Dave Lampson wrote:

>I'm aware of the mechanics inviolved.

A very Cremonan typo...

>I just don't know exactly why the different keys for different instruments
>came to be.

AFAIK for Brass there was a time when the pitch of an instrument (overall
length) which dictated which key the natural harmonics were based in, was
changed through the addition of "crooks" i.e.  extensions in tubing to "a
length" of tubing which was the "basic" instrument.  In the case of the
Horn as an example, when the time came that instrument builders managed
a decent valve system, i.e.  fixed inline crooks (and players realised
that the valves could render chromatic tunes) the point of departure for
chromatic horn writing was adopted to be the "basic" instrument length i.e.
F for the horn, Eflat sometimes, Bflat for the trumpet, C sometimes, now,
help me and explain why the trombone is length-wise in B-flat but written
in C...

Greetings from Bavaria
Anthony Morris