The song where I notice the rhythm being out-of-sync when depressed is "Astronomy" by Blue Oyster Cult.
I was just listening to it again, and the rhythms are still a bit annoying and out-of-sync to me but not as bad. It is like the period of the singing and percussion don't match. The percussion is incidentally very similar to the shamanic drumming rhythm - probably 4-7 Hz theta wave. I want to tell the singer to "shut up" and stop tromping on the drummer. LOL In the past, this song was very pleasant but it caused ear worms. Now I can't stand more than 30 seconds of it.
The drumming linked by
@TheOldWays in post #9 definitely induced a meditative state for me. When I am depressed I have nausea, shakiness, dizziness, brain fog, etc. I tend to stare at the wall and just zone out. I tell myself "get up and brush your teeth", but I find that all I can muster is a little twitch and I'm still staring at the wall.
I think this might be a clue that could allow objective measurements of depression. Rather than asking people how they feel better, you can measure the spectrum of brain waves.
Also I read a book claiming that each neurotransmitter is associated with a different brain frequency. So a doctor might be able to detect relative concentrations of the various neurotransmitters by measuring the electrical frequencies of the brain. This would better inform the treatment instead of simply asking people how they feel.
Another thing I have wondered about is nicotine. Maybe smoking was helping people feel better, because some of the neurotransmitters are triggered by nicotine. Maybe the growing depression problem is related to the decreasing popularity of smoking. (I have never smoked, but in earlier generations almost everybody smoked.)
EDIT: It is also possible that brain frequencies can be induced by rhythms that are not the same frequency. I suspect that a rhythm or even a melodic cycle in the music where the period is a precise
multiple of the shorter brain frequency period might induce the desired type of brain waves. Like if a pattern of drum beats is multiple of the alpha waves but not a multiple of the other types of waves, then the alpha waves might strengthen in the brain.