ear canal). If you were to extend this line further you would also see resonances at about 9kHz (3/4 wavelength resonance) and 15kHz (5/4 wavelength resonance).
Finally, we can sum all these gain contributions together to get a full picture of the differences between what a measurement mic hears in free space and what your ear drum hears when you place your body in front of a speaker. The solid black line labeled "Ear Resonance" shows the sum total acoustic response present at the ear drum. Another way to think about it is the acoustic transfer function of the ear, head, and torso. Because our brain is used to hearing with this response, it sounds flat to us. When we measure headphones at the ear drum, we are not looking for a flat response, rather, we are looking for a response similar to the curve in the graph above. We'll call the curve we're looking for the Headphone Target Response Curve (HTRC).
Unfortunately, there are some significant problems figuring out the exact HTRC to use.
Most obvious is that fact that all these specific response curves are generated by a specific geometry in the shape and size of a person and their specific ear shape. The particular graph used above is probably an average of many people, but the fact remains that your specific body, head, and ear shape will likely produce a different response curve at the ear. The Head Acoustics head I use for headphone measurements has an ear specified by international standards (IEC 60318-7:2011) to be exactly average for all humans, but it too will differ from your ear response.
So, this is the first thing to know about headphone measurements: They were not made with ears the same size as yours, so the sound you hear may objectively be somewhat different than the measured values. There really isn't much that can be done about this. For the sake of accuracy and relative consistency some one human looking ear needs to be used for all measurements, it seems to me the use of a standardized average ear is a good option. I wouldn't say the magnitude of this problem is hugeafter all we're all listening through human ears that do have significant commonalitiesbut I do think the differences could be enough for the same headphone to sound audibly different (mostly in the treble area above 2kHz) on two different people.
Sound Source Direction and Acoustic Environment
This is where things get very complicated (as if it hasn't been complicated enough already). In the above "Acoustic Gain Components" graph we've been using so far, you'll notice at the top left that this graph is for sound coming from a 45 degree angle. I'm pretty sure this graph was also done with a flat speaker in an anechoic chamber. If you change the angle of the speaker relative to the head, the geometry of the torso, head, and ear changes relative to the acoustic wavefront, which will in turn change the acoustic resonances and the associated peaks in response.
Also, if you take a speaker that measures flat in an anechoic chamber and put it in a normal size room with typical acoustic characteristics, it will sound (and measure) somewhat warmer as the room's volume reinforces bass notes (usually below 200Hz), and the speakers radiated power into the room decreases as they get more directional at high frequencies (results in aproximately 3dB tilt between 200Hz and 20kHz).
To summarize: the target response curve at the ear drum will change significantly as you change assumptions about the direction of the sound source and the acoustics of the room you're in.
Historical Target Response Curves
The world of audio engineering has historically had only two standardized ear drum response curves: Free-Field (FF), and Diffuse-Field (DF). The FF curve was the population averaged measured response at the ear drum for sound coming from directly in front of the listener in an anechoic chamber. The DF curve is the population averaged measured response at the ear drum for sound coming from all directions simultaneously in a very reverberant (hard-walled) environment.
The graphs above are simplified versions of the compensation curves for the Head Acoustics HMSII measurement head I use. You can see these curves are similar, but upside down, relative to the ear drum response curve we've been looking at. That's because these are compensating curves intending to reverse out the ear drum response and bring it back to flat. (The Independant of Direction curve is one invented by the company and is not an internationally adopted standard. It is essentially a DF curve with some of the head and torso effects taken out of the calculation. It is the compensating curve I use for InnerFidelity graphs.)
Historically, the DF curve had been generally adopted as superior to the FF curve as a target response curve for headphones. But over time, and largely due to discrepancies between the objectively derived DF curve and other subjectively developed target response curves, headphone makers have been moving away from the DF curve as their target response for headphones.
What makes sense as a target response curve?
I've been trying to make good headphone measurements for about twenty years now. I've given this subject a lot of thought, and the answer has always seemed simple and obvious to me: If music is mixed and produced to be played back on speakers, and if good headphones are suppose to sound the same as good speakers with recorded music, then the target response curve should be the ear drum response of a human head and torso in front of two ideal speakers in an ideal acoustically treated room of about living room size. In simpler terms, I've always thought that good headphones should sound like good speakers. It just makes sense.
The approach then would be to put a measurement mic in front of two very good speakers in a very good room and take a baseline measurement. Then place a measurement head in the same position and take the ear drum measurement. Then subtract the baseline room measurement from the ear drum measurement and you've got a new target response. Unfortunately, that is a lot easier to say than to do. To make that measurement very well there are a number subtle nuances to the measurement (like spatially averaging the response over a range of listening angles) and very expensive equipment and well trained operators are needed. This is an expensive undertaking to do well, so there had better be a darn good reason to go to the effort. My internal hunch is probably not a good enough reason. Fortunately, I'm not the only person to have this hunch.
Harman Target Response Curve in Development
I won't go into too much detail in this article as I've written extensively about it here, here, and here, but researchers at Harman International lead by Dr. Sean Olive have been working diligently for the last couple of years on defining a new headphone target response curve. Their very thorough research has lead them to the basic conclusion that headphones should sound like good speakers in a good room.
The graph above shows the ear drum response as measured on a dummy head at the normal listening position between a pair of speakers. The green dashed line shows the ear drum response for a speaker that has been equalized flat at the listening position. The black line shows the adjustment away from flat while wearing headphones that most people chose as more pleasing.
There are a couple of nuances to understand here. First, most speakers are designed to measure flat in an anechoic chamber. When a speaker is put into a room it gets a bass boost from the proximity of the wallsthis boost typically happens at about 200Hz and below. It also naturally gains a warm tilt due to the ever reducing sound power being put into the room as the frequency gets higher and the speakers directivity becomes more narrow.
The important thing to take away from this is that the goal is not actually for flat sound in the room. The goal is actually for the slightly warmer sound of speakers designed to be flat in an anechoic chamber and how they interact with the room. One of the underlying suppositions here is that we humans know what a room does to sound, and we acceptin fact, expectthat the sound from a good speaker will change in the room.
Another interesting subtlety in the research was that while the ear drum target response curves for speakers and headphones were quite similar, people actually preferred slightly bass and treble on headphones than they do on speakers (about 2dB on either end).
Headphone Frequency Response Measurements
And now, finally, we can talk about what to look for in a headphone frequency response measurement. All of InnerFidelity's headphone measurements can be downloaded as .pdf files for viewing. You can download them one at a time from the list on this page, or you can download them all in a single AllGraphs.pdf document. (CAUTION! AllGraphs.pdf is over 50MB and growing, so it will take a while to download.)
The top left graph on each of the measurement pages is the frequency response plot. You'll see two sets of response plots on this graph. The bottom set is the raw measured ear drum response of the headphone. I make this measurement five times and slightly move the headphones each time. All ten (five left and five right) are shown. The reason for doing this is that the measurement will change as various resonances change as the position of the ear within the headphone moves to different positions. By taking five measurements I can average them all together and remove some of these changing resonance artifacts. This is called spacial filtering.
The top plot is the averaged raw responses compensated by the Independent of Direction compensating curve that came with my measurement head. Over time I've come to look much more at the raw, uncompensated curves than the compensated plot, primarily because I know the ID (or DF or FF) compensation curves are not quite correct.
When I look at the frequency response plots above with an eye towards understanding its tonal balance, I am primarily looking at the raw response plots and mentally comparing them to what I understand of the Harman Target Response. The NAD VISO HP50 above is quite close, as is the Focal Spirit Profesional.
In the image above, I've crudely superimposed the raw FR plots of the NAD VISO HP50 (top gray lines) and Focal Spirit Professional (bottom gray lines) on the chart showing the preliminary Harman target response curve (black line). These two headphones are among the most neutral I've heard, and they do match the Harman target response quite well relative to other headphones I've measured.
One thing you'll notice with both these headphones is that the rise into the bass starts at about 400Hz, while the rise into the bass on the Harman response starts at about 200Hz. This causes the bass to mids transition to be a little too thick or overly warm sounding, and is quite common with many headphones.
Someday, I will convert my compensation curve to something like the Harman target response, until the you'll just have to use your imagination and keep the preliminary Harman curve in mind as you look at the raw plots. I've created this image to give you some numbers to remember as you evaluate the raw frequency response plots.
I'll also point you to this article where I select a number of well known headphones and apply an estimation of the Harman response curve. Personally I think it may have a tad too much bass, the peak at 3kHz may be a few dB too high and may need to slide up to 3.5kHz, and the area above 10kHz may be too rolled off.
We'll get into some of the specific characteristics to look out for in headphone measurements in part 2 of this article, but it's important to note early on that high frequency measurements are dominated by the wild swings of the resonant behavior of headphones. When you look at the profile of the frequency response curve at the high frequencies, you need to mentally average out all the peaks and dips to an average level to get a good feel for what's really there.
A Side Note About Other Headphone Measurement Systems
In the current article, I've been quite insistent on the importance of industry wide headphone measurement standards and instrumentation. It is of crucial importance that standards become adopted as it allows industry participants to operate on an apples-to-apples basis, and it allows for more efficient further progress in areas of research. The problem with this gear is that it's exquisitely expensive. Last time I checked, artificial heads like mine were around $25k by the time you got all the options properly sorted; and the simpler couplers were in the $7k region. Accuracy is expensive.
However, if you've read the above article carefully, you'll see that even with extraordinarily expensive equipment, accuracy is hard to come by. For many hobbyists who simply want to keep objective track of headphone modifications or want to do some basic headphone comparisons, home made headphone measurement systems are possible. A couple are mentioned in this article. I think this is an absolutely terrific hobbyist activity. (I didn't have a lot of time to research it, so I would love it if any InnerFidelity readers who have made their own measurement systems and written about them post links to your gear in the comments. Thanks!)
But it's important to recognize a few things about those measurements vs. the measurements from industry standard compliant instrumentation. Some hobbyist systems are designed to approach industry standard compliance, but many are not and aren't attempting to. Measurements taken on these various systems of a particular headphone model may be substantially different and should be considered apples-to-oranges comparisons. The only time you can even begin to compare headphone measurements from different systems is when industry standard compliance couplers are used. Even then, different operators will place the headphones on the couplers a little differently yielding varying results. Some manufacturers prefer to make measurements that will be presented to the public on the Neumann K100, a head shaped microphone that makes roughly flat response measurements for roughly flat headphones, but not compliant with headphone measurement standards.
The point is, all the advice in this article is only true when you're looking at headphone measurements taken with standards compliant instrumentation. And, if you're going to compare headphone measurements, always compare measurements that have been made on the same system. It's also helpful if you are going to look at any set of measurements to get used to the way that particular lab's measurements appear. To really get the feel for this stuff you have to spend a lot of time listening to headphones while you're looking at graphs. There's some good learning available there...but beware, there's also ample opportunity to create your own little rabbit hole of expectation bias.
On the other hand, measurements are the one thing you can look at with a sense that some truth is there to be had. Measurements are real...how meaningful they are isn't easy to answer, but we'll keep plugging away at it.
InnerFidelity AllGraphs.pdf and measurement data sheet page.
InnerFidelity articles on the Harman Target Response Curve here, here, and here.
Other articles on headphone measurements on Stereophile, Soundstage, Rin Choi's Blog, and Golden Ears.
Udauda's (Rin Choi) Head-Fi Listing of all sites providing headphone measurements, which, unfortunately, doesn't include a link to Marv's measurements at the very bottom of Changstar's home page or the wealth of information in their measurement forum area.
Jude Mansilla (Head-Fi Founder) comments on headphone measurement systems.