I'm not saying a loop can't be made to
cover the whole band with a single 10-365. I'm just saying that for
the average "box" type loops many will try to build, I don't see it
happening. I guess just general box/diamond loop info from what I see
here...

In my experience, a single 10-365pf cap has gotten me full MW coverage most of
the time on homebrew loops, just not all of them. I have a couple of MW loops
that need a switched-gang set-up like you mentioned, to get a fuller range.
But, I also have a big (nearly 3 feet across) quilting-hoop-frame loop, twelve
turns tightly spaced, with a single, tiny 10-365pf cap. Goes from nearly 500 to
just below 1850. I didn't go through any detailed formulae when I was just
experimenting with the big loop frame (I've got it put together like a Kiwa
loop, it will turn in azimuth and altitude, very helpful for nulls) so I must
have lucked out.
But those smaller 365 caps have also been perfect for crystal sets, with full
tuning range of MW, so I always figured they'd work for loop antennas in the
same range (if you've matched the inductance right) and so far, nine times out
of ten, they do.
Linus