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Upon some digging in my hard drive, apparently I had a set of measurements of the EARS I did earlier this year alongside a large number of measurements on my 4128C to quantify the variation between measurement sets - I suspect that the two together will be of some interest.
Methodologically, and I'll be honest I'm only being thorough about this because implausibly I kept good notes during this, all measurements were captured at a sample rate of 192khz using a 1.365s logarithmic sine sweep in ARTA, and analyzed with an FFT block length of 128k samples, then smoothed to 1/24th octave bands. Each headphone frequency response is an average of five reseats/replacements on the head. All measurements were conducted within the linear output range of the headphones, and at levels high enough to avoid room noise contributing significant response deviation above 100hz. All results were normalized to 1khz - this was arbitrary, and these days I tend to prefer 200hz or 500hz for such comparisons because it's further from the HRTF band's detailed region, but given that coupling produced some variations of meaningful magnitude with the EARS, this has the perk of mostly excluding that from impacting measures of difference at higher frequency. Though a high sampling rate was used, the EARS appears to be lowpassed around 22khz, and obviously >20khz data has no audible implications, so I've chosen to limit the plots to this scale.
The headphones used were not entirely in stock form, but represent a reasonably varied body of headphones while being primarily over-ear, and were constant between the test fixtures (and, per my notes, tested about 8-15 hours apart). They consisted of an Audio-Technica AD700 whose drivers had been replaced by AD2000 drivers (open rear volume, leaky front volume); A Yoga CD2500 branded by the gaming brand Fenix as "Aria" (closed rear volume, closed front volume); A Foster Electrics model 443741 branded as a Creative Aurvana Live (closed rear volume, mostly closed front volume, small/supraaural pads); A Foster Electric model 443742 branded as a Denon D2000 (closed rear volume, partially leaky front volume); an Audeze EL8C (closed rear volume, closed front volume, planar magnetic); a Sennheiser HD600 (open rear volume, leaky front volume); a Sennheiser HD800 (open rear volume, leaky front volume, very large front volume space); a Superlux HD681 (open or leaky rear volume - I haven't actually checked, I'll be honest - closed front volume, with fairly thin pads that couple inconsistently); a Hifiman HE560 (open rear volume, leaky front volume, planar magnetic with exceptionally low acoustic impedance); a Monoprice M1060 (open rear volume, sealed front volume, planar magnetic with a substantial high Q resonance in the upper midrange/low treble band); an AKG Q701 (open rear volume, leaky front volume); and a Tascam TH02 (closed rear volume, closed front volume).
As I usually do, I've started with a useless soup of lines. I'm not really sure why I feel compelled to show the raw responses on the two systems, because even if I gave each pair its own plot, it's a terribly way to infer the differences and their trends...but it feels somehow wrong to me to omit it at this point. Nonetheless, it's useless, so let's make it into something more useful.
Subtracting the measurements of a given headphone on the EARS from the measurement on the 4128 gives us a plot of the headphone-specific deviation between the two systems by frequency. At a quick eyeball, we can see some common trends in the difference, as well as the outlier behavior at low-mid frequencies of two of the closed designs most sensitive to leakage (the CD2500/Aria and 443741/CAL, respectively the orange and grey lines). Averaging these plots and taking minimum and maximum values by frequency gives us what could be considered a compensation curve, as well as "worst-case" variation which I encountered in this test set:
You can see a commonality with Oratory's average of difference here as well:
It might be tempting to take such an averaged curve as a correction for an EARS, and, if you happened to have an EARS, it's a better option than nothing, but as aforementioned its results will vary between headphones, particularly at higher frequencies. Out to 2-4kz, this seems like a reasonable choice to me (although as much of the lower-frequency variation will be due to coupling variation, a specific comparison <500hz with careful attention to seal might be a good addition), but past that band, things become less consistent. Subtracting the average from the individual headphone results shows us the degree of inaccuracy with a constant compensation:
Note that the scale has changed to 30dB in total from 50dB.
I know that it will be a concern that we're just measuring noise here - specifically the noise of placement variation/"run-to-run delta", so as a comparison, here is an overlay of the same sort of plot made from the absolute worst-case maximum deviations by frequency from five sets of measurements on my HATS (the 300 measurements that are embodied here took me a full day).
Note that this not a per-headphone per-set plot, as that would be even less readable, and instead represents the worst-case difference from all 12 headphones in each measurement set. The equivalent plot for the 4128-EARS looks like this, which as you can see is just the extremes of the second to last plot:
That is to say that in spite of being just one comparison, instead of the ten in total from the five sets of 4128 measurements, the upper end of the HRTF band shows greater worst-case variation.
Of course, the worst-case isn't necessarily what we care most about, so I've also calculated the standard deviation by frequency for the 4128-EARS data per headphone with the average subtracted (e.g. the "compensated" results you'd get):
And of course the entire point of the 300-measurements-on-4128 project was seeing what that looked like for my HATS itself, so here's that plot for your comparison purposes (each line being the stdev of the deltas between two measurement sets):
With 1khz as the alignment frequency, naturally deviation is zero there. The HATS results reflect only the "noise" inherent to the whole process, and so could be considered the noise floor here. By that measure, the EARS isn't substantially a compromise out to 4khz or so, but past there its dynamic interactions with headphones that differ from real ears dominate measurement noise. They aren't as large as those of an earless flat plate, but they are meaningful, and it's sufficient reason to take the results you get in that band with a grain of salt.
Methodologically, and I'll be honest I'm only being thorough about this because implausibly I kept good notes during this, all measurements were captured at a sample rate of 192khz using a 1.365s logarithmic sine sweep in ARTA, and analyzed with an FFT block length of 128k samples, then smoothed to 1/24th octave bands. Each headphone frequency response is an average of five reseats/replacements on the head. All measurements were conducted within the linear output range of the headphones, and at levels high enough to avoid room noise contributing significant response deviation above 100hz. All results were normalized to 1khz - this was arbitrary, and these days I tend to prefer 200hz or 500hz for such comparisons because it's further from the HRTF band's detailed region, but given that coupling produced some variations of meaningful magnitude with the EARS, this has the perk of mostly excluding that from impacting measures of difference at higher frequency. Though a high sampling rate was used, the EARS appears to be lowpassed around 22khz, and obviously >20khz data has no audible implications, so I've chosen to limit the plots to this scale.
The headphones used were not entirely in stock form, but represent a reasonably varied body of headphones while being primarily over-ear, and were constant between the test fixtures (and, per my notes, tested about 8-15 hours apart). They consisted of an Audio-Technica AD700 whose drivers had been replaced by AD2000 drivers (open rear volume, leaky front volume); A Yoga CD2500 branded by the gaming brand Fenix as "Aria" (closed rear volume, closed front volume); A Foster Electrics model 443741 branded as a Creative Aurvana Live (closed rear volume, mostly closed front volume, small/supraaural pads); A Foster Electric model 443742 branded as a Denon D2000 (closed rear volume, partially leaky front volume); an Audeze EL8C (closed rear volume, closed front volume, planar magnetic); a Sennheiser HD600 (open rear volume, leaky front volume); a Sennheiser HD800 (open rear volume, leaky front volume, very large front volume space); a Superlux HD681 (open or leaky rear volume - I haven't actually checked, I'll be honest - closed front volume, with fairly thin pads that couple inconsistently); a Hifiman HE560 (open rear volume, leaky front volume, planar magnetic with exceptionally low acoustic impedance); a Monoprice M1060 (open rear volume, sealed front volume, planar magnetic with a substantial high Q resonance in the upper midrange/low treble band); an AKG Q701 (open rear volume, leaky front volume); and a Tascam TH02 (closed rear volume, closed front volume).
As I usually do, I've started with a useless soup of lines. I'm not really sure why I feel compelled to show the raw responses on the two systems, because even if I gave each pair its own plot, it's a terribly way to infer the differences and their trends...but it feels somehow wrong to me to omit it at this point. Nonetheless, it's useless, so let's make it into something more useful.
Subtracting the measurements of a given headphone on the EARS from the measurement on the 4128 gives us a plot of the headphone-specific deviation between the two systems by frequency. At a quick eyeball, we can see some common trends in the difference, as well as the outlier behavior at low-mid frequencies of two of the closed designs most sensitive to leakage (the CD2500/Aria and 443741/CAL, respectively the orange and grey lines). Averaging these plots and taking minimum and maximum values by frequency gives us what could be considered a compensation curve, as well as "worst-case" variation which I encountered in this test set:
You can see a commonality with Oratory's average of difference here as well:
It might be tempting to take such an averaged curve as a correction for an EARS, and, if you happened to have an EARS, it's a better option than nothing, but as aforementioned its results will vary between headphones, particularly at higher frequencies. Out to 2-4kz, this seems like a reasonable choice to me (although as much of the lower-frequency variation will be due to coupling variation, a specific comparison <500hz with careful attention to seal might be a good addition), but past that band, things become less consistent. Subtracting the average from the individual headphone results shows us the degree of inaccuracy with a constant compensation:
Note that the scale has changed to 30dB in total from 50dB.
I know that it will be a concern that we're just measuring noise here - specifically the noise of placement variation/"run-to-run delta", so as a comparison, here is an overlay of the same sort of plot made from the absolute worst-case maximum deviations by frequency from five sets of measurements on my HATS (the 300 measurements that are embodied here took me a full day).
Note that this not a per-headphone per-set plot, as that would be even less readable, and instead represents the worst-case difference from all 12 headphones in each measurement set. The equivalent plot for the 4128-EARS looks like this, which as you can see is just the extremes of the second to last plot:
That is to say that in spite of being just one comparison, instead of the ten in total from the five sets of 4128 measurements, the upper end of the HRTF band shows greater worst-case variation.
Of course, the worst-case isn't necessarily what we care most about, so I've also calculated the standard deviation by frequency for the 4128-EARS data per headphone with the average subtracted (e.g. the "compensated" results you'd get):
And of course the entire point of the 300-measurements-on-4128 project was seeing what that looked like for my HATS itself, so here's that plot for your comparison purposes (each line being the stdev of the deltas between two measurement sets):
With 1khz as the alignment frequency, naturally deviation is zero there. The HATS results reflect only the "noise" inherent to the whole process, and so could be considered the noise floor here. By that measure, the EARS isn't substantially a compromise out to 4khz or so, but past there its dynamic interactions with headphones that differ from real ears dominate measurement noise. They aren't as large as those of an earless flat plate, but they are meaningful, and it's sufficient reason to take the results you get in that band with a grain of salt.
