Afraid the music will stop right after the last track you selected have been streamed ? The automatic play
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Do I have to expose my music on the webserver ?
No! Certainly not !
...unless - of course - you're running on some kind of shared hosting or similar...
In order to let AmpJuke access and stream music, you could (should, in fact) put the music outside your documentroot (where you store HTML, PHP and whatever is served over the net).
AmpJuke play/stream music, - no matter if it's "visible" (in your web-root or below) or not. So my advice is to put the music outside your documentroot.
For example, you might serve web-documents from /usr/local/apache2/htdocs (that's your documentroot).
However, your music might be stored in /usr/local/music (and several directories below that point).
Just make sure your 'web-user' has sufficient permissions to at least read from the directory where your music is stored.
The Apache Manual has some more info. about the documentroot, as well as information about the user directive (aka. the 'web-user').