I'm being very strict in my use of the term 'avant-garde'; I suspect it's current use has become divorced from the actual meaning of the words. Today it tends to be used for anything that goes off in directions that are against the norm.
As a label I've always found it a bit irritating, terribly self-regarding. I wonder how many performers really regard/ed themselves as 'avant-garde'? I suspect it's a label which is of more importance to a certain type of fan who likes to think of themselves as an admirer of the 'avant-garde.'
Look at the people who have broken through barriers or pointed the way for the future or just gone down a side-path where no-one else has really tried to follow - your Armstrongs and Bergs and Ellingtons and Ives and Parkers etc etc - and what in the end really counts about them? Is it that they were 'avant garde'? Not at all. It's because they created an utterly distinctive musical world which makes them enthralling years afterwards.
But the thing is...and this is where I really fall out with the 'avant-garde' luvvies...there are also plenty of musicians who work well within the bounds of the musical convention of their day who also create utterly distinctive musical worlds - your Vaughan Williams and Malcolm Arnolds - who have gone through periods of neglect because they were perceived to be yesterday's men. The 'avant-garde' can become a very powerful clique controlling what can get broadcast or recorded (as happened in the 50s and 60s in the UK with classical music) or what is deemed 'worthwhile' amongst the critics. You only have to look at the world of contemporary 'Art' (as in painting) to see that at work.
As Traned says there are thousands of musical tributaries - some will be familiar and some will be very odd and go through unfamiliar territory. Those who insist that only the groundbreaking is significant are as wrong-headed as those who dismiss the unfamilar out of hand.