Driver story, the acoustic system and the limits of EQ

Technical Discussion
41

The speed thing also vexes me a bit. But I’m open to being “learned” somethin new on the subject. :slight_smile:

The conventional audiophile wisdom is that lighter diaphragms move faster than heavier ones. And their faster response times lead to better detail and better rendering of quick transients. Which in turn leads to better, more precise imaging,… and so forth. The tradeoff is they have less slam/punch than the heavier diaphragmed drivers.

Here’s the way Google’s Generative AI put it, when I asked about the speed of different drivers:

Yes, some headphone drivers are considered “faster” than others, meaning they can react more quickly to changes in the audio signal, which can result in a more detailed and responsive sound, particularly noticeable in fast-paced music or gaming scenarios; this is primarily determined by the driver design and materials, with lighter diaphragms and certain technologies like planar magnetic drivers generally being considered faster than traditional dynamic drivers.

Key points about driver speed:

  • Diaphragm weight:

A lighter diaphragm moves more readily, allowing for faster response times.

  • Driver type:

    • Dynamic drivers: Common in most headphones, can be slower due to heavier diaphragms.
    • Planar magnetic drivers: Often considered “faster” due to their lightweight design and faster response to audio signals.
    • Balanced armature drivers: Typically excel in clarity and detail, also considered relatively fast.

Now we seem to be being told there’s no difference in the speed or responsiveness of different drivers, regardless of their mass or design. And the differences that we perceive as these effects between drivers is somehow all bound up somewhere in the frequency response. This needs some more explaining, I think.

My guess is that the minimum phase crowd with say it’s all about extension in the higher frequencies and/or lower distortion. But I’m still a bit skeptical about that. And have some difficulty accepting that all of those little impulse response blips that Tyll plotted are now irrelavent. (To his credit though, I believe Tyll would sometimes also say they were just another way of looking at or visualizing a headphone’s FR.)

42

I mean… if a driver moves faster that’s reflected in the higher frequencies. Comparatively speaking the HE6’s diaphragm is a lot thicker/heavier if memory serves correctly than say the Ananda driver, or many of the other lower end HiFiMAN headphones, yet people report it as more detailed, myself included. These really are just different parameters of drivers that manufacturers can make use of to achieve whatever their acoustic design goals are with a given product. Heavier, lighter, thicker, stiffer… tensioning. There is no ‘better’ here, just different parameters. They may tell you something is more resolving but that’s kind of just marketing at that point.

Nope, it’s about the in-situ FR and its relationship to the listener’s HRTF. As for what people prefer there, or how those things redound to ‘detail’, your guess is as good as mine. We don’t know, because the existing listening tests were geared around coarse-grained bass and treble balance, not fine-grained, nor did it consider non-HRTF related HpTF effects across listeners.

Yeah he was interested in square wave for ‘detail’, and on a very very coarse-grained view of things, there may have been some truth to that. But again, nothing FR doesn’t do a better job of visualizing.

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43

I used to think this. It seems intuitive, and potentially there an element of truth to the idea insofar as more power might be needed to make a heavier driver move than a lighter driver. But if both drivers are producing a frequency at 20khz, then both are oscillating 20,000 times per second, so the drivers are operating at the same ‘speed’.

So the perception of faster transients isn’t due to the driver moving any faster. My understanding is that it’s more likely to be about relationships within the FR, e.g. that the particular parts of the FR that relate to the leading edge of tones are sufficiently audible over other frequencies. This was discussed in the video.

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44

Thank you for the reply, Resolve.

When you refer to in-situ FR and a listener’s HRTF, I assume you’re referring to what some perceive as detail, not speed.

Even though you seemed to rebuff my remark about extension into the higher frequencies, if I’m interpreting your comments above correctly, then speed would in fact be directly related to a driver’s ability to produce higher frequencies. A “fast driver” then would be one that can move quickly, and produce higher frequencies at decent volume levels, without distorting or breaking up modally.

I don’t want to sound like an echo chamber, but I guess a “better driver” would be one that extends well into both the higher and lower frequencies, plays all those frequencies at decent volumes without audible distortion or modal breakup, and is tonally/timbrally balanced for a neutral frequency response.

45

Take your pick. For some it’s the same thing. The perennial problem with the subjective side of this hobby is that this is private language that an individual person uses to describe their experience, and not shared or universal language. And I’m going to keep bringing this up until the end of time because it really is the root of the vast majority of disagreements to do with audio, particularly headphones. Like this is ultimately why I don’t like to refer to this stuff in terms of these descriptions anymore. I still do it… because I have to, given the canonical nature of the whole ‘technicalities’ thing, but to me that’s kind of just playing the language game as best I can and not really all that interesting.

Basically yes, but that doesn’t mean anything goes. You can have similar treble SPL overall, where one sounds incredible and the other sounds horrible. But again since ‘speed’ in the audiophile sense is used to describe the phenomenal character of a person’s experience, this could also refer to the absence of a bass shelf, where flat linear bass extension makes something sound ‘fast’ and ‘tight’. Or a combination of factors, say flat bass with a forwardness around 8khz (or whatever). So in short [a ‘faster’ driver] is not a sufficient condition for [perception of speed/attack/tightness/etc.].

When I started out in this hobby, I always felt like there really was something to the idea of ‘detail’, ‘resolution’, ‘speed’ and so on, independent of what we’re currently able to measure from a metrological standpoint. Hell… my online name is Resolve, and yes partly for the double entendre. But that ultimately stemmed from not being able to draw a straight line between what I saw in measurements and what my experience was. I felt that the measurements didn’t exhaustively describe my experience, and when products I enjoyed were shown to be poor by the measurements, it made me think “there has to be more to it”.

I went down the rabbit hole of the alternative metrics, like CSD, IR, and so forth only to find there’s nothing there, and it’s all just worse ways of looking at FR. With respect to ‘faster’ drivers, I went as far as to work on and commission custom planar drivers (I still have them actually), with parameters I thought would lead to a more ‘resolving’ experience based on what I had been led to believe as far as driver stories are concerned. And it turned out that none of those assumptions were true - they were just parameters.

I had examples where a thicker, heavier material sounded more resolving, and then the opposite. I thought high flux density would be a key requirement… nope, turns out lower flux density is just fine, depending on the rest of the design. I thought minimal driver damping would be more ‘resolving’, no that just makes your driver have a more modal response, which is also fine…

Point being, when you consider the consequences of non-HRTF related HpTF variation, and even just the different ways in which sound from one headphone can propagate at the eardrums of two individuals (and we should think of a HATS this way too), this makes it entirely possible for FR to exhaustively describe my experience… if I’m able to get that picture at my eardrum relative to my HRTF. And again, I say ‘possible’ because there are all kinds of other factors, biases, framing conditions and the like, and potentially even things like acoustic impedance.

But ultimately this is also where EQ comes in, and especially as a tool to understand this point from an experiential perspective. You can meaningfully impact the subjective effects in exactly this way, regardless of driver story, or any of the other metrics.

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46

As far as what I look for in a driver, generally yes. I want a low resonance frequency, lowish distortion, though it doesn’t matter that much, and fewer modal issues to deal with. But I wouldn’t say ‘neutral response’ is really that easy to get a sense of just by measuring a driver on its own in free air. Like… you put it in an acoustic system that does things to help you achieve that, ideally.

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47

Yes, that seems to be the case from what I’m hearing here.

I’m still not up on the leading edges of tones thing. This is another popular Resolve-ism though. :slight_smile: So guess I’ll have to get the video out and watch again.

48

Sure. Been there, done that. :slight_smile:

Will have to think about this a little more. Some of what people perceive as tighter/faster bass could perhaps be related to overtones in the higher (and speedier) frequencies. I mostly associate this quality with lower distortion and good tonal balance.

I appreciate hearing a little more about some of your travails on these subjects as well. Helps to put things in a little better perspective and to understand better where you’re coming from on some of this.

Makes sense.

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49

how about the ability of a driver to start and stop quickly?

Can that be measured by impulse response?
For ringing?

And how about all the square wave tests that Tyll used to do.

Why aren’t those done anymore?

Legit questions btw. I’m not being snarky

Thanks!

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50

^These are not bad questions to ask imo, Nightjar.

My focus is still primarily on over-ear headphones. And even after listening to Blaine’s talk, and looking at his graphs comparing HRTF-compensated measurements on different rigs or heads, I’m still not that convinced of the importance of personalizing a headphone’s FR for different heads. At least for over-ears. (Especially the open-back over-ears.) IEMs are probably a somewhat different story, since they don’t interact with the outer ear.

I wonder though if you’d also want to include lower acoustic impedance on your list of qualities for a better driver or better headphone, because it might provide better compatability with compensated measurements on a HATS, and potentially more reliable EQ/FR adjustments based on that.

51

This is quite an interesting discussion. It motivated me to take a little refresher on calculus and signal theory which I studied more than fifteen years ago, and I have to admit that what I expressed above is not correct.

I used chapters on Fourier Transform and Inverse Fourier Transform from the book called " Digital Signal Processing" by Jonathan M. Blackledget, as well as Wikipedia and some other resources from ScienceDirect, in case you’re interested in the real math of it.

Let’s do some very simplified math (e.g. omitting phase, integrals, complex variables, etc.) of evaluating signal in time and frequency domain.

Statement

Our starting point would be the following definitions:

  • t - time variable in time domain
  • f - frequency variable in frequency domain
  • A(t) - our original signal as an amplitude function of time. It is important to note that for simple signal like a sine it is a periodic function, while for a music fragment it is usually a non-periodic signal function.
  • F(f) - the original signal in frequency domain, as a continuous Fourier transform of the time-domain signal.
  • FR(f) - the measured frequency response at the measurement rig.
  • HpTF(t), HpTF(f) - is a headphone transfer function represented as operations or filter functions applied in time domain and frequency domain accordingly.
  • HRTF(t), HRTF(f) - is a head-related transfer function represented in a similar way.
  • FT(x), IFT(x) - continuous Fourier Transform and Inverse Fourier Transform operators.
  • DFT(x), DIFT(x) - discrete Fourier transform operators.

For simplicity, let’s ignore HRTF for now and imagine that we have a perfect measurement rig that is capable of measuring the signal at the ear drum.

We measure the frequency response as a way to evaluate the HpTF of a headphone, because working with frequency-domain information is much easier, and the properties of the Fourier Transform and Inverse Fourier Transform claim that an operation applied in time domain will be reflected in the frequency domain accordingly, and vice versa. So, for instance:

HpTF(f) = FT(HpTF(t))
FR(f) = FT(HpTF(A(t))) = HpTF(f)*FT(A(t)) = HpTF(f)*F(f)

which we can use to calculate how the headphone affects the signal:

HpTF(f) = FR(f)/F(f)

In the ideal circumstances (more on that below) we could use the Inverse Fourier Transform to go back from frequency domain to time domain without losing any information:

HpTF(t)=IFT(FR(f))/A(t)

Which means that indeed, if we could take a perfect measurement of the frequency response at the eardrum, it would represent all the characteristics of the time domain as well.

However, in reality there are several important constraints introduced both by mathematical properties of the Fourier transforms and physical properties of the measurement system.

Mathematical constraints

First of all, the original Fourier Transform (FT) and (IFT) Inverse Transform functions are defined for continuous analog signals on an infinite integral range (i.e. infinite range of time and frequency values). They also have a simplified version for periodic signals defined on a finite range.

So, if we wanted to know the HpTF for continuous music signals we would need to take infinite integrals and get a continuous infinite analog spectrum as a result.

In practice we use the discrete versions of FT known as DFT or FFT and DIFT or IFFT accordingly. Discrete means a certain level of approximation.

Quoting some of the important properties of continuous and discrete FT:

The signal with different time domain characteristics has different frequency domain characteristics; these are as follows:
• Continuous-time periodic signal is transformed to discrete non-periodic spectrum.
• Continuous-time non-periodic signal is transformed to continuous non-periodic spectrum.
• Discrete non-periodic signal is transformed to continuous periodic spectrum.
• Discrete periodic signal is transformed to discrete periodic spectrum.

When we are measuring the FR of sine sweeps, we are effectively measuring the discrete non-periodic spectrum of a continuous periodic signal.

If music is a continuous non-periodic signal, the correct representation of it in frequency domain is a continuous non-periodic spectrum though. But our goal is not to measure the music, our goal is to get to the HpTF.

What does this say about our FR measurements? Two things:

  • If we use periodic signal for measurement, we can get a discrete non-periodic spectrum. And measure HpTF as a discrete non-periodic function. Blaine WINS!
  • As we are moving from continuous signal to discrete signal, discretion resolution becomes important if we want to lose as little information as possible

This leads us to obvious physical constraints.

Physical constraints

These have been discussed many times and include to name a few:

  • HRTF variation
  • Positional variation
  • Ability to measure the FR at the eardrum
  • Accuracy of the measurement rig and the errors introduced by the rig itself
  • Precision of the digital processing used

Conclusion

Here are the takeaways from this exercise:

  1. FR at the eardrum measured with a sine sweep can indeed represent full information about how a headphone reproduces sound.
  2. Resolution of the FR matters. For example, the “trailing ends of tones” might be present in several areas of the plot as tiny spikes or dips, but if the plot is smoothed too much or the measurement rig was not able to capture them, we won’t see this feature in the visualization.
  3. The FR measurements that we make on the rig is still an approximation. The more HRTF details we add to it and the more accurate the measurement, the better the approximation.

This brings us to a couple of other interesting topics, such as using smoothed FR graphs to describe fine sonic features of a headphone, as well as using EQ filters (which have limited accuracy) to make a perfect match of one headphone to the other, but I’ll leave it here for now.

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52

This was basically my question after reading the OP. Are we defining “frequency response” to incorporate the time domain, or is it just a two-dimensional function we can show on a graph? If yes, then I agree with all of the claims. If the latter, then none.

53

Probably depends what you mean by an approximation here. We’re specifically interested in using the DFHRTF (high res), because that matches the use condition of headphones. But it’s true this is not the most straightforward thing to get, certainly for real people. And even the rigs don’t come with high res DFHRTFs, so you have to measure or calculate them, and that introduces another variable. We’re fairly confident about the 5128’s and now the KEMAR’s, but less so about the 4128’s for example.

But generally speaking, yes to all of this.

54

Yeah it’s because it doesn’t show anything separate from FR - like it doesn’t show anything that FR doesn’t do a better job of showing. Headphones are minimum phase, meaning anything you’d see there is proportional to FR - see the post above ^ that goes over this.

The one consideration I still have there is that there may be benefits to readability of certain time based views where raw FR may obscure a more modal issue. But this is also why we calibrate it, to avoid such visual illusions. And the bigger issue with time based views is people erroneously think they mean things they don’t.

Tyll was interested in square wave for sure, and I’m not entirely sure the degree to which he thought this was a separate metric by which to indicate ‘detail’ - even though he did talk about it in this way at times. If he did, then that would’ve been a red herring. He may as well have been using FR for that.

55

It’s morning here.
When did you do all this math??
Lol

Anyway….you should send all of what you said here to someone with the same math knowledge to peer review it, since I’m sure most of us aren’t as proficient as you in math.
No offense, but I personally am not as good as you at math so I can’t confirm or argue your points.
Good work nevertheless and interesting points.

On your point of FR.
From using REW and doing freq sweeps we derive different info based on one measurement method.
So why wouldn’t we use an impulse response to show ringing or other time domain info rather than use a non smoothed FR graph.

I hope that made sense as I’m navigating through this as well.

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56

Maybe he was just using it as another metric to help interpret a trend he saw in the FR.
From reading some of his reviews I think he was always skeptical about what he saw in the square waves and how he interpreted them.

I dunno. Too bad he isn’t available to bounce stuff off him.

57

Yeah and that really is the best way to think about some of these other metrics. If you have trouble reading the FR for whatever reason, there could be merit in the alternative views. But as we saw even in this thread, people seem to take them to mean things they don’t.

58

A thought that just occurred to me, thinking about this thread: If I were approaching this problem, I wouldn’t assume without evidence that bone conduction could result in no more than negligible differences. Is bone conduction ever considered when attempting to measure frequency response?

59

Inner bones?

Would have to be loud to make a diff I guess?
Who knows.
Interesting thought.

It’s too early for me in California to think too much on the weekend. Lol

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60

Probably, but I’m not sure. The contact for the wave transfer I would imagine is most important. Anyhow, if you get a hearing test, the audiologist should also check your sensitivity (up to 4 kHz) through bone conduction. And it should be equal to your sensitivity at the eardrum. Now how they calibrate things to normalize those two tests, I don’t know.

Back to headphones: There are some headphones that by design deliver sound energy through parts in contact with the skull, e.g. the pads, as I believe is the case with the Meze Liric. So perhaps something is going on there.