[ADUHF]

I just finished listening to Resolve's latest live stream, and thought there were a couple interesting topics that came up which sort of tied into some of the discussions in this forum, that might be worth commenting or expanding on. So thought I'd post a few thoughts on it here.

One contributor to the live feed, for example, asked for an explanation of the diffuse field. And Resolve really only scratched the surface a bit on that. I think maybe the easiest way to grasp the concepts of a diffuse and free field is to think of them as being sort of opposite ends of a continuum.

In a free field, the sound is only coming at the listener from a single angle or direction. And the "free" part simply implies that it's free or absent of any reflections. A diffuse field is sort of the opposite of this, where the sound is coming at the listener at equal levels from all directions and angles.

https://en.wikipedia.org/wiki/Free_field_(acoustics)
https://en.wikipedia.org/wiki/Diffuse_field_acoustic_testing#Diffuse_field_principle

It's really not much more complicated than that. And since the sound fields that usually surround us are typically a much more complex mixture of free/direct, diffuse and reflected sounds, both the free and diffuse fields are really more abstractions of the sort of thing we typically encounter in normal circumstances. Because it is rare for us to be in a space which is either completely reflective, or completely non-reflective.

That does not mean they are totally useless though. Far from it in fact. Because when these types of sound fields are measured at the eardrum of a dummy head, for example, they can provide alot of useful info about how the shapes of the ear, head and torso interact with and distort free or diffuse sounds at different frequencies, before they reach our nervous system and brain. Another term for this type of interaction is a transfer function.

Since the diffuse and free field are abstractions though, which rarely occur in daily life, they don't provide all the info we need to understand how a source with a non-uniform sound signature or dispersion at different frequencies might potentially behave in a semi-reflective room. Why is that important?... Because that's how we normally hear sounds from a set of loudspeakers in a room. And a complex sound field of this type will have a different response at the eardrum than either a free or diffuse field. So we have to look in a couple other places to fill in some of the information gaps on this kind of thing...

The first and easiest method is simply to measure the actual sound of loudspeakers in a room at the eardrum. Another method is to make an educated guess at the sound, based on listeners' subjective preferences. And a third method is to combine a loudspeaker's room curve with the measurement of a loudspeaker at the ear that has had all of the room effects nullified. These are all methods that Harman has explored in their development of the Harman target.

It will probably come as no great shock though that I'm going to propose a fourth method, which I think could be just as potentially good or accurate as most of the others above. And maybe also a bit easier to calculate. And that is to combine the diffuse field curve at the ear with a speaker's sound power curve.

https://en.wikipedia.org/wiki/Sound_power

Imo, the sound power of a loudspeaker, and the diffuse field response at the ear are like two different sides of the same coin. One is simply measured from the perspective of the sound source (ie speaker in a room), while the other is measured from the perspective of the sound receptor (ie the eardrum).

Recall that the diffuse field is a measurement of the in-ear response to sound coming equally from all directions. At all frequencies. And what gives a diffuse field curve its shape or spectral characteristics are the head, torso, and ear interference, both constructive and destructive, with that sound at various frequencies before it reaches the eardrum.

When it comes to the in-ear sound of a loudspeaker in a room, there are really only a couple quantities which are missing from this diffuse field equation, and those are primarily the effects of the loudspeaker's dispersion at different frequencies, and the effects of the semi-reflective room on those frequencies at the listening position, before reaching the torso, head and ear. And we seem to get both of those things (or something awfully damn close to it) from the speaker's sound power measurement.

If we were actually measuring the sound of a speaker in a room, at the eardrum, then there are some other characteristics which could also come into play, such as the speaker's direct sound, and early reflected sounds. Which are accounted for in a speaker's room curve calculation. Since we are only looking at the ear's response to diffuse sound though in this last method, we need only to look at the speaker's correlate for this to derive its in-ear characteristics. Which is its sound power.

That is my theory anyway. And I think there is quite a bit of both subjective and also objective evidence to potentially back it up.

 

[ADUHF]

Revised the Wikipedia link for a diffuse field above. For some reason I had previously posted the link for a "direct field" instead, which is not the same thing. So I apologize for the confusion on that. It was quite late when I posted the above last night though. So that's my excuse.

 

[ADUHF]

Diffuse field curve (shown in light gray) vs. raw DRP measurements of several headphones with a neutral-ish overall frequency response...

Another question which often comes up when discussing the different compensation curves for headphones is-- why is a diffuse field curve so bright or brightly tilted in the treble and upper mids compared to the frequency responses of most of the better or more "neutral-sounding" headphones? This is also something that Resolve didn't really attempt to explain in the above video. (And it's really asking the wrong question imho.) The answer though is that the diffuse field curve is simply the head, torso and ear's response to a spectrally flat sound field coming equally from all directions... And that's pretty much it. So nothing else.

The shapes of the torso, head and ear all have their own resonant and/or harmonic characteristics. Particularly the ear canal, which is the tube-shaped part of the ear's anatomy between the outer ear and the ear drum. And when these characteristics are all combined together, they produce a fairly pronounced boost in amplitude in the higher frequencies, particularly in the upper midrange frequencies at around 3 kHz, which is the primary resonance of the ear canal. But also in the treble frequencies to some degree as well. They have little to no effect though on the lower frequencies, below about 160 to 200 Hz. So that's why that area of the diffuse field curve is essentially flat in the bassier frequencies, below that range.

 

[ADUHF]

A better question to ask than the one above is-- why is the frequency response of many of the better headphones more darkly-tilted overall than the diffuse field curve?

If you look at the raw FR plot in the last post above, you can see that most of the headphones appear to have about a -10 to -15 dB overall tilt (or -1.0 to -1.5 dB per octave tilt) from the bass to the treble when compared to the diffuse field curve. And that is exactly how they appear on a graph corrected or compensated with the diffuse field curve...

There are a few bumps, dips, and wiggles here and there, but the overall trend is a downward slope of about -10 to -15 dBs from the sub-bass to the upper treble. The question is why?... And the answer is basically contained in my first post above.

The reason headphones with a neutral-ish response have a downward slope on a diffuse field plot, and appear tilted on a raw plot compared to the diffuse curve is because they are emulating the non-uniform dispersion and frequency response of a loudspeaker in a room. Which results in a reduction in amplitude in the higher frequencies vs. the lower frequencies.* This applies to both closed headphones with a neutral response. And also to open-back headphones with a neutral response, in at least the midrange and treble. Open headphones will tend to drop off or flatten out a bit more though in the lower frequencies, because their open design does not as easily permit the same extension of this slope into the lower frequencies as most of the better closed-back headphones. (Though that can be tweaked a bit on some open HPs with an EQ.)

The headphones on the above graphs are a mixture of both open and closed backs though. And the two which start to drop off below about 50 Hz are the open models. Most open-backs will begin to flatten out or drop off at a somewhat higher frequency in the bass though, generally somewhere more in the 100-200 Hz range. So the two open headphones above, which are the Sennheiser HE-1 e-stat and Onkyo A800 dynamic HP, are somewhat unusually well-extended in the bass for open models... Which is why I included them in above sample (to better illustrate that this tilted behavior is not limited solely to closed HPs.).

(*According to folks like Floyd Toole, it's really an increase in the lower frequencies vs. the higher frequencies, rather than the other way around. But the net result is really the same, however you choose to look at it.)

 

[bigshot]

I once had a car stereo installed in my car. After it was installed, the salesman took me out to my car to demo it for me. He immediately grabbed the bass and cranked it. It sounded boomy and awful, but he had a big grin, nodding his head enthusiastically. "Doesn't it sound great?!" After I set the tone controls back to a normal range, it did sound great. Some people think more bass is better. I find too much bass messes up the midrange.

 

[ADUHF]

I once had a car stereo installed in my car. After it was installed, the salesman took me out to my car to demo it for me. He immediately grabbed the bass and cranked it. It sounded boomy and awful, but he had a big grin, nodding his head enthusiastically. "Doesn't it sound great?!" After I set the tone controls back to a normal range, it did sound great. Some people think more bass is better. I find too much bass messes up the midrange.

Fwiw, I wouldn't necessarily disagree with this.

Linearity (or something close it) should be the objective imo. But there are practical reasons why this does not always work or sound the best. So one has to keep a bit of an open mind on the subject.

Linear does not always mean "flat" as well. This is particularly true when looking at the sound of a speaker in a room. The KEF Reference 5 loudspeaker, for example, appears to have a very linear in room response, as indicated by its sound power and early reflection curves (based on KEF's own measurements). But it is not "flat" in the sense of having equal volume or amplitude at all frequencies in a room. Nor should it be.

https://pierreaubert.github.io/spinorama/KEF Reference 5/KEF/index_vendor.html

And its highly linear in-room response may not necessarily be an "ideal" response with most content, because most other loudspeakers used in homes and studios will tend to have a somewhat less linear, and slightly more U, V or L-shaped in-room response in the midrange, due at least in part to a reduction in dispersion at the ~2k cross-over of the midrange and tweeter drivers.

 

[bigshot]

Any response target is just a starting point. We are all free to adjust to taste. The target is just a baseline. Your amp has tone controls, or an equalizer... That is the same as salt and pepper shakers on the dining table. Feel free to use them. Just don't pour ketchup on a good steak!

 

[ADUHF]

I still have a couple more thoughts on last week's live stream, including on the Beyers/studio HPs, and treble resonances, among other things. Today's stream is up though, and posted above.

I've already listened to a good bit of this, maybe a third or so of the whole stream. And Resolve is touching on a couple of the same or similar themes. I'll have to finish listening to the whole think before offering any in-depth comments. But I've already heard a couple references to "ear gain". Which I assume refers to the boost in amplitude that often shows up on raw headphone frequency plots in the 3k range.

This is a slightly confusing topic. Because alot of people seem to think that the boost in amplitude in that range is caused by the headphone, and not the ear. And listening to some of Resolve's comments on the subject, you might also easily jump to that conclusion. However, the boost in amplitude in that range is, to a large extent, caused by the ear resonances, and not the headphone. Some headphone manufacturers will deliberately try to "compensate" for that boost in amplitude at 3k though, and try to flatten it out. Which is usually a mistake.

IEMs may work somewhat differently than over-ears on some of this. Because they have to make up a bit more for some of the missing effects of the outer ear than most over-ear headphones would.

 

[ADUHF]

The above plot shows the contributions of different parts of the body and ear which effect the measurements made at the eardrum (aka DRP). And there is a slight general overall boost in amplitude due to the shape of the head, which would would be missing in pretty much all headphones. The lion's share of the boosting effect comes from the primary resonance in the ear canal though at around 3k. So not the headphone, per se. There is also a pronounced boost by the concha in the low treble as well.

This boost in the upper mids and low treble will show up in the in-ear measurements of both speakers in a room (or in a free or diffuse field, for that matter). And also on headphones with a reasonably neutral response that approximate the sound of a speaker in a room. Because it occurs mostly within the ear itself.

The graph above is based on a free-field measurement taken from a 45 degree angle to the head btw. So it does not contain any of the low frequency gain that would result from the wider dispersion of sound in that range with a loudspeaker in a room. And is missing the generally darker tilt in overall response that tends to result from that.

I'm a bit further along in today's stream now. And Resolve is getting into a bit more detail on some of the above, including bass boosts and the Harman target as well.

 

[ADUHF]

https://www.stereophile.com/content/innerfidelity-headphone-measurements-explained

Just to reinforce the above points on ear gain, the green curve on the above plot is based on the in-ear response of speakers in a room (presumably made in Harman's reference listening room). The speakers in this case were equalized though to remove the overall tilt and gain in the lower frequencies, so they measure flat at the listening position with a standard free-standing microphone (as opposed to an in-ear mic in a head and torso simulator). What's left after this "room gain" is removed is largely just the gain at around 3k caused by the ear canal and to a lesser extent the shape of the head.

It is not a coincidence that the green curve above looks similar to the combined results of different parts of the head and ear shown on the previous graph above, because they are measuring more or less the same thing.

 

[ADUHF]

This plot of the original Olive-Welti curve is also based on the in-ear measurements of a speaker in a room. And it also shows the same pronounced boost at 3k as most raw headphone plots, and the other in-ear measurements shown above.

This was probably measured on a different type of rig than the other graphs above though. Which is why it has a more pronounced dip in the sibilant range at around 6 kHz. And a more pronounced peak or resonance at around 9 kHz.

https://www.aes.org/e-lib/browse.cfm?elib=16768

 

[ADUHF]

I have listened to most of this week's stream now. And the Harman commentary begins right at around the 1 hour mark in the middle of video, and continues for a good bit from there.

It probably goes without sayin at this point, but I disagree with a good bit of Resolve's take on this subject. It is important to put some of his comments on this topic into an appropriate context though, since he's openly admitted that his reviews and channel are intended mainly for users of more expensive audiophile type gear, than equipment for the masses or average listeners. Which will have an implicit effect on some of his opinions and preferences. In spite of this though (or perhaps because of it?), there are a couple main areas where my feelings and opinions on this subject don't align particularly well with his.

The first is the notion that anything below a certain frequency in the midrange (I think he mentions ~900 Hz) is largely subjective. Resolve touches a bit on this in this week's video, and also last week's if I remember correctly. And I think the general argument goes a bit like this... Speakers come in all shapes and sizes, and levels of extension in the bass. Therefore people's experiences with them, and their expectations of how a headphone should sound will be different.

There is obviously some truth in this. And most speakers will begin to roll off a bit before they get into the sub-bass frequencies. So people's experiences will be different if they're using speakers with a sub-woofer versus without, to give a simple example.

There are also variations in the way content is mixed and mastered, which could make it sound better or worse on a speaker (or headphone) which is well-extended in the sub-bass versus one which is not. It can potentially go either way. Because audio engineers do not always mix and master their content for transducers with a neutral response in the bass, mids and treble. Sometimes that's intentional, and sometimes it's not. Since their job is to make the content sound good on whatever their customers are actually listening to though, they will often listen to and in some cases optimize their content to sound best on speakers that may have a less than ideal response or extension in the sub-bass or treble frequencies.

The bass response on speakers is also highly dependent on where they are positioned in a room. And how the room is treated. And whether it is more reflective or less reflective. All of the above factors can contribute to people's different perceptions of how a piece of music should sound.

There are other factors as well such as the amount of hearing loss in the upper frequencies, or "hidden" hearing loss that a listener may have, which could also influence their preferences or perceptions for more or less bass. Or more or less midrange emphasis relative to the rest of the frequency response range...

https://www.audioholics.com/room-ac...ons-human-adaptation/what-do-listeners-prefer

The counter to all the above though is the in-room and sound power response data of actual loudspeakers. Which, while not completely 100% consistent across the frequency range, shows a general (and highly predictable) trend towards greater amplitude in the bass and sub-bass. I have, in fact, looked at the spinorama plots of all of the loudspeakers shown here, which includes a broad cross-section of speakers from bookshelves, to studio monitors, to floor models, with and without built-in subs...

https://pierreaubert.github.io/spinorama/

...and there is no single speaker included there which has a relatively flat direct response, that does not also have a corresponding tilt or rise in its lower frequencies when looking at its sound power or in-room response. It is about as predictable as the sun rising in the morning and setting at night. There simply are no exceptions.

You can argue till the cows come home about how much of a rise is appropriate, and where it should begin to falloff. And those are probably good debates to have. But there are no exceptions to this rule!... It occurs with disturbing consistency across the board, regardless of how well or poorly extended the speakers are in the bass. You do not have to take my word on this though. Because you can look at all the spinorama data in the link above, from both the vendors and review sites. And start with the more highly-rated speakers with the best extension and flattest direct/on-axis responses at the top of the list, and work your way down to those which are less flat and less extended in the bass (and also less relevant). And the gain due to greater dispersion in the lower frequencies in the sound power curves is consistent across all brands, models and sizes of speakers. It is simple physics, and occurs like clockwork.

So suggesting that a headphone should not contain some appreciable and comparable level of gain in the same frequency ranges on diffuse field graphs just seems a bit silly to me... unless you simply reject out-of-hand the theory that headphones should sound more or less like a pair neutral speakers in a typical, semi-reflective room.

If you are used to listening to speakers that are not well-extended in the bass, then headphones which are better-extended in the sub-bass may very well sound too punchy in the lower frequencies to you. But you can't immediately leap from there to the conclusion that they aren't "neutral". Because you're basing your opinion on your own limited experience.

Ideally, both the loudspeakers and the headphones should have a fairly linear response across most of their frequency range. In speakers, this applies to both the direct sound, and also the sound power and in-room response. On headphones this applies only to their compensated diffuse field response (with the 3k ear gain removed). And not to the raw response.

Most speakers (and headphones) will deviate a bit from this ideal response though. And generally dip below a linear response in the upper midrange at around 2k where the crossover of the tweeter and midrange driver tends to occur. And there are many headphones which will mimic this behavior as well.

The headphones which most closely mimic this type of linear-ish response though will have a general downward slope on a diffuse field plot, from the bass to the treble, roughly approximating the sound power response of speakers with a flat direct response. And this will often include a similar dip in the midrange, which is generally the most pronounced at around the 2k or 2.5k range.

It is simply silly imo to suggest that headphones which have a flatter, more level response in the lower frequencies on a diffuse plot are somehow "more neutral" than those with a more speaker-like downward slope toward the treble. Because the wealth of the data, and measurements simply contradicts this. So its not something I can really even take seriously.

Since essentially all halfway decent speakers objectively have a rise in their in-room or sound power response in the lower frequencies, it should also be possible to compute some average values for this rise (which should also be applicable to headphones imho), based on a statistical sampling of the loudspeaker's spinorama data. And this could potentially be done both with and without the addition of a sub-woofer.

 

[DivineCurrent]

I do like most of the things Resolve/Andrew says in his videos. He digs deep into the technical performance and frequency response of headphones, which I very much appreciate. However, it seems he’s got contradictory views about DACs and amps, because he claims to hear differences between DACs, and honestly I think he’s full of it, or he’s just lying to himself. Objective data and blind tests confirm over and over again that human hearing can not in any way shape or form, tell the difference between DACs that have been volume matched and confirmed by measurements to have distortion/noise below the threshold of hearing. Same can go with amps, but I’ll be a little more lenient because you got tube amps and stuff like impedance that does change the frequency response.

As far as subjective preference, I tend to agree with most recommendations the Headphone Show gives, and it’s not a coincidence at all that the headphones recommended are often close to the Harman target.

 

[ADUHF]

Thank you for the reply and your thoughts, DivineCurrent.

For the record, I should also say that I think Resolve offers a lot of great advice in these streams. And I hope he continues doing them. And they can also be a great forum for people to post and get some quick feedback from some other participants on their questions.

I agree with him (and have said so elsewhere here) that the Harman curve is probably too rolled-off in the upper treble, for example. And there are probably some errors in the way Harman averaged or treated the response in that area. It depends somewhat on how you interpret their curves though. Because I'm usually looking at the levels of the peaks in those areas, rather than the average response which may be somewhat closer to what they used.

I can't really offer any opinions on the more expensive gear that he mostly discusses though. Because I have no personal experience with it. The most expensive headphone I've every owned is the 250-ohm Beyer DT-770, which ran me about $150. And the most expensive amp I've purchased is my Bellari HA543 for around $100. And they generally seem to do the job pretty well.

 

[bigshot]

I don't see how the Harman curve can have errors. It's an averaged preference of a wide range of people. It isn't intended to be an absolute thing. It is what most people prefer. Are you saying most people don't prefer the Harman target?

If you think the Harman target is attempting to replicate the experience of listening to a speaker system, then yes it's riddled with errors. Headphones can only replicate certain aspects of speakers. The most important and unique aspects of speaker listening are impossible to reproduce using headphones without heavy digital signal processing, head tracking and custom HRTF. Response may be the most important aspect of headphone listening, but with speakers, that is only half of it. There are many more things that affect timing and directionality and the way each person hears that are completely beyond the realm of headphone listening.

I think the attempt to make headphones sound like speakers is kind of like having your cake and eating it too.