First Crunched Data From Harman Head Measurement Session
I don't think I'd make a very good researcher. I get too pissed when the numbers don't look like I'd like. Guess that's why so many engineers are less in touch with their feelings than the average Joe. Oh well, here we go.
First I'll show you all the data.
In this test, a 256 point stepped sweep was performed from 20Hz to 20kHz. The head was positioned at the reference listening point and fifteen measurements were made at different angular positionsazimuth angles (left to right) were +/-20, +/-10, and 0 degrees; these measurements were repeated with the head level, and tilted up and down 10 degrees. Left and right ear data were taken as separate files.
The speakers were set up in the room to provide the Harman preferred listening EQ. Here's a plot from a measurement microphone used to set up the the room for my visit.
Data recorded from the head was stored in Excel spreadsheets, one for each angle. The raw data was quite noisy. In my initial previous post, I smoothed the data with a moving average filter that I can manage to pull of in Excel. Good for a rough idea of what's going on, but not good for developing a compensation curve that doesn't have a lot of weird artifacts in it.
Fortunately, I know Arnaud well enough that I knew he might give me a hand with a bit of complex best-fit curve fitting math that can't be done in Excel...which he agreed to do (bless his nerdly heart). On all the data shown here, Arnaud has used a "d-2/xhat-6OB" Tikhonov 1/6th Octave Band smoothing derivative 2 best-fit filter. Don't ask me what that means...hell, don't ask Arnuad for an exact meaning. Here's what he wrote me:
Started looking at smoothing functions:
- I used open source code Octave and some data-smoothing package that was made available for a kind soul.
- I have to be honest with you and I am not a math guy per say so I could not explain the method in detail, but description of the package here mentions about Tikhonov regularization.
- I also tried the "standard" interpolation function using spline method (interp1 mentioned before)
- After interpolation, the curves go through a second fit (cubic interpolation using interp1 function) in order to get back to the original frequency resolution (e.g. so that you can use these directly in Excel to normalize all your existing spreadsheets)
- All interpolations are made directly in dBU scale, which is the way to go I think because your data is quite jaggy (would have helped to perform longer averages but time was of essence I assume)
Have played a bit today with the various options using 3 files and have attached the results.
- "d-" value corresponds to smoothing derivative used to perform smoothing (Tikhonov method)
- "xhat-12OB" is a best fit to 1/12th Octave Band set of frequencies (Tikhonov method)
- "xhat-6OB" is a best fit to 1/6th Octave Band set of frequencies (Tikhonov method)
- "gcv" is magic to me, could not tell you what it does (Tikhonov method). Besides, it does not systematically converge (iterative method) and you'll notice some blue color curves that do not seem smoothed (failed at 50 iterations…)
- "spline-6OB" uses a spline interpolation method onto 1/6th Octave band set of frequencies (standard interp1 function)
From what I have seen so far, "d-2/xhat-6OB" interpolation is the one to go for (red color curve in …_SmoothingTest4.png).
Here's one of the plots he sent. He modified about 30 spreadsheets for this project. Thank you, mate.
I then took all Arnauds data and re-built and modified my pre-existing spreadsheets to be able to display an array of summary data. We'll start with the stereo data with both speakers active.
Stereo Response Tests
The above plot shows the left (top) and right (bottom) ear family of plots for movements in azimuth (left to right). At each angle, measurements from the three elevation angles are averaged to provide some angular averaging to remove fine features from the HRTF (head related transfer function).
A few things to notice right off the bat:
I would have expected the bass to come down to the 0dB line by 150Hz. The room tuning clearly shows a shelf in the bass that ends at 200Hz. Looking back at the initial data, it seems the best fit smoothing algorithm is extending the bass boost curve upward in frequency and taking too much detail out of the bass profile.
The right ear (bottom traces) shows a significantly more apparent downward inflection as the curve rises between 1kHz and 3kHz. Keep an eye on this area as it seems pretty lively in the measurements. Something is going on here and I know not what.
I've really liked how the presence and coherence of vocals improve when I EQ to match the tonal profile of the Harman curve (below) in the 200Hz to 3Khz area. The recorded data shows the Harman curve might need a little tweak to raise the peak to 3.5kHz and re-shape the inflection at 2kHz a bit for application with my head.
It's very clear to me from these measurements that the prescribed ever-increasing fall in response above the 3.5kHz peak prescribed by the preliminary Harman target response (shown above) does not match my head's response.
While the fall from 3.5kHz to 7kHz is very similar as head angle changes, the the area above 7kHz seems quite effected by angular change. We'll see this more clearly in the left speaker only data.
The above plot show the family of measurements of the left and right ear for up and down movement. Each plot is the average of all left to right movement of the head at each elevation.
Generally speaking, the plots don't show much change except for the area between roughly 600Hz and 3kHz. In that area there is significant change...especially at that 2kHz inflection. Maybe...just maybe...there's a null in the room at 2kHz near the right ear and as I tip the head up and down the ear moves nearer and farther from the null. Dunno.
The above plot shows the sum of all measurements combined for the left and right ear, and the sum of both ears together. This, it seems to me, is a reasonable candidate for a headphone compensation curve for my head. I continue to dislike the bass bump extending to 400Hz, however. That's never sounded right to me...I'm going to have to do something about that.
Left Speaker Only Response Tests
The above plot show the family of measurements for azimuth changes of the left and right ear with only the left speaker playing. Each plot is the average of all up and down movement of the head at each azimuth angle.
It's cool when things look as expected, and the above plot is cool in that way. First notice the peak at 3.5kHz: This peak occurs due to the sound focusing effect of the concha bowl (the small bowl around the entrance to the ear canal). The left ear is variously facing the left speaker, and you can see that it is quite stable at achieving the needed gain on that side of the head to hear sounds at this frequencylike a twig snap. (Evidence of evolutionor Godhelping us hear the approaching tiger?)
But the right ear, on the far side of the head from the left speaker, is shadowed from the directly propagating sonic wavefront of the speaker, so is ever more unable to focus the sound and looses gain. Yet another psychoacoustic cue to know where that sound just came from.
Higher resolution localizing cues are to be found in the area above 7kHz. This is a noisy area, but if you look closely you can see the trends. The first thing to ignore is the dip and bump at 11kHz and 13kHz. These occur from a tertiary resonant mode in the ear canal. All the plots show evidence of itthe more direct the sound into the ear canal, the more pronounced the wiggle. Just smooth it out in your head.
Now look carefully at the area between 7kHz and 10kHz and compare it to the area above 10Khz. What I see is that as the face of the dummy head is ever more pointing directly toward the speaker, the stuff 10kHz to 15kHz rises, but between 7Khz and 10kHz it sort of falls off. Essentially, the tilt in response above 7kHz goes upward as you face the speaker and downward as you turn away. As you directly face a sound source, the top octave tips up; as you turn away, it rapidly falls off. If you want to hear very high frequency sounds, I guess you should face directly towards them.
It seems to me, when looking at the plots so far, the data shows that the fall after 3.5kHz should end at about 7kHz 3dB above the midrange baseline, then remain about flat 'til 15kHz at which point it may roll off. This is substantially different than the Harman target response.
Very interesting to me is that I know this response would be too bright for my personal tastes. The Audeze SINE has a fairly similar response, and while I knew it would be a lot of people's cup of tea, it was still too bright in those top octaves for me.
This exercise have given me new insight into where neutral is, and a more precise understanding of my preference for a more laid back sound. I will certainly be dialing that into my understanding of how to review headphones more fairly when my taste drags me away from neutral. John Atkinson brought up our differing appreciation for the treble range in his LCD-4 review, and he like this profile much more than I.
One interesting thing to keep in mind though is that if the area above 7kHz is tipped up, it may be that we begin to perceive the sound as coming from more directly in front of us. This may psychoacoustically narrow the stereo image as the sound is perceived as coming from more directly in front, rather than 30 degrees to the side. May!
The above plot show the family of measurements of the left and right ear for up and down movement with the left speaker playing. Each plot is the average of all left to right movement of the head at each elevation. Nothing too terribly important here, but a couple things worthy of note.
The inflection at 2kHz seems to be more pronounced in the left channel where in other data it seems to be more pronounced on the right. No idea why this is so.
It's clear that the region above 7kHz is tipped up in the left ear, and downward in the right, reinforcing the idea the more your head is turned toward the speaker, the more this region tips up.
The above plot shows the average of all measurements from the left and right ear with the left speaker playing. The right ear show a clear loss of concha gain relative to the left ear, which faces the speaker. Again, above 7kHz the left ear is tipped up and the right ear rolls off.
The top green plot is the sum of both curves. This is the second potential plot I will consider as a compensation curves for my system. With speakers, both ears hear both speakers. The left ear hears both the left and right speaker. It's (somewhat) reasonable to assume that the right ear hearing the left speaker will be quite similar in response to the left ear hearing the right speaker. Therefor, adding the left and right channels together on this plot may be like the left ear hearing two speakers and is therefore a reasonable model for a compensation curve.
The above plot shows the averaging of all measurements in the stereo test to those measured with the left speaker only. It may be reasonable to assume that the difference in these to curves comes mostly from having two speakers playing in the room vs. one. Bass increase due to the confinement of long wavelength sounds may account for the added bass of the stereo plot. I have no rational guess as to why the area between 500Hz and 3kHz looses response with the stereo signalmaybe acoustic cancelations at those frequencies? (Wild-ass guesses in the comments are welcome!)
In the coming week I will try to contact and get comments on these findings from some of the (much better educated in the field than I) researchers and engineers who have been following along and helping me through this process. I will summarize and report later.
For now, I've taken a first quick stab at compensating a few headphones with the two above empirically derived curves. The following plots show the Audeze LCD-4, and Sennheiser HD 800 and HD 600, compensated with both the stereo and left channel only total sum curves shown above. The left channel of each headphone (top blue trace) is compensated with the stereo data; the right channel (top red trace) is compensated with the left speaker data.
I'd love to hear your which you prefer and why in the comments. (Note that the HD 600 looks like there is more difference in the compensations; this is happening because the channel matching of that headphone is a bit off.)
Trial Headphone Compensations
Sennheiser HD 800
Sennheiser HD 600
As I mentioned, I'll be reporting back on comments from engineers, but I'd like to do a few more things.
I'll be asking Arnaud for a little more help. I want to see if he can play around with the smoothing algorithm coefficients to get some more detail back in the bass. Also, the gathered data sets aren't exactly the same size and length as the headphone data I gather. Data was gathered for this experiment from 20Hz to 20kHz in 256 log steps; my headphone measurements are 10Hz to 22kHz in 512 steps. We'll need to convert the curves above into ones I can just tip into my spreadsheets. (I did a crude scale conversion by hand for this article, but want a really clean one for further exploration.)
Once I have some usable compensation curves in hand, I will produce a series of graphs showing the raw response; responses compensated with the two above plots; a Harman target response compensation; and with diffuse field, free field, and independent of direction compensations. I'll do this for maybe a dozen headphones, and then I'll post each headphone plot as a poll in which readers can vote on which compensation curve they think best represents each headphone. This should give us some interesting feedback on these curves.
That's it for now.