Your Lie in April (Shigatsu wa Kimi no Uso) is a Japanese manga created by Naoshi Arakawa. It became an anime in 2014 and this past September was released as a film in Japan. The plot centers around piano prodigy Kōsei Arima who, after his strict mother's death, lost his ability to hear notes and no longer plays the piano. He meets violinist Kaori Miyazono through mutual friends, and she slowly begins to bring Kōsei back to the world of music. This series is both visually stunning and heartbreakingly beautiful. There are some dark moments, and some very sad moments. Prepare to cry. Your Lie in April is available for viewing on Crunchyroll and on Netflix.
If you've already discovered this beautiful manga and anime and are looking for something else to read and/or watch, I recommend A Silent Voice by Yoshitoki Ōima, which was also released as an animated film this past September; as well as My Neighbor Seki by Takuma Morishige, which was released as a home video animated film and a 21-episode tv series.
A Silent Voice: "Shoya is a bully. When Shoko, a girl who can't hear, enters his elementary school class, she becomes his favorite target, and Shoya and his friends goad each other into devising new tortures for her. But the children's cruelty goes too far. Shoko is forced to leave the shcool, and Shoya ends up shouldering all the blame. Six years later, the two meet again. Can Shoya make up for his past mistakes, or ist it too late?"
My Neighbor Seki: "Toshinari Seki takes goofing off to new heights. Every day, on or around his school desk, he masterfully creates his own little worlds of wonder, often hidden to most of his classmates. Unfortunately for Rumi Yokoi, his neighbor at the back of their homeroom, his many games, dioramas, and projects are often way too interesting to ignore; even when they are hurting her grades."
Both of these mangas are similar to Your Lie in April in that they have a very quiet, gentle setting and are good for readers who love a good story but don't necessarily need a lot of action and fighting.