Bob Cain wrote:

Using three identical capsules, one for the front and two
for the side and reasonably matched is pretty near optimal
for M/S IMO.

Bob, as you know I've posted some messages here saying that matching
the sonic character of the M and S mikes is not a particular virtue,
and that a flat/smooth/accurate characteristic for S matters far more.

Then you sent me your more detailed thoughts off-list, which gave me a
chance to rethink this issue. I have to admit that there's more to it
than I thought before (i.e. there may be something to it at all).

Here's how I would express it non-mathematically. The issue is how
the stereo image will be affected by the response characteristics of
the two microphones after the M/S signals have been matrixed to L/R.

If the M microphone emphasizes certain sound components (e.g. the high
frequencies) while the S microphone doesn't, then in the eventual L/R
stereo output of the matrix, those components will tend to gather at
the image's center more than the midrange sound does. The apparent
left-right position of any given instrument or voice would thus be
blurred. Conversely, if the S microphone boosts the highs while the
M microphone doesn't, high frequency energy would tend to be shifted
more toward the left and right than the midrange sound--increasingly
so with individual voices or instruments that are already off-center.

Both effects are undesirable, but they do work in generally opposing
directions--either one would tend to compensate for the other to some
degree. So I think I see the intended point of "matching" the general
sonic characteristics of the M and S microphones now. I don't endorse
it completely, but I see a possible rational hope behind it at least.

It will take me another little while to say where I don't agree; the
main issue is the fact that most microphones (except for the best
small-diaphragm figure-8s and certain rather noisy omnis) don't have
the same frequency response at all angles of incidence. So all our
"virtual microphones" have rather complex, irregular response--that's
another reason I tend to favor a super- or hypercardioid for "M".

However, I'll also point out that the analog of using a non-flat S mike
is processing the S channel independently of the M channel--and there is
a long tradition of doing exactly that. One of the attractions of M/S
(whether the recording is made originally that way, or whether another
type of X/Y recording is matrixed to M/S) is that the M and S channels
can be equalized independently or processed in other ways independently,
then rematrixed to L/R stereo.

For example, LP disc cutters would often matrix a stereo signal to sum
and difference channels (equivalent to M and S), and limit the difference
channel and/or roll off its low-frequency energy, since the difference
energy corresponds essentially to the vertical component of the groove
to be cut, while the M channel corresponds to its horizontal component.
Excessive vertical modulation could cause skipping, and would tend to
limit the playing time of the side and the maximum modulation of the
groove--which in turn would limit the playback volume and the signal-
to-noise ratio. Cutting the loudest possible record was an obsession
with LP mastering engineers, too--not something that snuck into the
business with the diabolical introduction of digital recording.

This also addresses a point made by "Sugarite"--he's right that X/Y
(coincident) recordings often lack a sense of spaciousness, and that
spaced microphone recordings are sometimes preferred for that reason.
But one other way to increase the sense of spaciousness, or at least
to help compensate for some of the relative lack of it, is to boost
the low-frequency response of the "S" channel.

If anyone remembers Bob Carver's "Digital Time Lens" processor--a
surprisingly useful general-purpose "feel-good box" that doesn't add
distortion--that's one of the tricks he was using in that circuit.