As has already been mentioned, free reeds in particular (but other instruments also) produce harmonics and other 'overtones' that are perfectly audible to dogs and cats, though we can't hear them. An old cat of mine used to behave in exactly the way 'elfscape' describes. He'd even come back into the house from the end of the garden in order to get me to stop playing. The concertina in question was an elderly and rather poor Salvation Army system duet, which won't have helped; but he had no problem with any other instrument, and he certainly encountered a wide range over the years.

A later cat had similar problems with violins, no matter how good -or bad- the instrument or player, but reacted not at all on the (by then) very rare occasions when the concertina came out. He'd exit the house at speed if anybody even made to open a fiddle case; but was perfectly happy to sleep in the case if he came in and found it unoccupied.

Neither cat ever took exception to recorded music.

Even if I played one I wouldn't inflict a didgeridoo on an animal, but whether the problem there is ear-piercing harmonics or gut-churning subsonics I can't begin to guess. You'd need to check with an elephant.