Bob Cain wrote in
:

The angle remains the same? Would you not need a narrower angle to
maintain the -3 dB point at center?

Could you explain what you mean by -3 dB point at the center and why you
want that?

The -3 dB point is the angle at which the microphone picks 3 dB less signal
than straight forward. For a perfect cardioid pattern that's 65 degrees
off-axis (a 130 degree spread). For a hypercardioid pair I recall that
it's closer to 55 degrees.

Summing the -3 dB level in two microphones of uncorrelated signal gives you
back the original volume level, so two cardioids spread to 130 degrees
would have the same volume at the center as a single microphone pointed
dead ahead.

Some will say that the center signal of a stereo pair is highly correlated
and therefore the -6 dB point sums to full volume. With a cardioid pair,
that's a 180 degree spread (the "omni from summed cardioids" equation).
This applies to highly correlated signal. I find in practice that such
close correlation seldom happens, and the -3 dB value is more useful.