I suppose all this Gaelic piping terminology can get confusing so here's a few terms:

piob: pipe, pronounced something like "peep" (due to the devoicing of medial and final stops in Gaelic)

piobaire: piper "peepiruh"

piobaireachd: piping, playing upon the bagpipes. "peepiruXt" (the X standing for a sound like in Scots loch, German mach, etc, a sound not found in standard English, and the final d becoming t due to devoicing.)

ceol: music "kyoll"

mor: big, great; so piob mhor ("peep vore") great pipe; ceol mor great music etc.

beag: small "beck" so ceol beag small music (but usually called "light music")

crun: crown "kroon"

luath: fast "loouh"

In any case piobaireachd is a theme-and-variation type of music, not dissimilar to the ostinato form of the European Baroque.

ostinato: a persistently repeated musical figure which may occur during a section of a composition or even throughout a whole piece. (From a music dictionary)

So, there is nothing uniquely Highland or Gaelic to the form of the piobaireachd, just as there is nothing unique about the scale of the Highland pipes, at least as they are now tuned, to the scale musicologists call Just Intonation, which is based on the harmonic series.

There is clear evidence that a music form like piobaireachd existed in Gaelic culture before bagpipes were introduced to Ireland and the Highlands. It was played on the harp. Traditional Gaelic harping died out so that today we must look to the way piobaireachd is played on the pipes to try to guess what the original harp music might have sounded like.

There are tantalising similarities between piobaireachd and the classical music of northern India (Sanskrit and Gaelic representing the Eastern and Western extent of the Indo-European language family save for extinct Tochrian).