Funny story: I searched "Two Trees" looking for papers on Lucas's fruit-tree example of capital pricing. With the papers, I discovered Ludovico Einaudi's piece, "Two Trees", and the rest of his beautiful background music opus. His music got me through the night working on that macro problem set. Einaudi even played Oxford a couple of times since then (maybe one day I'll see him). Indaco and Passagio are two favorites, but it's all really good.
I recently found these guys on NPR's Tiny Desk Concert series, and I fell in love with their album An Awesome Wave. The Intro 1 and Taro songs hit that trance-drama balance just right.
He gets more ambient and just better, better with every album. His mournful, wry lyrics help me get my motivation back on long slogs. Especially because they focus on such broad themes of strength, self-improvement in retrospect, and bearing difficulty.
The Wonder Years, Four Year Strong, A Day to Remember, Set Your Goals
The "desperate youth" themes of pop punk bands got me through exam season. Too much TWY and I get depressed, but the defiance of FYS helps me suppress that. The two balance out well and keep the energy up. These bands are for when I feel, "Oh God, I'm trying, I'm trying SO HARD."
Blink 182, Fall Out Boy, No Use For A Name
Further afield but same as above. The lyrics don't quite get the "I'm trying" theme out, but they capture youth and insecurity well. The tunes are perfectly emo, fit to purpose.
For when I need someone to acknowledge and independently manifest my angst. Words can't describe how much I love Say Anything.
Classic. Keeps perspective on life, there are plenty of ways to get your S F'd up, grad school surely isn't the worst way.
The Bouncing Souls -- Better Things
Perfect song to see the silver lining in anything.