"My neighbour's freedom to force their music upon me interferes with my need for sleep."
Or even,
"My neighbour's freedom to pollute my private property interferes with my private enjoyment of it."
Somehow it seems like an easier question to answer, now.
It's just different ways of describing the conflict between the need to sleep and the neighbour's loud music.
Your restated question doesn't pick up on this, you are just stating how someones liberty to do as they please interferes with your ability to do as you please on your property in a simpler format. No one is being freed from the other.
"My neighbour's freedom from interference when forcing their music upon me interferes with my need for sleep."
"My neighbour's freedom from interference when polluting my private property interferes with my private enjoyment of it."
Easy-peasy.
Freedom from something requires them to have power over you. Your neighbor really doesn't in the same way the government does, an invading foreign power, or, the way GNU argues it, the way corporations do with their software licensing and copyright.