Robert, didn’t even know I could mix and render to a new track. Let me try your instructions, not sure what the rendered new track provides, but let me find out.
Note: I have always been curious what happens when you add sound to sound. Does adding a -10dB sound to another -10dB sound, does it remain -10dB? Is there an appropriate forum here to discuss?
Thank you.
Best,
Jack
Mixing two sounds of equal amplitude will produce a signal that is at most +6dB higher than the individual tracks. The exact level depends on the relative phase of the two signals (and rare cases may even be less than the peak level of the original signals).
If you want to discus this further, I’d suggest starting a new topic in this part of the forum: Audio Processing - Audacity Forum
When calculating with dB, one should transfer it back to the linear scale in order to do it right.
6.02 dB = 2.0 linearly.
0 dB FS = 1.0 linearly
-6.02 dB = 0.5 linearly.
and -20 dB is 0.1 linearly.
Let’s add up -20 dB audio:
If the tracks are identical, we will naturally sum the maxima (peaks in both tracks.
The peak is 0.1 (-20 dB), either positive or negative, doesn’t matter.
The sum is 0.1 * 2 = 0.2.
A linear multiplication is just the same as addition of dB values.
Thus, -20 dB + 6.02 dB = -13.97 dB.
That’s the peak of the mixed track.
It is more complicated if the tracks do not have the same content but the same peak of -20 dB.
The peak in the mixed track can be anything between
0.1 + 0.1 = 0.2 (what we’ve had before) or
-0.1 + -0.1 = -0.2 (again, same as before, at least in dB) or
-0.1 + 0.1 = 0 = -inf dB.
The value lies therefore between 0 and 0.2 linearly.
The statistical average gives forecasts a value of 1.4141 instead of 2 for the multiplication:
1.4141 * 0.1 = 0.1414 or in the dB scale:
3.01 dB + -20 dB = -16.98 dB.
Different tracks mixed down will practically always have a lower peak than identical ones (unless you’re unlucky).
The 3 dB rule does actually apply to the summation of noise. I think that a song comes nearer to the 6 dB rule since the peaks will coincide on the main beats.
However, the conclusion is that you can’t tell the peak of the rendered track before you’ve added up the audio sample by sample.
To answer your specific question from above:
Adding up two tracks with -10 dB will give a peak from -inf dB (one track is identical but inverted) up to -4 dB (both tracks are the same).
The calculation with linear values is even more advantageous if the tracks have different dB values.
Robert
Ps.
Why didn’t I make the examples with -10 dB?
Because the linear number is too odd. Halving the dB is equal to taking the square root of the linear term:
-20 dB = 0.1, -10 dB = root(0.1) = roughly 0.32 (0.32*0.32=0.1024)
or more accurately 0.31622776601683789.