Mid/side widening moves the centre too

The wider master with the smaller singer

You put a stereo imager on the mix bus and push the width a little. The pads open out, the room around the drums gets bigger, the chorus feels expensive. Ten minutes later you notice the vocal sounds further away than it did, and the snare has lost some of its crack. You did not touch either of them.

The width control turned them down relative to everything around them, which makes it a balance control with a different label. The mid/side maths shows why, and it is simpler than the plugin graphics suggest.

Why it matters

The side signal is full of instruments

Mid/side is another way of writing the same two channels. The idea goes back to Blumlein's stereo patent, and the sum-and-difference matrix is the basis of M-S microphone recording (Dooley and Streicher, 1982). This lesson uses the convention

Some tools scale both by $1/\sqrt{2}$ instead of 1/2. That changes the numbers on the M and S meters, but none of the conclusions below.

A part in dead centre has $L = R$, so it lives entirely in $M$ and $S = 0$. Anything else has some side. A guitar panned hard left is $L = x$, $R = 0$, which gives $M = S = x/2$: half of that guitar is side signal. So the side channel holds far more than reverb and air. Every panned instrument, stereo synth patch and room mic is in there, in proportion to how far from the centre it sits, so a width move on the mix bus is a level move on all of them.

The science

What a side boost does to each part

Multiply $S$ by a gain $g$ and decode. For the hard-left guitar with $g = 2$, a 6 dB side boost:

The left channel rises 3.5 dB, and the right speaker, silent before, now plays an inverted copy of the guitar 9.5 dB below the left. That inverted leak is where the extra width comes from, and it is one reason heavy side boosts can sound phasey.

Now sum the power over both channels. Because $L^2 + R^2 = 2(M^2 + S^2)$, raising $S$ raises every part by an amount that depends on how much of it is side. The centred vocal has no side and does not change. The hard-left guitar has equal M and S power, so it gains $10 \log_{10}(5/2) \approx 4$ dB. A reverb with unrelated left and right channels also splits its power evenly and gains the same 4 dB.

So the centre moves without its level changing: everything around it came up by as much as 4 dB, and the vocal, kick, snare and bass now sit relatively lower. Some wideners also turn the mid down to keep overall loudness steady, and then the centre drops in absolute level as well.

Panned parts move outward too. A guitar halfway left on a sine/cosine pan law has gains of 0.92 and 0.38, a 7.7 dB difference between the channels. After the same boost it is 1.19 and 0.11, a 20.6 dB difference.

The mono fold is the one thing that does not move. $(L' + R')/2 = M$ for any $g$, so the widened mix and the original fold to exactly the same mono signal. That is why a side boost disappears in mono: a hard-panned guitar now drops 4 dB more between stereo and mono than it did before the boost.

In the demo, listen for two things: whether the centre feels smaller as the side comes up, and how the correlation meter moves when it does.