This is a recurring obstacle that I'm sure many people can relate to. There's a particular part of my mind that likes to play certain songs over and over and over again that I don't seem to be able to silence with Shamatha, even as other facets of my mind calm down. I usually end up doing the practice (in this case, ngondro) while gently ignoring whatever arbitrary piece of music plays alongside them, and making a conscious decision to place my attention on the practice at hand. This seems to work out well, but I imagine the practice can be taken deeper in actual silence. Has anyone discovered any sneaky tricks to quiet the musical part of the mind?
Sometimes if I look directly at it it will cease for a bit.
I've found that during Shamatha, I cannot quiet it, only choose not to focus on it as you are. Moving into more of a vipassana deal though, if I can "see" it clearly, sometimes it will kind of morph into whatever the next object of awareness ends up being, and so is gone for a bit.
Are you a musician? it's really hard when you are, especially if you have been working on something for a while heh, I usually take a break with a bit of silence beforehand for just this reason.