Changing the "Jukebox/Note Blocks" volume while a record is playing has no effect until the record is finished.
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This is a bug still I believe, if you put a jukebox to play a tune and then edit all of the in-game volume settings the overall volume of the jukebox is unaffected by the updated game volume (both sounds and music).
this is a bug yes, when you change even the sound volume the music stays the same.
Is this still a concern on Minecraft 1.4.4 Pre-Release? If so, please update the version affected.
Can you replicate this issue in latest version of the minecraft? If so, can you please update the ticket?
It appears to be happening on 1.4.5 as well.
Success on 12w49a, its still a bug.
Still on 1.4.6. My friend said this issue has been around forever and never addressed, so not expecting it to be. Here's hoping, though.

Confirmed in 13w06a. I can turn down the Sound slider to "Off" and the Music Slider to "Off" in the Options menu and music will still play loud an clear. It's apparently independent of all sound controls besides system volume.

Can we get a confirmation of whether this happens in 13w10a and an update to the affected versions?
happens in 13w10b
I checked the code (1.4.7 Unpacked with MCP not modded). It checks that sound is on only when starting playing the disc. Not every tick.
This may be intentional, for you can play the disc, then turn off your sound so while playing you can listen to the jukebox only.
YESS IT IS FIXED! 😃
Same issue in version 1.8.9
Is this happening if you turn down the Music volume? I believe jukebox is treated as a sound effect and this is working as intended.