Well obviously there was the harp/ lyre/ the gleewood, pipes, drums and probably rattles. Fittings from the former were found in the Sutton Hoo burial. Signalling horns may have been used to musical effect, but I'm not musically literate enough to say how.
One thing I do recall is that nobody heard true harmonies in music until, at least, the first hurdy-gurdies came along in Late Medieval times. Some churchmen called the hurdy-gurdy "the voice of the Devil" because it was the first time anyone heard a harmony. Hitherto, because the tuning was too closely bound up with how this or that particular harp or pipe was carven, it was too difficult to get any two to play in harmony with each other.
Also, if surviving pre-Renaissance pipes are anything to go by, medieval folk were quite happy to play on the gaps between the notes. The big deal about the Renaissance is that musical instrument making became sufficiently precise for true harmonies to be played, which is how Vivaldi made a much bigger hit in his own day than we easily realise. The access of creativity this gave promoted the development of the baroque orchestra, the forerunner of the classical orchestra of today.
Pipes, if memory serves, could be carven from bone as well as wood, and I think elder sticks are more easily cored than most for this purpose.
Hope this helps.