I've had the same problem with my Lumia 520. I chatted with a Windows mobile support guy and can you believe the guy told me that the only way to have the phone recognize the music was by subscribing to XBox pass thing?! I was outraged, why would I have to pay to listen to the music I already own! This was clearly a lie I later figured, the problem is basically really bad app programing and compatibility.
Some other day I tried syncing again and it recognized the music files! But for no apparent reason... I later synced my music again and WP decided it doesn't want to recognize the music files anymore, again... I still insisted in going through the music app, and noticed some duplicated playlists and started deleting them, then tried to play a song aand it started playing... even though the storage sense classifies my music as "other files", then I noticed the music app started to slowly update the last sync, including the playlists! Very slowly though.
The Music App in WP is really bad and veery slow even if you have a fast Lumia 920, or so I've read. I haven't made the switch to Android hoping Windows 10 will improve the music experience and from what I've read it seems this will receive an extreme makeover, so I'll probably stay in WP and get a Lumia 840, but if I start reading all the negative stuff is still there, then I'll jump to the upcoming Nexus 5 never to comeback to WP. I cross my fingers hoping WP10 isn't another mediocre attempt from Microsoft.
EDIT: WP still hasn't recognized the music files. The music app still plays all the music, but the playlists are not getting read properly, each time the app is opened, the playlists read different songs, but never all of the ones that are supposed to be included.