Tena on S-String Vol 2

Tena on S-String by Sesuna Mikabe. A Romance manga rated Older Teen, published in English by Yen Press.

Every person's life is written in a soul score, a kind of musical composition running from birth to death that very few can hear and fewer still can change. After nearly dying in a car accident, Kyosuke Hibiki gains the ability to hear these scores, and soon meets Tena, a tuner who restores harmony by removing the off-key notes. Tena has decided Kyosuke will be her partner, and despite his loud objections, the two end up in an uneasy alliance.