In Audacity, you can split a stereo song to mono and invert the phase to remove center-panned audio (usually vocals).
Can someone explain why inverting the result and adding the original (in mono) doesn't result in an isolated vocal track?
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Yeah it would appear to work that way, but the math reveals something else:
You have two channels, Left and Right, and you invert one, that is flip the sign on one channel and mix* them: Left + (- Right), or simply:
L - R.
What you are doing here is essentially isolating the
side channel. What was equal in both channels is now removed. What is different stays.
Now pay attention to the "formula" L - R. It will leave the original phase orientation of L intact and flip that of R. If you were to reverse it (which is just as good), R - L, the R orientation would be intact and L flipped.
So, you ask why mixing the inversed side channel equally back into the stereo mix will not produce the isolated center material:
The inverse side channel is equal to
- (L - R)
Then we calculate new left and right channels:
Left = L - (L - R), or simply R.
Right = R - (L - R), or simply 2*R - L.
So that is really not an attractive result ;-) It does not get better if you already mixed* left and right into a mono file:
(L + R) - (L - R), or simply 2*R.
And if the side were not inversed:
(L + R) + (L - R), or simply 2*L.
The best you can do is to mix L and R equally to double the volume of the center material. That is what we normally call the
Moreover you can try some other things on the main LR stereo track:
*for the sake of simplicity mixing means adding here, attenuation has been left out.