Google is not my friend tonight - I can’t find a cite for a single one of the following anecdotes. Take them for what they’re worth…
Jeff Berlin supposedly wrote Joe Frazier while watching a boxing match on tv. The rhythm of the bass line reflects the movement of Joe Frazier’s feet.
Glenn Gould allegedly watched tv while he practiced.
When you practice while watching tv, the analytical and visual parts of your mind are engaged elsewhere, which helps to get the tactile, aural and intuitive parts of your mind engaged in the music. That helps to develop your musical ear and your touch without the interference of your eyes.
It’s especially useful for groove, but it’s also good for classical pieces. ‘Rubato’ is 19th century fancy talk for ‘groove’. It’s also really good for memorizing.
I prefer sports, myself - regular tv will have music I don’t necessarily want to play along with interspersed with the show. And the mute button gets hit all the time for commercials.
Something I do all the time with singing - I will sing softly along to recordings of my coachings and rehearsals while I do various physical tasks, ranging from dishes, vacuuming, laudry to taking long walks to working out. I haven’t read any proper studies about it; I just find that it helps me to memorize into a deeper place.
If that sounds too newage for you, let me try putting the idea this way - onstage, I will have to perform from memory while doing other tasks. I can’t drop a line just because I’m carrying a large prop, or tying my shoes, or any other thing a director asks me to do in the course of a show. So I might as well memorize while having to pay attention to other tasks - this phrase repeats twice (there’s still a bit of schmutz on the carving knife.), now sing in thirds with the tenor (take the compost out.), now we’re into the stretto (take the other pants out of the drawer and fold the works.) Practicing while dealing with a secondary physical life makes it easier when I’m onstage dealing with the music and a secondary physical life.
Another good exercise with the metronome - set the tempo for half the target metronome mark and play along with it as if it’s the snare drum on 2 and 4. So a piece at 120 gets practiced at 60, but it helps to keep the groove and the tempo at the same time.
And now, I have to crash - the kids and the dog have completely worn me out on this PA day…