It's a bit more complicated than you guys make it seem.

The AFM negotiated an exception with the TSA that
allows musicians to take a carry-on, a personal item,
plus a musical instrument through security. It is entirely up
to the airline whether to allow this exception to apply to
any particular cabin. As of my most recent experience, US
has done so; practically speaking BoeingBoy is correct so
far: I have never been denied access when I carry on two
things plus an instrument, except once when I was very late
boarding (but then the instrument eventually got to fly in
the cockpit). But then I'm an elite on US and have not tried
the trick on any airline with which I have no status. Plus, out
of courtesy to the other passengers, in these days of 90%
loads, I have actually deigned to check a bag instead of
trying to find twice as much overhead as I'm ethically or
whatever you'd call it entitled to.

In addition, the aircraft has to actually have the space. If
you can't get better than zone 3 or 4 boarding, you're up
a creek without a paddle. If you are in some of the smaller
aircraft, a shaped case will make it into an overhead; a
square case may well not. A viola case will almost definitely
not on, say, a DH8. A case will fit across underneath two
seats on regional equipment, but owing to the braces will
not do so on most mainline equipment, including in first class,
but boarding in zone 1 or 2 will grant access to enough bin
space to accommodate both a violin and a carry-on; and on
the newer aircraft, I have managed to put a shaped case
behind a row of rollaboards.