Distortion down to -300 dB, what exactly does that mean physically?

[voodooless]

As some of you guys might know, the famous Rob Watts has mentioned on more than one occasion that he can hear and measure distortion down to -300 dB. Cited by @amirm here for instance. He also says something similar in this video:

Staring at roughly the 17min mark.

Now I was thinking about a thought experiment that you guys can probably help me with, especially the physics nuts. I'd like to explore what this actually would mean on a physical level? So how little is the voltage change? How many electrons would that actually need? And if we're talking, what about air pressure difference? But you guys can come up with other stuff. Probably the infamous shoutometer will come up, which I find rather uninteresting because it just not model the practical world very well.

So I had a crack at voltage. So let's see how small of a voltage difference -300 dBV is. Well, I had to resort to Wolfram Alpha because my go-to calculator gave me just zero So Wolfram was more helpful and gives 1*10^-15, which is 1 fV RMS (so femtovolt). To count electrons, we need to add some assumptions: we need current. So let's assume it's a DAC, and it's syncing into 20K input impedance of a pre. Now we can calculate the number of electrons needed for this 1 fV voltage. So 1A has 6.24 quintillion electrons (10^18). So, how many electrons does out -300dbV signal have into 20k? Well, it's not even 1 electron per second: it's 0.312 Already feeling silly Rob?

Hope you guys can fact check me on this. Would be fun to do the same for the air pressure difference.. Once again my go-to calc gives 0

 

[solderdude]

I don't think that's what he is claiming.
He can't measure -300dB obviously nor can he hear something in level 150dB below the hearing limits.

What the good man claims is that in the digital domain (enough bits are needed) he states that he can hear audible differences between filters that seem to only show some simulated differences as low as -300dB.

Of course it is a bunch of nonsense but that's what he appears to mean. The man knows darn well about practical noise levels.
With those statements he wants to affirm to potential buyers that his 'stuff' matters and even an old geezer like him can hear that.
Advertising ... that's it.

 

[bigjacko]

Physically means he can hear what Elon is singing on Mars.

 

[voodooless]

I don't think that's what he is claiming.
He can't measure -300dB obviously.

What the good man claims is that in the digital domain (enough bits are needed) he states that he can hear audible differences between filters that seem to only differ in some differences as low as -300dB.

Yes, he also claims that indeed. I did see a video where he indeed made the claim about distortion directly, but can't seem to find it anymore... could be imagining things. But we're still talking about distortion here, even if it's in the frequency response domain. So, if I have digital files with two tones of different frequency and the exact same amplitude, and a DAC with -300dBv passband ripple, there would not even be one electron per second of difference at the output of the DAC, if you were the tones so that they would align optimally in the high and low part of the ripple.

Physically means he can hear what Elon is singing on Mars.

No, a vacuum prevents us from ever hearing any sound from Mars, as does our local noise environment.

 

[Frank Dernie]

I am impressed
My way to get an idea of the audibility of distortion was to play music at my normal level then start to reduce the level. By the time I have turned it down by 60dB I can just barely hear it. Now I am not listening to distortion artefacts, of course, but what I am doing is listening to sound as loud as the distortion artefacts would be.
Now my judgement is that were this sound level to be playing whilst I was listening to music at my normal level I would be unlikely to hear it - since I can barely hear it on its own.
That is a good enough practical evaluation for me and so far nobody has come up with any reason I am misunderstanding the situation.
Being able to hear a change that creates an artefact another 240dB quieter is impressive. Or is completely ludicrous.

 

[solderdude]

Yes, the -300dB (not dBV) claim is nonsensical.
He should demonstrate his abilities which he never will so I just ignore bold statements like the ones he makes.
Those that fall for it.. well.. to them Chord will sound 'better' because they believe it will.
When folks want to pay extra for the story, the build quality and looks and can afford it then no harm is done.

I won't buy it, that what he claims nor the products.

 

[alex-z]

Well considering 194dB is the peak SPL possible within Earths atmosphere (anything more is simply a shockwave), and Microsoft's anechoic chamber is -20dB, a 300dB differential isn't even possible, let alone audible.

 

[voodooless]

Yes, the -300dB (not dBV) claim is nonsensical.

I think we all know the claim is nonsensical. The whole point of the topic is to explore how much so. It's more a fun thought experiment than some serious critique. Meanwhile, if we can poke some (good natured) fun at the expense of Rob, all the better.

 

[voodooless]

Well considering 194dB is the peak SPL possible within Earths atmosphere (anything more is simply a shockwave), and Microsoft's anechoic chamber is -20dB, a 300dB differential isn't even possible, let alone audible.

Actually, they are only 3dB of the quietest possible in normal air. Air molecules colliding are at about -23 dB.

 

[solderdude]

When one assumes 1uV as a very low practical noise level then for the DAC to have a 300dB dynamic range the max output voltage would have to be 2,828,427kV

 

[Jimbob54]

I don't think that's what he is claiming.
He can't measure -300dB obviously nor can he hear something in level 150dB below the hearing limits.

What the good man claims is that in the digital domain (enough bits are needed) he states that he can hear audible differences between filters that seem to only show some simulated differences as low as -300dB.

Of course it is a bunch of nonsense but that's what he appears to mean. The man knows darn well about practical noise levels.
With those statements he wants to affirm to potential buyers that his 'stuff' matters and even an old geezer like him can hear that.
Advertising ... that's it.

I was going to ask that. Regardless of his hearing claims, how can he measure miniscule linearity? The AP555 reaches its limits around -140dB so? (Around 18 minutes) . At which point I am way outside my very limited understanding.

 

[Don Hills]

... Now my judgement is that were this sound level to be playing whilst I was listening to music at my normal level I would be unlikely to hear it - since I can barely hear it on its own. ...

Bill Waslo created some string quartet / choral test tracks with a sousa band mixed in at various levels. Its almost imposssible to pick out the sousa band even when you know it's there. Sadly I can't find a link to the tracks, hopefully someone with stronger google-fu can find them.

 

[escksu]

As some of you guys might know, the famous Rob Watts has mentioned on more than one occasion that he can hear and measure distortion down to -300 dB. Cited by @amirm here for instance. He also says something similar in this video:

Staring at roughly the 17min mark.

Now I was thinking about a thought experiment that you guys can probably help me with, especially the physics nuts. I'd like to explore what this actually would mean on a physical level? So how little is the voltage change? How many electrons would that actually need? And if we're talking, what about air pressure difference? But you guys can come up with other stuff. Probably the infamous shoutometer will come up, which I find rather uninteresting because it just not model the practical world very well.

So I had a crack at voltage. So let's see how small of a voltage difference -300 dBV is. Well, I had to resort to Wolfram Alpha because my go-to calculator gave me just zero So Wolfram was more helpful and gives 1*10^-15, which is 1 fV RMS (so femtovolt). To count electrons, we need to add some assumptions: we need current. So let's assume it's a DAC, and it's syncing into 20K input impedance of a pre. Now we can calculate the number of electrons needed for this 1 fV voltage. So 1A has 6.24 quintillion electrons (10^18). So, how many electrons does out -300dbV signal have into 20k? Well, it's not even 1 electron per second: it's 0.312 Already feeling silly Rob?

Hope you guys can fact check me on this. Would be fun to do the same for the air pressure difference.. Once again my go-to calc gives 0

I don't think your calculations are correct. This is because its definitely sound is not measured in dBV.

 

[HammerSandwich]

Well considering 194dB is the peak SPL possible within Earths atmosphere (anything more is simply a shockwave)...

Turn down that $&%^ing hi-fi, Rob! You're clipping the atmosphere again! - Rob's mother

 

[Vini darko]

@RayDunzl. Your usful chart helps here
https://www.audiosciencereview.com/forum/index.php?threads/the-shoutometer.2555/

 

[rkbates]

When one assumes 1uV as a very low practical noise level then for the DAC to have a 300dB dynamic range the max output voltage would have to be 2,828,427kV

At least you don't have to worry about cable lifters

 

[amirm]

I attended of his latest talks. At the end I asked him if he could hear such differences blind. He said he didn't believe in blind tests because they are too stressful. I let him be at that point.

 

[roskodan]

Screw distortions, all I need is those 18W RMS 8Ω of the Hugo TT 2 output buffer. XD

Uh, oh, anyone sending the Hugo TT 2 and M Scaler in for review? :3

I know amirm said their UI is a diabolic mind torturing exercise... I love it. ¯\_(ツ)_/¯

 

[RayDunzl]

How many electrons would that actually need?

If talking electrons, they are usually measured in Coulombs.

Coulomb is defined as 6,241,509,074,460,762,607.776 electrons

An Ampere is a Coulomb of electrons passing a point in one second.

-300 dB is a ratio of 1 to 8.91e-16, or 0.000000000000000891

If I have the math right -300db in current would be 5,561 electrons passing a point in a second if compared to an ampere.

If starting with a milliamp (closer to signal level), 5 electrons.

If I have the math wrong it's mostly in the 10log vs 20log part.

 

[roskodan]

When one assumes 1uV as a very low practical noise level then for the DAC to have a 300dB dynamic range the max output voltage would have to be 2,828,427kV

If I remember correctly, in his lectures?, the focus was the time domain, what sampling rate would that be I wonder? XD

dynamic range ~= no. of bits x 6 dB -> 2 ^ 50 = 1.12589991e15 Hz

The problem is, does his dac support such resolution back to front? No way!