Northumbrian bagpipe music with six-fingers-down making a G

No it doesn't. Northumbrian pipes are actually a transposing instrument. When you play a written G, Northumbrian pipes in traditional tuning actually play an F. Well, actually, about 20cents sharp of F since we are in pedant mode. Many Northumbrian pipers these days will have a G chanter so they can play in sessions with the usual collection of instruments. I have been in a session led by pipers and I played a C whistle as a transposing instrument and the fiddler tuned down a tone. Mind much of the time I was playing bass on my F contrabass recorder and playing a bass line fell quite naturally under my fingers in C and F.