Chopin is Always in my Pocket

This is the story of Asako, a young girl with a cruel mother and not many friends but a grandmother who has been encouraging her to become a pianist. Asoko competes with one student in particular, a boy who happens to be quite gifted. After her grandmother’s death and the passage of a few years, Asoko and the boy (now a young man) run into each other again at a piano competition…

Also includes a short story: Gin no ito Kin no hari

source: https://www.mangaupdates.com/series/prvz5zn/itsumo-pocket-ni-chopin