[Tom McC]

Originally Posted by didier.brest

From my previous post, it seems that even if X, Y and M are exact cardioids and S exact figure of eight, MS cannot be made exactly the same like XY.

When you generate a "virtual" XY pair by sum & difference matrixing of an MS pair, the included angle of the virtual pair will of course vary with M/S ratio, but the polar pattern of the new directional mic also varies. If you matrix a cardioid M with a narrower Fig-8 S, it's logical to expect that the new virtual mic will have narrower pattern than the mother cardioid, because it has a tad more cosine stuff in its maths.

Only when a Fig-8 mic is used for both M and S does the X and Y polar patterns stay invariant of M/S weighting (viz. Fig-8 shape; ignoring the trivial case of two coincident omni's <g>)

Consider the case of MS using an ideal cardioid and Fig-8, with the mics having equal sensitivity and equal gain settings: Referenced to the cardioid straight-ahead angle,x, = 0 deg., the virtual mics will have the polar patterns:
L = 0.5(1 + cosx + sinx) R = 0.5(1 + cosx -sinx]

This will deliver an XY array with main axes 63.4 deg. left- and right of straight ahead, i.e. an included angle (not recording angle) of 127 deg. And their X,Y polar patterns? They will be ca. 12dB down at 90 deg. off their major axis, i.e. hypercardioid-like (a cardioid is 6dB down at 90 deg. off axis). I find it helpful and illuminating to set up a simple spreadsheet to run various scenario's of M pattern and M/S gain ratio.