Is my math correct?

[Mr. PC]

So if my recording noise level is at -70dB, and I've got 10 tracks, that'll add up to a -10dB noise floor? (each doubling of noise increases the floor by 6dB).


I'd like theoretical, and also practical perspectives. I cannot *hear* -70dB noise (unless the actually signal is gone), but this seems like something that can creep up without you hearing, especially if the noise it in the bass frequencies.)

[jrk]

noise would be incoherent? So it's not as bad as that?

http://www.sengpielaudio.com/calculator-leveladding.htm

[The Byre]

No, your maths is not correct!

1. Noise is not strictly additive, as it 'interlocks' one noise with another. A great deal depends on what kind of noise we are dealing with. Tape hiss? Mains hum? Clicks and pops?

2. Volume is not doubled at 6dB, but at 10dB - in other words, you have to increase the signal by 10dB in order to get a subjective doubling in perceived volume.

You could easily test the additive effects of noise, by recording various noises and reading off what sort of levels you get each time a noise source is added.

[alanofoz]

Originally Posted by jrk

noise would be incoherent? So it's not as bad as that?

http://www.sengpielaudio.com/calculator-leveladding.htm

I believe that's correct (I think I've linked to that site from this forum before). This means that you need to find the total noise power. What follows depends on the 10 sources of noise being uncorrelated/incoherent).

For simplicity let's say that FS (signal) power is arbitrarily 1W.

If each track is 70dB below that, you have 10^-7 W per track.

That's 0.1 micro watt for 1 track. For 10 tracks it's 1 micro watt.

1 micro watt is 60 dB below 1W. That's your answer: -60dB total noise floor.



If you don't like to calculate dB conversions you could use this site:-

http://www.sengpielaudio.com/dB-chart.htm

[alanofoz]

Originally Posted by The Byre

No, your maths is not correct!

1. Noise is not strictly additive, as it 'interlocks' one noise with another. A great deal depends on what kind of noise we are dealing with. Tape hiss? Mains hum? Clicks and pops?

Quite right. As an electrical engineer I'm more used to the word "correlate".

2. Volume is not doubled at 6dB, but at 10dB - in other words, you have to increase the signal by 10dB in order to get a subjective doubling in perceived volume.

Sorry, I have to put this in context. The 10dB figure has always seemed to me to be a guesstimate, with the operative words being "subjective" and "perceived". One person's perception is not necessarily the same as another's. But I've never seen the results of rigorous testing with multiple subjects. I also don't really think it's very relevant to this situation.

You could easily test the additive effects of noise, by recording various noises and reading off what sort of levels you get each time a noise source is added.

Following on from my comment above, it's always good to test such things if you have the resources.

[Heart Doctor]

Originally Posted by Mr. PC

So if my recording noise level is at -70dB, and I've got 10 tracks, that'll add up to a -10dB noise floor? (each doubling of noise increases the floor by 6dB).

No, this is not correct. No matter how many tracks you record and mix together: If the recording noise level of each track is at -70 dB, then the noise level of the resulting mix will also be close to -70dB.

In other words: The final mix will have a similar signal/noise ratio as the used tracks.

The reason is simple: When mixing, you must pull down the volume fader of each track. This ensures that the level of the final mix is similar to the one of each track. And pulling down the faders will lower the recording noise of each track that ends up in the mix.

Typical peak levels during recording and mixing are 0 dB VU = -18 dB FS.

If we look closer, we may find that the noise level of the mix will be somewhat higher than the noise level of individual tracks. The reasons are:

• Makeup gain of compressors raises low level signals (including noise)
• Plugins may add noise intentionally (analog emulations)

Final mastering will increase the overall loudness of the track, and typically peak levels of 0 dB FS are reached. Signal level and noise level are increased by similar amounts. S/N ratio does not change significantly.

[ashcat_lt]

Originally Posted by The Byre

2. Volume is not doubled at 6dB, but at 10dB - in other words, you have to increase the signal by 10dB in order to get a subjective doubling in perceived volume.

That's not even what we're talking about. We're talking about adding signals. 1 + 1 = 2, and 2 is quite definitely 6db more than 1.

The rest of the points above are correct. With different instruments even, you can't really predict how they're going to add, but we usually figure closer to 3db per doubling of tracks. But yes, the peak levels are going to add together also, so you'll end up turning the whole mix down.

If you had one track with its noise floor 70db below its loudest peak, dublicate it so there's 8 of them (cause 10 is awkward math ) with exactly the same noise, and then mix all of those together at unity, the loudest peak of the mix will be 18db higher than the original. The noise floor will also be 18db higher. The dynamic range is still 70db though.

[DVDdoug]

In the real world mixing improves the (perceived) signal-to-noise ratio. Solo vocals & instruments are the most difficult to record.

With multiple sources there are (usually) fewer very-quiet passages or silence where the noise becomes audible... There is always some signal masking the noise. (That's also true if the sounds are mixed acoustically and recorded in stereo or mono.)

You can also gain resolution when you mix, since mixing is done by summing. In order to sum two (full-volume) 16-bit signals you need 17-bits. (Typically you don't sum at full volume so it's more of a weighted average but it's still possible to increase the digital resolution if you render at higher resolution than you record.)

[Philbo King]

If you mix correlated signals, such as sine waves at the same freq and phase, you get a 6 dB increase on each doubling of the input voltage. So, starting at -70 for one signal, you'd get -64 for 2, -58 dB for 4, -52 dB for 8 and so on.

Since noise is uncorrelated, you'd need to use vector sums of the voltages instead of additive doubling, changing the 6 dB rise to something less, like 3 dB or so.

[alanofoz]

Originally Posted by Philbo King

If you mix correlated signals, such as sine waves at the same freq and phase, you get a 6 dB increase on each doubling of the input voltage. So, starting at -70 for one signal, you'd get -64 for 2, -58 dB for 4, -52 dB for 8 and so on.

Since noise is uncorrelated, you'd need to use vector sums of the voltages instead of additive doubling, changing the 6 dB rise to something less, like 3 dB or so.

Yes, you've simplified what I said in post #4.

So for the uncorrelated case, starting at -70dB for one signal, you'd get -67dB for 2, -64dB for 4, -61dB for 8.

And -60dB for 10 as per post #4. But I guess nobody reads mathematical posts.


This also illustrates Ashcat's comment about 10 tracks leading to awkward maths. He also pointed out that you don't mix at unity gain and why not, and what happens when you reduce the gain to a more practical level. (But Ashcat used 6dB per doubling, when 3dB would be more appropriate in this context).

[somebodyelseuk]

Depends if all your "noises" are the same frequencies AND in phase with each other...

When it comes to summing and cancelling of 'sounds' it depends on frequency not sound type - 'noise' from one pre-amp is not necessarily exactly the same 'noise' as from another pre-amp even two 'identical' models.

[alanofoz]

Originally Posted by somebodyelseuk

Depends if all your "noises" are the same frequencies AND in phase with each other...

That's right - in this case they'd be correlated. In the case of the OP however, I can't see how the 10 different noise sources could be correlated, even if they are from pre-amps in the same device.

When it comes to summing and cancelling of 'sounds' it depends on frequency not sound type - 'noise' from one pre-amp is not necessarily exactly the same 'noise' as from another pre-amp even two 'identical' models.

The OP was referring to noise. See the first part of my reply.

[Justin]

Originally Posted by Mr. PC

So if my recording noise level is at -70dB, and I've got 10 tracks, that'll add up to a -10dB noise floor? (each doubling of noise increases the floor by 6dB).


I'd like theoretical, and also practical perspectives. I cannot *hear* -70dB noise (unless the actually signal is gone), but this seems like something that can creep up without you hearing, especially if the noise it in the bass frequencies.)

Even if you assume that the noise in question is completely correlated (it wouldn't be), and that the +6dB increase in noise amplitude for every doubling of tracks was correct, then by going from 1 track to 10 tracks, you'd only be doubling the track counts 3.25 times (1 * 2 * 2 *2 * 1.25 = 10), so 3.25*6 would be a 19.5dB increase in amplitude.

That was just a correction of the math side, and assumes that the noise is completely correlated on each track, which it almost certainly would not be. If it were, I'd bet that the signal was correlated as well, which means that the overall output would be +19.5dB too! So the signal/noise ratio would remain the same.

Edit: ah alanofoz beat me to it.. I should've read more thoroughly...

[Judders]

I'm useless at maths, but even I can see where your maths is incorrect...

You forgot the "s"!

[Justin]

Originally Posted by Judders

I'm useless at maths, but even I can see where your maths is incorrect...

You forgot the "s"!

Not here in murica =)

[Judders]

Originally Posted by Justin

Not here in murica =)

Doesn't make it correct!

[ashcat_lt]

Originally Posted by Justin

Even if you assume that the noise in question is completely correlated (it wouldn't be), and that the +6dB increase in noise amplitude for every doubling of tracks was correct, then by going from 1 track to 10 tracks, you'd only be doubling the track counts 3.25 times (1 * 2 * 2 *2 * 1.25 = 10), so 3.25*6 would be a 19.5dB increase in amplitude.

Wow. Is that really your final answer? I sure hope you of all people know better. I said above that the math was awkward, but...

If all 10 are the same, then the summed total is 10x the original. Log of 10 is 1. Times 20 is 20. The correct exact answer is 20db.

[Justin]

Originally Posted by ashcat_lt

Wow. Is that really your final answer? I sure hope you of all people know better. I said above that the math was awkward, but...

If all 10 are the same, then the summed total is 10x the original. Log of 10 is 1. Times 20 is 20. The correct exact answer is 20db.

That's true, but that requires understanding of a logarithm, and I was trying to explain it without using that concept. And I fucked up by calling 1.25 a quarter of a doubling, which was completely wrong, it would be closer to a third of a doubling, but anyway the point is the explanation was there for someone who gets multiplication but not log()...

[ivansc]

...and a final postscript.
The subject (when not abbreviated) is called Mathematics in the UK.
As usual you sloppy colonists decided to save effort and removed the "S" from the accepted abbreviation.

Sorta like sox - color - nite - using Z in all the wrong places....
One of these days we WILL be back and teach you scruffy oiks how to do it properly.

Sincerely, Ivan Idear.

943rd President of Grand Fenwick.

[alanofoz]

Originally Posted by ivansc

As usual you sloppy colonists decided to save effort and removed the "S" from the accepted abbreviation.

Hey!!!

We colonists here in OZ aren't sloppy! It's maths. Plural.

[alanofoz]

Originally Posted by ashcat_lt

...The correct exact answer is 20db.

Or 10dB if uncorrelated.


(But I established that in post #4 )

My problem is I've been doing logarithms since 1958 - that's 60 years of logs. (Or log as they probably call them in murica! )

[Judders]

Originally Posted by alanofoz

Or 10dB if uncorrelated.


(But I established that in post #4 )

My problem is I've been doing logarithms since 1958 - that's 60 years of logs. (Or log as they probably call them in murica! )

Are you a professor of mathematic?

[ivansc]

FWIW even the Germans get closer than the Murkins!


Alan: The only people I refer to as colonists are the aforementioned Murkins.

The antipodean connection I generally refer to as "the colonials".

Hm. S.A., W.I., Canada and all the rest??? Colonics? Canada being the High Colonics and S.A. the Low Colonics I suppose... Endless possibilities

[somebodyelseuk]

Not everything that ends in 's' is a plural.

In fact, the point of the thread is not whether your 'maths' is correct - one assumes you can add, subtract etc - but the question is whether you got the PHYSICS right.

[alanofoz]

Originally Posted by ivansc

FWIW even the Germans get closer than the Murkins!


Alan: The only people I refer to as colonists are the aforementioned Murkins.

The antipodean connection I generally refer to as "the colonials".

Hm. S.A., W.I., Canada and all the rest??? Colonics? Canada being the High Colonics and S.A. the Low Colonics I suppose... Endless possibilities

Ah! yeah, "colonials" is infinitely better!

Also colonials are infinitely better!

[alanofoz]

Originally Posted by somebodyelseuk

Not everything that ends in 's' is a plural.

In fact, the point of the thread is not whether your 'maths' is correct - one assumes you can add, subtract etc - but the question is whether you got the PHYSICS right.

Right. Just as one math is not enough, one physic isn't either.


Also, this forum's spellchecker doesn't like "math", "maths" is OK though. (Or is it Chrome's spellchecker?)

[alanofoz]

Originally Posted by Judders

Are you a professor of mathematic?

Perish the thoughts.

[karbomusic]

Originally Posted by alanofoz

Also, this forum's spellchecker doesn't like "math", "maths" is OK though. (Or is it Chrome's spellchecker?)

It's the browser and/or region, "math" doesn't get a spellcheck complaint here (US) in Chrome, IE et al, but "maths" does; overall, both are considered equally acceptable and correct depending on region FWIW.

It’s sometimes surprising how much argument and disagreement small differences such as that single letter can make. Readers in the UK, for example, sometimes get very upset if someone writes “math” rather than “maths”.


https://www.dailywritingtips.com/math-or-maths/

Ya' don't say?

[Mr. PC]

Here in Canada we use 'are' with plural nouns, for example "maths are".

Also, can Her Majesty's Government please leave our country, so we can get back to our stateless existence.

I've decided to simply de-noise no matter what, on principle. I hate noise so much.