Full Moon wo Sagashite, Shigatsu wa Kimi no Uso Recommendations
This show also stars someone who has a passion for music and wants to impress a specific person. But the main character here has a medical issue that prevents her from singing and is on her deathbed basically. She's granted two guardian angels to fulfill her dying wish.
-Music is a consistent major theme within both
-Romance and tragedy heavily influence the story of each
-The main characters in each go through great struggles to try and achieve their goals, both of which revolve around music.