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Resolution, speed, do these things really exist?

NTK

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You still don’t address the decay.
What is the difference when the system is LTI? A rectangular pulse is just a summation of two step functions, one positive and one negative with a delay.

Rectangular Pulses.png

The response will just be summation of the two step responses. As a matter of fact, you can compute the system response to an arbitrary input if you know the system's step response by decomposing the input into a series of steps. Doing this with the system impulse response is the much more common way. (See link)
 

bkdc

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What is the difference when the system is LTI? A rectangular pulse is just a summation of two step functions, one positive and one negative with a delay.

View attachment 192759
The response will just be summation of the two step responses. As a matter of fact, you can compute the system response to an arbitrary input if you know the system's step response by decomposing the input into a series of steps. Doing this with the system impulse response is the much more common way. (See link)

This is not electrical or digital. It is mechanical. The speaker cone is VIBRATING and moving. And the vibration does not stop instantaneously. It rings. And as it continues to vibrate after the electrical signal has stopped, it smears the sound. You want instant on and instant off reflected in the physical movement of the transducers. Or do you think a car can go 0 to 60 in 0.0000001 seconds and then stop again in 0.0000001 seconds too? At the beginning of the signal, the sound _does_ instantaneously start... or is instantaneous enough not to make a difference. It does _NOT_ instantaneously stop. The transducer continues to vibrate for fractions of milliseconds to milliseconds. Resonances and speaker cone break-up issues show up here. A speaker that has a poor spectral decay smears sound. You can think of it as a time delay distortion.
 
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bkdc

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Why would you believe a different model applies to mechanical systems as for electrical systems?

Math is math yo…

Look at what was stated above. He is trying to explain a physical transducer with an explanation of an electrical signal. If you think they are the same, then I don't know what to say.

1647381176027.png


BTW, for the Revel fans, look at those two tweeter dome break-up resonances. Thankfully they are at very high frequencies that are inaudible to anyone 30 years or older. BTW this is a instrinsic tweeter design problem and I suspect if Amir cared about this kind of graph the way he cares about those pesky jitter spikes, he would make a harsh comment . And find me a mathematical explanation that has anything to do with a square wave. This is a very typical behavior of a dome tweeter and is seen on even high end tweeters and speakers. I'm not bashing Revel. The M105 with the same tweeter will have the same problem. It's still an awesome bookshelf speaker and has no glaring flaws.

I firmly believe you can judge an amplifier purely based on measurements. And I think you can also judge a DAC mostly on measurements alone (this is outside of reliability and build quality). I do not think you can do the same for a headphone or speaker. You need to listen and judge whether you like the sound or not although some measurements are helpful.

But back to the original topic on the perception of "speed" in a headphone. My take on this is the same way you would judge tight bass versus loose sloppy bass on a subwoofer. You want sound to be tight and accurate and not loose and sloppy. Instant on AND instant off.
 
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Beave

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Look at what was stated above. He is trying to explain a physical transducer with an explanation of an electrical signal. If you think they are the same, then I don't know what to say.

View attachment 192768

BTW, for the Revel fans, look at those two tweeter dome break-up resonances. Thankfully they are at very high frequencies that are inaudible to anyone 30 years or older. BTW this is a instrinsic tweeter design problem and I suspect if Amir cared about this kind of graph the way he cares about those pesky jitter spikes, he would make a harsh comment . And find me a mathematical explanation that has anything to do with a square wave. This is a very typical behavior of a dome tweeter and is seen on even high end tweeters and speakers. I'm not bashing Revel. The M105 with the same tweeter will have the same problem. It's still an awesome bookshelf speaker and has no glaring flaws.

I firmly believe you can judge an amplifier purely based on measurements. And I think you can also judge a DAC mostly on measurements alone (this is outside of reliability and build quality). I do not think you can do the same for a headphone or speaker. You need to listen and judge whether you like the sound or not although some measurements are helpful.

But back to the original topic on the perception of "speed" in a headphone. My take on this is the same way you would judge tight bass versus loose sloppy bass on a subwoofer. You want sound to be tight and accurate and not loose and sloppy. Instant on AND instant off.

There aren't two tweeter break-up resonances. The lower frequency resonance that you see is the same on all of JA's plots - it's from the line rate of his monitor, not from the speaker. The one that *is* from the speaker is tiny (of short duration and of low magnitude), and it's above 20kHz. So it's likely a total non-issue.
 

Merkurio

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No need to go that far. I tried my old DT 1990 with both balanced and analytical pads. Balanced pads have more bass, analytical one little leaner. However no matter how i eq the analytical pad, it didn't gave me the punchy bass of balanced pads.

That's because the pads interact in different ways (given their own materials and properties) with your own head shape and ears, thus changing the whole FR, not the bass response alone.

With the analytical pads boosting other frequencies aside of bass, you may well be experience frequency masking, so it's not as simple as "bass go brrr" using EQ and then boom, the same sound.

It's not magic guys, everything is defined with FR and the interactions that happen within it, even the hardest things to explain out there, that's why acoustical principles haven't changed dramatically from the last century.
 
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reasons

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A lot of great information by some knowledgeable people here. Unless I’m missing something if a headphone measures well all around, the only subjective thing differentiating them is slight deviations in the FR, comfort and esthetics..

There is one thing that needs to come from all of this….

A list of 10 headphones (WITHOUT EQ) that are the “OBJECTIVE” best at any price point.

Then we can all argue over which headphone subjectively looks better and is more comfortable.
 

Jose Hidalgo

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A lot of great information by some knowledgeable people here. Unless I’m missing something if a headphone measures well all around, the only subjective thing differentiating them is slight deviations in the FR, comfort and esthetics..

There is one thing that needs to come from all of this….

A list of 10 headphones (WITHOUT EQ) that are the “OBJECTIVE” best at any price point.

Then we can all argue over which headphone subjectively looks better and is more comfortable.
Define "measures well all around". What are the criteria exactly?
  • Let's assume you manage to define all the main criteria: for example distortion, group delay, etc.
  • Now you need to define their relative importance to each other (is distortion more important than group delay? etc.)
  • So you need to give them factors in order to calculate a weighted average and have an objective headphone ranking.
  • Except that those measurements aren't just numerical values! They are entire graphs, each with its own variability from 20 to 20.000 Hz.
  • So we can hardly compare them objectively, unless we are able to define a precise comparison protocol. Which looks impossible to me.
And BTW, why "without EQ"? I'd much prefer a list of 10 headphones (WITH EQ) that are the "OBJECTIVE" best at any price point.

Squeezing the best out of any given headphone. Forgetting about their default FR to focus on their objective features: driver quality, impulse response, lack of distortion, lack of internal resonances, impedance, group delay, etc. Comparing them ONLY when EQed to the SAME target curve (whatever it may be), instead of comparing apples and oranges. That's what makes sense to me. :)
 

Garrincha

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I just so happened to write a Reddit post about the topic of "resolution" and why it's not really a thing, and frequency response is the most important factor by far.

First of all, any good headphones produce distortion that is low enough not to be audible. This is helpful because it simplifies our reasoning. Now that we've put distortion aside for a second, your question can be divided into two parts:

1. Headphones/IEMs being minimum-phase systems means FR fully describes their output.

Minimum-phase is a mathematical concept that applies not just to loudspeakers. In this case, it means that at any time, the loudspeaker's movement (and the resulting sound pressure at the ear drum) is within one phase-cycle of the input signal, and does not lag behind. This means there is no such thing as "attack", "decay", "driver speed", etc because the driver is tracking the original signal perfectly in the time domain. Now, you can totally get a subjective sense of "this headphone has bad decay compared to this other headphone", but what you're describing is a difference between their FRs.

"Wait, you're saying the headphone tracks the input signal, how come different headphones sound different?" Well, how a headphone changes the input signal is called frequency response, but the point is the "not lagging behind" thing (the output is stable and time-invariant).

2. Since FR is what matters, this means FR is what determines the subjective sense of resolution and soundstage. How can that be?

So what does this mean for headphones like Stax, where the driver is super thin and lightweight? Surely the lighter membrane can accelerate faster, stop moving faster, and can therefore track every little nook and cranny of the analog waveform of the recording, thus extracting more details, right?

Well yes, but just about any driver can move fast enough to do that. They are minimum-phase, remember? The mass of the driver is important when designing a headphone because it affects FR, but that's something the headphone designers need to worry about, not us.

CD quality cuts off at 22.05 kHz, not to mention the hearing of most adults cuts off below that. This means any driver that can do that many wiggles per second (at a usable amplitude or volume) is fast enough to extract every "detail" in the recording. Even an entry-level headphone like a Koss or a cheap Grado can do this. You want your driver to go faster? Sure, there are headphones that can reach up to 40kHz or whatever, but it doesn't really matter because you can't hear details that would require more than 20kHz to describe.

"Ok, sure. If two drivers are playing a 20kHz tone at the same volume, their drivers are moving at the same speed. However, that's just a static sine wave, not a complex musical signal with multiple frequencies of varying amplitudes!"

How the driver reacts to a complex signal like music, which has multiple frequencies of varying amplitudes, that's called "frequency response" :)

When reviewers say X headphone is more detailed than Y, they are describing differences in FR, sometimes with price bias or other cognitive biases thrown in the mix. The classic example of this is Stax, not because the drivers are these super light membranes with extremely low distortion, but because they generally lack sub-bass and have exaggerated upper midrange and treble, things that get associated with the sense of "detail".

"But wait, we can EQ two headphones to have the same FR and they won't sound the same! You can't EQ Stax levels of detail into an HD650, therefore there must be something other than FR at work here!"

That's because we're not actually EQ'ing to the same FR. If two headphones have the exact same FR at the ear drum (not just on a measurement rig, but on your actual ear drums), they would sound the same. This is impossible to do in practice because a) the measurement rig's ears aren't shaped the same as your individual human ears, which affects FR of the treble, b) simply taking a headphone off your head and putting it back on will change the FR in the treble due to imprecise seating c) the bass response will be affected by how tight of a seal you can get on your head vs on the measurement rig. These are all frequency response differences, mind you.

Oratory1990 has mentioned a few things that a headphone needs in order to respond well to EQ:

- perform reliably, with repeatable seal across multiple users
- easily obtain the amount of seal that it was designed for (rip glasses users or people with large beards)
- have good quality control = little unit variation and no channel imbalance
- have a relatively smooth FR free from high-q artifacts (sharp peaks and dips)
- deform the pinna as little as possible
- have little reflections inside the earcup, especially those that lead to destructive interference. You can't fix a notch in the FR with EQ (non-flat excess group delay).
- have suitably low distortion

Most headphones do not meet all of these conditions which affect FR, so their FR will be a pain to EQ accurately. What I'm trying to explain is that there will always be a FR difference when comparing two headphones, even with EQ. Therefore, there doesn't "need" to be some other variable at play, and indeed if you do a blind test, FR tracks very closely with listener preference, but no other metric does.

With IEMs, everything I said applies, except it's even simpler. They don't interact with the outer ear, only with the ear canal. Depending on the shape of your individual ear canals, the treble response will be affected, which crinacle has covered in his article about interpretation of FR graphs. You can have quite significant variations in the treble response just by inserting IEMs differently. This may affect one's subjective notion of "detail" and "resolution". Are your ear canals identical to mine? Are you sure the two of us are not just hearing a different FR?

Now for the soundstage thing. When it comes to speakers in a room, soundstage size is determined by the directivity characteristics of the speaker, which in turn affect how the sound reflects around the room and back to the listener's ears.

In headphones, it's basically frequency response. the "room" is the interior of each ear cup, so does that mean the ear cup reflections are responsible for soundstage? Well... ear cup reflections affect group delay, which in turn affects FR, like oratory's quote explained above. There have been attempts at measuring soundstage, to questionable degrees of accuracy (see RTings' attempts). We know it is affected by the FR of the headphone and how your ears affect the FR that reaches your ear drum (called HRTF/PRTF), although there would also seem to be a "trick" where large earcups that do not touch your ears contribute to the perception of this effect (think HD800 vs HD650).
This is a very nice and reducionist expostion, but while some arguments have been given, it still remains in the realm of statement and opinion and not in validated or established scientific truth. While I agree on the points made on resolution, I am not so sure what the temporal aspects are concerned and the soundstage. We recently had the ML 5909 headphone which follows nicely the Harman curve but still not sounded very good nor had a wide soundstage.
 

Garrincha

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majingotan

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Is It Possible for Headphones to Sound Fast? (Or Slow?)​



202112_hesh_vs_sendy_FR.jpg


This chart shows the frequency response of the Hesh and Peacock headphones; I also threw in the response of Focal’s ultra-high-end Utopia headphones to hammer home the point. You can see how far off the Heshes are from the other headphones. In this case, the most important characteristic to note is the Heshes’ relative lack of output between about 2 and 7kHz. Almost all of the good-sounding headphones I measure show a peak in output around 2 to 3kHz, which not only gives them much more upper-midrange and lower-treble presence, but also makes them sound more spacious and natural because it more or less mimics what your eardrums experience when hearing good speakers in an acoustically decent room. Without that peak, the Heshes sound dull, indistinct . . . and slow. While the Peacocks and the Utopias, with much more presence right in the range where the human ear is most sensitive, sound fast.

Respectfully disagree. I have the Andromeda 2018 Blue edition IEM (I always listen without EQ) which is just as "fast" as Focal Utopia in audible hearing range which has a DIP rather than a peak at 2-4 KHz range. Compared to Sennheiser HD600 that has that 2-3 KHz peak, Andromeda and many BA IEMs are perceived to have "fast" sound subjectively speaking. Diaphragm attack (on) and decay (off) of balanced armatures is a lot quicker than a large dynamic driver physically hence the perception of "fast" sound.

Andromeda-S3-Pre-2020.jpg


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