Acoustic Measurements: Understanding Time and Frequency

Hi Mark. Good to see our resident experts here :).

Nice note on a difficult to communicate topic. The key I think many miss is what does a practical ideal even look like? The comments from Raffle speak directly to this. The notion of fine time resolution and bass frequencies is mutually exclusive. Without sufficient time duration, those frequencies don't exist, and they can't be measured. What might be useful is to first loop back a subwoofer signal (complete with low pass filter) and show the decay plot of the electrical signal only. It can't get any better than this.
Agree and I think I noted that there is little reason to run waterfalls and stare at them :). I personally would make the correction in frequency response and not worry about what the time domain is doing. Agree that the standard amplitude response is easier on the eye with respect to the decay. I ran the waterfall because that also addressed what Ethan had done on his web site.
 
Thanks. This is more clear. Looks like the tuned absorber is operating at a higher frequency since the noticeable improvement is at 50 Hz or so in amplitude. At 36 Hz, the amplitude has not changed. The change in ringing may not be that but rather, just lost energy. Your min level is still too high relative to what I think the noise floor of your room is. Can you run the noise test with no output as I did to make sure?

The absorber membrane is tuned around 37 Hz - I checked it an accelerometer and a generator. Can you explain me what do you mean by "just lost energy"? Is it the function of the bass trap?

I will carry the noise measurement soon.
 
I meant any absorber in the room is going to take out some of the bass energy. To the extent the reverb tail was almost in the noise anyway, it may have bit the dust that way :). I am speculating because I am not seeing amplitude reduction. So the noise response would be good to see.
 
Terry, again I am not trying to make this article about how to fix the bass. The article is to demonstrate mathematical principals that are in play. These principals are disputed by Ethan with the conclusion that only acoustic products are proper solutions. That just isn't so in this region. So no, in here and now, I am not trying to convince you of anything but the core mathematics of the problem. If you agree that by changing frequency response I also correct the time domain, then we are done.

We are done?:D

Nope, not completely. ;)

As you should know by now, I am completely on *your* side when it some to the utility of dsp solutions. Also, I get that it is not a treatise on bass correction. Firstly, regarding Ethan, perhaps it was just plain old 'bad luck' he chose to test the theory with audessy. That Sean Olive too had similarly poor results seems to strengthen that thought. IF that lies somehow at the bottom of this, then Ethan is making the mistake of extrapolating unfairly from a limited test base.

Oh, I should also add not for a second do I dispute the science here. (what seems to be the audio equivalent of the uncertainty principle) I think it only fair to point out that all this applies strictly to minimum phase conditions. The question then becomes 'are there NON minimum phase conditions that we can come across in everyday listening'? If so (and I hinted at this question earlier) then under those circumstances 'mere' eq won't fully solve the problem. I guess it remains to be seen if acoustic solutions will solve it, but that's another ball game.

Hopefully my quoting will isolate the right graphs!

i-2MGmS4B.png




i-mKkg4Dd-X2.gif


Ok, good enough. (hmm, the bolded text seems to be embedded with the graphs, oh well)

TBH, I don't really see anything that is definitively 'reduction in ringing' other than your say so based on others interpretation of these graphs. For starters, what would be a definition of ringing we can all agree upon?

I initially though these might have been simple impulse graphs, tried running a few just before yet I did not get anything that remotely resembled them, so can't chase that further sadly.

Still, at least one way I can see those 'time' graphs is the following. We have amplitude vs time. To me, I don't really see any change in time. All the peaks and valleys exactly co-incide, all we see is a reduction in the corresponding magnitude at those times. That is fully in keeping with the knowledge that we have reduced those amplitude with eq.

Somewhere recently I recall someone using a pendulum as an analogy? Might have been this thread. Anyways, keeping with that analogy what I see is a lesser time to come to a stop simply because it had a lesser initial impetus. the basic parameters of the pendulum remain unchanged (from very vague memory it is only dependent on weight and length???) Similarly here, we have not 'changed' the room parameters, we have simply given the bob less of a push.

I mean if 'ringing ' is a room function, we can only really change it by changing the room no?


This and the fact that time and frequency are at war with each other with respect to resolution are the central points. I think the case is made clearly here for what is right and if we agree, then Ethan's notion that such processing is not as good because it only deals with half the universe creates the wrong impression of the technology.

Yeah, for sure. But we also have to be wary about creating yet another 'false' notion?

Beyond that, if you separate your bass and allocate it to multiple subwoofers, and optimize their operation, you can get remarkably flat response even without acoustic products aimed at bass frequencies. This is not to say you should not use acoustic products. But that you are better off starting with those techniques and then see what is left over to be corrected. If you cannot deploy DSP or multiple subs then acoustic products are your only means.

"I canna argue with that capt'n.'
 
Very interesting discussion, guys - it's what WBF does best!
I take the point that if the amplitude of the ringing is low enough then it is probably inaudible but is this the same as saying that fixing the Freq response solves the time response? Don't think so in the strict sense as I imagine there are still moments where the amplitude of the ringing will still be audible.

Just to throw in a curve ball - I posted this paper on a retired thread but it seems cogent to this discussion (but not central to it) - "Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle" http://arxiv.org/pdf/1208.4611.pdf Maybe the mathematics isn't everything???
 
(...) Agree and I think I noted that there is little reason to run waterfalls and stare at them :).

As far as I understand you are mainly questioning the way REW or similar software computes the waterfalls at very low frequencies?
 
As far as I understand you are mainly questioning the way REW or similar software computes the waterfalls at very low frequencies?
No, I am not questioning REW. What it does is governed by the underlying restrictions of time vs frequency resolution so it is not possible to do better (there is an advanced point regarding windowing of the edges which I won't go into). What I meant is that if you accept that time domain ringing similarly improves with pulling down the peaks, other than satisfying one's curiosity, then there is no reason to look at time domain response. Simply run the standard frequency response ("SPL" graph in REW lingo) which you can then run at the highest resolution with no smoothing. Once there, focus on pulling the peaks down there. That's all I did and as I said, the subjective improvement was really high. It took me just a few hours to do all of this. Same if you are using acoustic products. If there is no improvement in frequency response, then it is not doing its job as our ears are very sensitive to the anomalies there. Ringing is secondary to that.
 
No, I am not questioning REW. What it does is governed by the underlying restrictions of time vs frequency resolution so it is not possible to do better (there is an advanced point regarding windowing of the edges which I won't go into). What I meant is that if you accept that time domain ringing similarly improves with pulling down the peaks, other than satisfying one's curiosity, then there is no reason to look at time domain response. Simply run the standard frequency response ("SPL" graph in REW lingo) which you can then run at the highest resolution with no smoothing. Once there, focus on pulling the peaks down there. That's all I did and as I said, the subjective improvement was really high. It took me just a few hours to do all of this. Same if you are using acoustic products. If there is no improvement in frequency response, then it is not doing its job as our ears are very sensitive to the anomalies there. Ringing is secondary to that.

Just to clarify one point before I go on - you are using the word ringing as a synonym of decay?
 
In this context it literally means how long the note lasts. So if you like you can call it decay.

OK. What is worrying me is that I now understand the mathematical limitations of the nice waterfalls of REW. However, in my previous ignorance I have used the waterfall graphs to develop some treatment in my room with success. My room is narrow and long, I focused in the second and third longitudinal modes, after reading Toole about room modes, but also because analysis of the waterfalls given by REW suggested (it seems wrongly) that the delays at 36 and 54 Hz were too long. I used the waterfall to experimentally tune two large bass membrane traps (6'x2'x1.5' each ) at 36Hz and later positioned them in a particular position that used with a previous existing set of RPG abbfusors to reduce the decays at 56 Hz. Any modification in the bass traps resulted in measurable differences in the waterfalls that agreed with the tuning checked using a piezo accelerator. During development the bass traps were positioned in wheeled platforms and I could take them out and in of the room and all measurements seemed to confirm the predictions. Although the changes in FR are very small the waterfall graph shows a 15dB variation at the level of the decay at 36 Hz at 600 ms with or without bass trap. This result is repeatable. What is the meaning of this measurement? Is REW being biased by my expectations? ;)
 
Hi Mark. Good to see our resident experts here :).


Agree and I think I noted that there is little reason to run waterfalls and stare at them :). I personally would make the correction in frequency response and not worry about what the time domain is doing. Agree that the standard amplitude response is easier on the eye with respect to the decay. I ran the waterfall because that also addressed what Ethan had done on his web site.

No, I am not questioning REW. What it does is governed by the underlying restrictions of time vs frequency resolution so it is not possible to do better (there is an advanced point regarding windowing of the edges which I won't go into). What I meant is that if you accept that time domain ringing similarly improves with pulling down the peaks, other than satisfying one's curiosity, then there is no reason to look at time domain response. Simply run the standard frequency response ("SPL" graph in REW lingo) which you can then run at the highest resolution with no smoothing. Once there, focus on pulling the peaks down there. That's all I did and as I said, the subjective improvement was really high. It took me just a few hours to do all of this. Same if you are using acoustic products. If there is no improvement in frequency response, then it is not doing its job as our ears are very sensitive to the anomalies there. Ringing is secondary to that.

I would argue that you are mostly correct below ~100Hz, but there can be benefit or further confirmation/insight in looking at the waterfall plots. If you dig through some of what has be posted at HTShack related to PEQ & REW, you will see a bit of discussion noting how more precise matching of Q and Fc can be significant in reducing ringing. A quick look at the waterfall plot before and after or while fine tuning filters will give some insight as to how well you have matched the filters to the acoustic issues. It's not required, but can be useful, especially for those less experienced in determining what is "good enough" in a frequency response.

As was loosely discussed in the early posts, our ears respond to acoustic power, not momentary intensity. If you smooth the frequency response and still hear some excessive energy, a waterfall is a good second look to see what's going on. While the vast majority of issues are minimum phase, not every issue is, and not all will disappear with EQ. Structural resonances like a floor acting like a trampoline can be particularly annoying, a sometimes the best subjective results come from further reducing stimulus to that resonance.

I would also take issue with the note about room treatments having to make a noticeable impact on frequency response. IMO wide band treatments can have the most audible effect in the 50-250Hz range (on up to ~500Hz or so is certainly important as well). Having measured many rooms before & after adding treatments targeted to have real effect below 250Hz, the observed frequency response changes are often 1-4dB, and the 4dB examples are much less common than 1-3dB. If you instead look at a waterfall measurement you will see changes in the decay at those frequencies you observe a small change. To translate this to useful terms. In terms of sound power (intensity over time) a ridge of energy dropping in 1/2 the time it did before treatment has half the acoustic power.

In the end you also have to look at what tools available to change the system. If I'm working with physical acoustic treatments I would want to be looking at a waterfall measurement. If I'm adjusting the input signal with electronic EQ/PEQ I would start with magnitude response.
 
Thanks for the comments Mark. My focus here is strictly for low frequencies below 100 Hz. Above 200 Hz, the perceptual effects of time domain is very different. We start to get into the land of psychoacoustics which I am trying to avoid by staying with very low frequencies :).
 
Amir,
While waiting for your comments I looked in my files and found some data from RPG about bass traps. One of reasons I got REW as a tool to check bass treatments and started carrying measurements was that RPG used waterfall graphs to illustrate the performance of their very low frequency absorbers. Please see the attached picture from the RPG Modex™ Edges brochure.

I have to say that at that time if the Modex Edge corners were easily available in my country I would have bought them immediately! These waterfalls looked nice down to 20Hz.
 

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Amir,
While waiting for your comments I looked in my files and found some data from RPG about bass traps. One of reasons I got REW as a tool to check bass treatments and started carrying measurements was that RPG used waterfall graphs to illustrate the performance of their very low frequency absorbers. Please see the attached picture from the RPG Modex™ Edges brochure.

I have to say that at that time if the Modex Edge corners were easily available in my country I would have bought them immediately! These waterfalls looked nice down to 20Hz.
Hi Micro. I have seen that brochure. You may know this already but what they show is not the result of a single unit but many. They don't say how many :). We can tell there is a lot of absorption from the much reduced levels in bass. The overall level in "before" is -10 db while the after, is -25 or so for a total reduction of 15 db (scales are different in each graph). If you simply lowered the signal by 15 db, you would also get a fair bit of reduction in ringing! A bunch of the tail would wind up in the noise.

Anyway, what is different about their case is that they show both frequency response change, and massively so, and time domain. Here is the SPL graph:

i-LdXMjT8-X2.png


You could by just looking at this one display know that you have done good in smoothing out those peaks, putting aside the loss of total energy in that region. One advantage of electronic control of those peaks is that you have better control of how far you pull down those peaks. You can listen quickly before and after and adjust.
 
Hi Micro. I have seen that brochure. You may know this already but what they show is not the result of a single unit but many. They don't say how many :). We can tell there is a lot of absorption from the much reduced levels in bass. The overall level in "before" is -10 db while the after, is -25 or so for a total reduction of 15 db (scales are different in each graph). If you simply lowered the signal by 15 db, you would also get a fair bit of reduction in ringing! A bunch of the tail would wind up in the noise.

Anyway, what is different about their case is that they show both frequency response change, and massively so, and time domain. Here is the SPL graph:



You could by just looking at this one display know that you have done good in smoothing out those peaks, putting aside the loss of total energy in that region. One advantage of electronic control of those peaks is that you have better control of how far you pull down those peaks. You can listen quickly before and after and adjust.

Amir,

Thanks. I had seen their reference about using a lot of units, and even in their literature about the other types of bass traps they warn that considering the involved areas a minimum of six units in needed to show any significant absorption. I could guess that they are using around 18 units in this test by the placement description.

But my concern in this thread is mainly on understanding the limitations of the waterfall type analysis bellow 100 Hz. Going through many sites, even reputed manufacturers and professionals I see they seem to use it as a tool for the bass zone of rooms - sometimes specifically in the 40-100 Hz band. Frequently I see references to RT60 measured in the 20, 40, 63, 80 and 100 bands. Is this type of information misleading or can it be used for room diagnostics and correction?
 
As the thesis of my original set out to show, there is no question that waterfall displays are subject to misleading information. The math simply cannot be escaped. I showed earlier what happens when you go from coarse time resolution to fine:

Coarse:
i-TJJ8khP-L.png


Fine:
i-xjBLBRM-L.png


The coarse resolution shows 2X higher reverbration tail than the fine resolution. I think we both agree that if we want to look at time domain, then increasing resolution there is only goodness. So one is faced with the fact that on this basis alone, we were scared to think there was more problem in time domain then there really was. To wit, with fine grain resolution in time, we would up with poor resolution in frequency. You would readily accept that you would NOT want to optimize the frequency response using the second image as there is too much smoothing of frequency response. Yet, when tables are turned and we are looking at time, we seem to happy to proceed with the poor resolution in that domain with the same problem.

These tools do have value if you know the limitations and can work around them. If you do not, you can easily be looking at the wrong data. This is why I emphasize, as does Dr. Toole and other Harman researchers to simply look at the frequency domain response. Run that with little to no smooth for bass and optimize that. Once there, you will have far better performance. What the time domain response has or has not done is really secondary in that regard.

Does this run counter to a ton of reporting and analysis out there? Sure. But the fact that so many people do things doesn't make it right. I am about to put up my WSR article on first reflections and the issues around that. 99% of the what is talked about online runs counter to that research. But the research is incredibly strong and convincing if one digs in. The fact that so many people are not exposed to it or are but look the other way doesn't remove its weight and convincing conclusions it creates for us :).
 
As the thesis of my original set out to show, there is no question that waterfall displays are subject to misleading information. The math simply cannot be escaped. (...)
Does this run counter to a ton of reporting and analysis out there? Sure. But the fact that so many people do things doesn't make it right. I am about to put up my WSR article on first reflections and the issues around that. 99% of the what is talked about online runs counter to that research. But the research is incredibly strong and convincing if one digs in. The fact that so many people are not exposed to it or are but look the other way doesn't remove its weight and convincing conclusions it creates for us :).

OK, but is there any useful information that can be taken from the "misleading" graphs I have shown below 100 Hz? After all, they showed that introducing a bass trap tuned at 36 Hz reduced the decay at this frequency at 600 ms by 15 dB.

I have to say that I was somehow expecting your conclusions since after I read the F. Toole pages - it is why I have been postponing a promised specific objective thread on the acoustics treatments of my room. It seems that for these matters I have to rely mostly on subjective evaluation or just believe that FR is all we have to care. :eek:
 

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We are done?:D

Nope, not completely. ;)
Darn it :).

Firstly, regarding Ethan, perhaps it was just plain old 'bad luck' he chose to test the theory with audessy. That Sean Olive too had similarly poor results seems to strengthen that thought. IF that lies somehow at the bottom of this, then Ethan is making the mistake of extrapolating unfairly from a limited test base.
It is not as much that it was Audyssey but the fact that he didn't pay attention to the fact that the EQ did not do what it was supposed to: pulling down the peaks. Further, he mixed up auto-eq with EQ.

Oh, I should also add not for a second do I dispute the science here. (what seems to be the audio equivalent of the uncertainty principle) I think it only fair to point out that all this applies strictly to minimum phase conditions. The question then becomes 'are there NON minimum phase conditions that we can come across in everyday listening'?
As Mark indicated, there are room conditions that are non-minimum phase. In this context though, which is application of EQ to pulling down the peaks, experience and research shows that they are minimum phase phenomena. Here is Dr. Toole:

"For now, it is sufficient to say that low-frequency resonances in
rooms behave as minimum-phase phenomena, meaning that if there is a prominent
“bump” in the frequency response, it is probable that this will be heard as
excessive loudness at that frequency and that for transient sounds, there will be
bass “boom” at that frequency. Using equalization to reduce the bump also
attenuates the ringing so both problems are solved simultaneously."


What is potentially not minimum phase are the nulls. We know this intuitively as the reflection is zeroing out the wave. Changing the level of the source changes the level of reflection so nothing gets accomplished.

If so (and I hinted at this question earlier) then under those circumstances 'mere' eq won't fully solve the problem. I guess it remains to be seen if acoustic solutions will solve it, but that's another ball game.
This is where multiple seats and SFM come to help us. Here is a four sub configuration at quarter points in the room (with ceiling the realistic implementation):

i-9ZjsPjN-XL.png


We see that for sub frequencies design decisions such as these eliminate resonances to be fixed.

Hopefully my quoting will isolate the right graphs!

i-2MGmS4B.png


i-mKkg4Dd-X2.gif


TBH, I don't really see anything that is definitively 'reduction in ringing' other than your say so based on others interpretation of these graphs. For starters, what would be a definition of ringing we can all agree upon?
Look to the right in the first image. That is showing an impulse that goes way "instantly" yet the room keeps playing that note at lower and lower levels until it gets down to noise. Application of EQ, the solid line, shows that flattening the peak in frequency response, likewise lowered the amplitude of ringing and hence, the amount of time it lasts audibly in time. I did not show the graph for the second research but I can. It is very similar to Dr. Toole's.

What the EQ does is that it generates a time response that is reverse of the ringing on the right so the two cancel out (in the ideal case).

Somewhere recently I recall someone using a pendulum as an analogy? Might have been this thread. Anyways, keeping with that analogy what I see is a lesser time to come to a stop simply because it had a lesser initial impetus. the basic parameters of the pendulum remain unchanged (from very vague memory it is only dependent on weight and length???) Similarly here, we have not 'changed' the room parameters, we have simply given the bob less of a push.

I mean if 'ringing ' is a room function, we can only really change it by changing the room no?
The room acts like a pendulum at certain frequencies. If we measure the pendulum effect, and inverse how much energy we put into the pendulum, we can nullify its effect. This is no different than if you had an amp with a 2 db peak and I put a -2 db eq in front of it. By definition, minimum phase systems are reversible so they work the same way. But sure, you can also change the room. Question is what is easier and more convenient. I think better placement and number of subs and EQ are far easier than using acoustic products to tame low frequencies.
 
Darn it :).

Ahh, flushed you out! :D

It might pay to reinforce a few things first. To start with, how about something I agree with completely. Hopefully to show I am not challenging you per se, but trying to get a better handle on it all.

But sure, you can also change the room. Question is what is easier and more convenient. I think better placement and number of subs and EQ are far easier than using acoustic products to tame low frequencies.


Tis what I do and have done. Whether we factor in the cost and complexity is another matter for each to decide. And now might be a good place to mention (have not thought to mention it 'anywhere' till just now tbh) that you can easily stuff it up! We are taking 'as granted' that it is a properly set up and competent install. It is trivially easy to mess it completely, esp if we take the stereotypical audiophile with an abhorrence of measuring and loaded with typical audiophile myths (dunno, big drivers are slower than small drivers as but one example in a million!) Why could such a myth arise? How about a poor install.

As a diyer that did not particularly occur to me till now, it could very well tip the scales in favour of room treatment.

Again, I 'get' the math and concept that the two are inextricably entwined and opposite sides of the same coin. Minimum phase behaviour can be treated by eq.

I get the idea and do use multiple subs/bass sources (with sufficient power and capability) with SFM (if sfm means something like sound field management ?)

i-9ZjsPjN-XL.png




Look to the right in the first image. That is showing an impulse that goes way "instantly" yet the room keeps playing that note at lower and lower levels until it gets down to noise. Application of EQ, the solid line, shows that flattening the peak in frequency response, likewise lowered the amplitude of ringing and hence, the amount of time it lasts audibly in time. I did not show the graph for the second research but I can. It is very similar to Dr. Toole's.

(Dang, got rid of the wrong graph!!! I refer to the other one, just above.)

Yep, this is the graph I have questions about. Do you know how it is generated? Is it at the lp (has to be), what program type does it use? I have never seen anything like it in my travels so have not the foggiest how to duplicate it.

I do NOT see (necessarily) a lowering of ringing. I DO see a lowering of amplitude. I also look at the left graph and note (maybe significant) that 'basically the entire range has been reduced', that filter, whilst centred at a certain frequency with suitable q has an effect across (almost) the whole range in question. Hence yes, it takes less time to sink into the noise floor. Earlier here I used the example of less push of a bob of the pendulum, elsewhere I used the examp[le of having the same brakes, but taking less time to stop from 60 than at a hundred.

That is what I see in the right hand graph. I am not saying *your* interpretation is wrong, just that I can see an equally valid (?) explanation.



The room acts like a pendulum at certain frequencies. If we measure the pendulum effect, and inverse how much energy we put into the pendulum, we can nullify its effect. This is no different than if you had an amp with a 2 db peak and I put a -2 db eq in front of it. By definition, minimum phase systems are reversible so they work the same way.

I guess this is the crux of my question...are there different pendulums at different frequencies. Sure, swing them all different amounts (giving us the smooth equal amplitude FR we see and want) YET, due to the properties of each individual pendulum they decay at different rates.

Ie ringing.
 
Ahh, flushed you out! :D
No, I have just been busy getting my next article out. I will be posting that shortly on first reflection. It is a long article with a good number of pictures which makes web publishing difficult.

I get the idea and do use multiple subs/bass sources (with sufficient power and capability) with SFM (if sfm means something like sound field management ?)
Yes, that is SFM. It is the science of driving multiple subs differently and with it, solve a key problem which is the fact that rooms are not symmetrical.

Yep, this is the graph I have questions about. Do you know how it is generated? Is it at the lp (has to be), what program type does it use? I have never seen anything like it in my travels so have not the foggiest how to duplicate it.
The graph is generated using computer modelling. The line you see is the average response for a 16 seat location in the center of the room so easily encompasses the typical listening position. Before you worry about the average vs a single point :), these optimized sub locations work their magic by cancelling room modes. As such, the seat to seat variation within that central area is sharply reduced. Actual simulation shows next to no variations between seats in the sub frequencies. The variations start to show about 75 to 80 Hz but even there is very small.

I do NOT see (necessarily) a lowering of ringing. I DO see a lowering of amplitude.
That's all you need to see :). If the room mode is eliminated, then there is no reason to wonder about time domain. The resonance is gone and gone with it are time domain ringing.

I also look at the left graph and note (maybe significant) that 'basically the entire range has been reduced', that filter, whilst centred at a certain frequency with suitable q has an effect across (almost) the whole range in question.
I think you are reading the graph caption wrong. Most of the magic came from using 4 subs. What the subs do is that they eliminate nasty nulls. But they also at times create more energy at certain frequencies. The EQ they talk about is applied to that peak and bringing that down to the level of the rest of the graph. So it is not one magic filter that gave you flat response.

I guess this is the crux of my question...are there different pendulums at different frequencies. Sure, swing them all different amounts (giving us the smooth equal amplitude FR we see and want) YET, due to the properties of each individual pendulum they decay at different rates.

Ie ringing.
That's correct.
 

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