Uchuu no Ongaku

Rei Takaoki is a boy who loves brass music, with a father who is a professional trumpet player. However, he suffers from asthma, which prevented him from becoming a trumpet player himself. He gave up on his dream and went to a high school that does not have a band. There, he meets Mizune Hoshino, a free trumpet player, and the leader of the school's newly formed brass band. She recognizes Rei's "love for brass" and invites him to join the club...

(Source: Monthly Shonen Magazine, translated)