I tried to clarify these aspects in http://mail.gnu.org/archive/html/lilypond-user/2003-12/msg00088.html
Yes, you did a great job!
In fact, by suggesting Andrew throw the \global into every staff, I am taking your advice from that very post:
The easiest is probably to try and see what happens if you are uncertain about what LilyPond will do.
I have not yet had the time to follow your subsequent advice:
The systematic way is to look at the definition of the different contexts at [URL]
even though it may be hard to know what engraver takes care of what command.
Once I do that, I'm sure I'll have a better understanding of what is going on, and will be able to advise others better than I can at this time.
Thanks again, Kieren.
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