A square piano is one that doesn't rock, man
.

...whereas an upright oozes moral rectitude and the grand is just stuck up.

I've just realised I have a rather nicely produced 'coffee table' book about pianos with all sorts of lovely pics of weird and wonderful historic instruments (including a square by Adam Beyer dated 1777). It is called, unsurprisingly, 'Piano' and is written by David Crombie
ISBN 1-871547-99-7. It also has a pull-out of a modern concert Steinway showing all the gubbins.