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MS or 'mid-side' stereo microphone technique is where you point a cardioid microphone directly at the sound source (M) and place a figure-of-eight microphone pointing left and right (S). The M microphone picks up the sum of the left and right signals (L + R) and the S microphone picks up the difference (L - R).
There are two advantages of MS technique. Firstly, with a conventional LR stereo pair, neither microphone points at the center of the sound stage. The on-axis pickup of every microphone is better than the off-axis response, so the center stage response of an LR pair is less than optimum. This is particularly significant if you are recording a solo instrument since neither mic points at the sound source. With an MS pair, the M mic points directly at the instrument.
The other advantage is that a single MS stereo microphone can be manufactured that is 'pointable'. Give a non-sound engineer an LR pair on a stereo bar and they won't know what to do with it. Give the same person an MS stereo microphone, that incorporates both the M and S capsules in one housing, and they will instinctively point it at the sound source. This is significant in news and current affairs where the reporter might have to hold the microphone.
But the output of an MS pair plainly is not stereo. So it has to be converted to LR stereo through an 'MS matrix'.
Mathematically it works like this...
M = L + R
S = L - R
M + S = (L + R) + (L - R)
M + S = 2L
M - S = (L + R) - (L - R)
M - S = L + R - L + R
M - S = 2R
So by adding the outputs we get the signal for the left channel. By subtracting the outputs we get the signal for the right channel.
This can be done on a conventional mixing console. The M signal is fed to one channel panned centrally. The S signal is paralleled to two channels. One channel is panned left so that it adds to the M signal. The other channel is inverted in phase and panned right so that it subtracts from the M signal. (If your console doesn't have a phase button, then make a Y-cord with pins 2 and 3 on one of the two male XLR connectors swapped).
It works! The levels of the two S signal faders should always be the same, but you can adjust both together to control the width of the stereo image. If you push the faders for the S channels higher than that of the M channel, you will get 'super wide' stereo.
It may sound too easy to be true, but this simple stereo recording system really does work. Try it!