On 2013-05-09, Justin Bennett wrote:

You can always record an omni along with your MS mic and get horizontal B-format!

only, of course, if you are using 2x figure-of-8 mics, or a double MS set up.

Theoretically it works with a pair of cardioids (XY; call them a and b), the Blumlein pair (c and d) you're describing, or conventional M/S with a cardioid and a fig-8 (M and S), and a number of intermediate pickup patterns and microphone axes. That's because as long as your signal set spans WXY, you can matrix from any combination to any other. So, modulo scaling and sign convention, I believe you get W as-is, then X=a+b-2W=c+d=M-W, and Y=a-b=c-d=S. The third extra channel doesn't need to be W either, as long as it's not a linear combination of the others.

In practice your mileage may vary, because of imperfect matching between the mics, failure of full coincidence, variance of the mics from an ideal first order response which breaks the cancellation in the matrix and leaks in higher order harmonics, and the fact that the farther you go from WXY, the more illposed the matrix becomes, so that noise amplification differs between the setups (think two subcardioids facing just a few degrees off front center).
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