Old 04-16-2017, 07:30 AM   #1
read
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Default -6DB + -6DB ?

Hi

if i have two channels at -6db how much do they add to?

i was wondering how many of them it will take for the master to go over 0db

trying to understand the mathematics of it

Thank you
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Old 04-16-2017, 08:17 AM   #2
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Originally Posted by read View Post
Hi

if i have two channels at -6db how much do they add to?

i was wondering how many of them it will take for the master to go over 0db

trying to understand the mathematics of it

Thank you
I experimented with -6dB of white noise and -6dB of pink noise and they basically reached +0.0dB.

Pink noise has a modulation affect and is not real steady but I think you could say it was +0.0dB.

Two -6dB sources of white noise will reach a steady +0.0dB.

I think the sources have to be complex wave forms otherwise there will be phase issues.
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Old 04-16-2017, 08:18 AM   #3
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it varies depending on what you are summing.
but assuming the same signal on each track, -6dBFS + -6dBFS = +0.02059991327962...dBFS.
now assuming the same signal, polarity inverted on one channel, -6dBFS + 6dBFS= -inf dBFS.
so it ranges from nothing to a little over full scale.
all depends on the tracks being summed.

this is a good resource, there is more than enough information about dB's and conversions, etc...(prob too much)>http://www.sengpielaudio.com/calculator-db-volt.htm

Last edited by bezusheist; 04-16-2017 at 08:27 AM.
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Old 04-16-2017, 08:41 AM   #4
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thank you guys

so it matters if its a kick, a bass, guitar etc or noise that reaches -6db? when it comes to adding them up all together later
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Old 04-16-2017, 08:50 AM   #5
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I believe it takes 4 signals @ -6 to get to +0.02 - At least considering pure sources like a sine wave. Roughly +3dB per two identical sources.
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Old 04-16-2017, 09:01 AM   #6
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don't confuse "power" with "voltage" here.
digital gain is voltage.

-6.02059991327962..dBFS = 0.5 volts.
2 x 0.5v = 1 volt = 0 dBFS

Last edited by bezusheist; 04-16-2017 at 09:06 AM.
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Old 04-16-2017, 09:01 AM   #7
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Originally Posted by bezusheist View Post
it varies depending on what you are summing.
but assuming the same signal on each track, -6dBFS + -6dBFS = +0.02059991327962...dBFS.
now assuming the same signal, polarity inverted on one channel, -6dBFS + 6dBFS= -inf dBFS.
so it ranges from nothing to a little over full scale.
all depends on the tracks being summed.
I used generators for both sources so they won't cancel with reversed phase.

I also experimented by using "band pass" filters on the white noise, both high and low with a bandwidth of 1-octave and they sum close to 2dB lower then 0.0dB. Actually it was between 1 & 2dB.
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Old 04-16-2017, 09:05 AM   #8
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Quote:
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I used generators for both sources so they won't cancel with reversed phase.
i was speaking about the exact same signal. to do this with a noise generator, render it to an audio file and use the file for both tracks, not a separate generator for each track, because white noise generators are "random" by nature and they will not null.
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Old 04-16-2017, 09:07 AM   #9
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Quote:
Originally Posted by karbomusic View Post
I believe it takes 4 signals @ -6 to get to +0.02 - At least considering pure sources like a sine wave. Roughly +3dB per two identical sources.
Actually I tried sine waves too, using different frequencies and I think you're pretty close karbo. It did fluctuate some. I started with 440hz and set each successive generator 100hz higher.
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Old 04-16-2017, 09:09 AM   #10
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Quote:
Originally Posted by bezusheist View Post
i was speaking about the exact same signal. to do this with a noise generator, render it to an audio file and use the file for both tracks, not a separate generator for each track, because white noise generators are "random" by nature and they will not null.
Right, and that's why I made the distinction.
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Old 04-16-2017, 09:10 AM   #11
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Actually I tried sine waves too, using different frequencies and I think you're pretty close karbo. It did fluctuate some. I started with 440hz and set each successive generator 100hz higher.
set the pan law to "0" like it should be...
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Old 04-16-2017, 09:16 AM   #12
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so panning affects the total DB on the master?
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Old 04-16-2017, 09:17 AM   #13
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i'll have to start testing i guess...i tried once but didn't understand much, thats why i was asking here maybe i understand better
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Old 04-16-2017, 09:25 AM   #14
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Quote:
Originally Posted by read View Post
so panning affects the total DB on the master?
if your pan law is set to something other than "0".
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Old 04-16-2017, 09:31 AM   #15
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Ok lets say i have a kick thats -6db


Does it make a difference to the master level if i add to it a high hat (higher frequency) thats -6db or another same kick thats -6db

or will the result be the same?

also what i'm noticing is that hi hat goes up and down in volume much less than the kick...so i guess it will have different impact to the master volume over time
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Old 04-16-2017, 09:39 AM   #16
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at least this conversation will keep me going thank you guys
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Old 04-16-2017, 12:22 PM   #17
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With real world sources it's almost impossible to accurately predict.

Consider that kick and high hat. Each of them only really hits -6dbfs for one or maybe two samples in the duration of the hit. If it accidentally works out that they both reach their maximum on the exact same sample, then mixed together they should be right above 0. It's very unlikely that this would actually happen, so they will probably add up to something less than 0, and unless every hit is exactly on the grid and exactly the same, they're likely to add to different levels each time they hit together.

It's further complicated by the fact that the db scale is necessarily full wave rectified - we take the absolute value of the actual sample value and then do the log conversion because log is undefined for negative numbers. So basically -6dbfs on the meter means the sample value is either 0.5 or -0.5 with no way of knowing for sure without looking. If the kick happens to hit 0.5 exactly when the hat hits -0.5, they will add to 0, and look like -infinity dbfs.

For tracks that are exactly the same, a doubling of tracks should mean the mix is (approximately) 6db louder. If they're all at -6, 2 will sum to 0, 4 will sum to +6, and it would take 8 to get to +12. But since there's never any good reason to have the exact same thing on multiple tracks, we're always mixing things that are different, and all we can do is guesstimate. Usually in the real world, it's more like +3db for every doubling of tracks that peak around the same level.
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Old 04-16-2017, 12:35 PM   #18
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It's an ... entertaining distraction - to banter about the numbers but it has very little to do the final level in the master bus which wil be, literally speaking, anywhere you want it to be, depending on where the faders are.
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Old 04-16-2017, 03:38 PM   #19
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I think ashcat has nailed it.

Now for the mathematical bit (asked for in the OP, dBs rounded to whole numbers)...

If you sum two identical signals, at each instant you are doubling the voltage, i.e. increasing the level by 6dB. The rms and peak levels are increased by 6dB. Result: 0dB.

If the two signals are uncorrelated, the maximum peak values might coincide, so the peak value might sometimes be doubled, therefore the peak value of the sum could be increased by 6dB. You might need to allow for that possibility.

If you need to calculate the rms value of the sum, you need to do an rms addition: square each of the two rms voltages, add them and take the square root, i.e. sqrt(V1^2 + V2^2).

e.g. if each had an rms voltage of 0.5 (i.e. -6dB), the result will be sqrt(0.5^2 + 0.5^2) = 0.7071. You'll probably recognize that value - it's -3dB. (i.e. you've doubled the power).


Hence the answer to the original question is somewhere between -3dB and 0dB.

Note that in a musical project you would expect some correlation, even if it's only the rhythm.


PS:
So I did a search for "uncorrelated signals" and found these:

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

Try entering -6.02dB into either of these calculators.
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Old 05-05-2017, 05:34 PM   #20
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Nice post Alan. Understanding the difference between 'correlated' and 'uncorrelated' signals is the first step in predicting summing.
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Old 05-06-2017, 07:29 AM   #21
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Nice post Alan. Understanding the difference between 'correlated' and 'uncorrelated' signals is the first step in predicting summing.
Thanks
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