Two I have seen are:
Nodame Cantabile
At a top music academy in Japan, Shinichi Chiaki's arrogance is matched only by his top-notch piano playing. But when Chiaki and the teacher get into a fight, he's demoted to the reject class. Chiaki is left to pursue his dream of being a composer while surrounded by a bunch of loser musicians and one annoying girl, Noda, who has proclaimed herself Chiaki's girlfriend. It doesn't help that Noda, who insists on being called Nodame, lives right next door to him.
You can watch it here
https://www.crunchyroll.com/showseriesmedia?id=1480
Kaikan Phrase
After the break up of their old band, guitarist Yuki & drummer Santa decide to form a new one. They recruit bass player Towa, young guitarist Atsuro, and after much persuasion, vocalist Sakuya. Together they form Lucifer and they struggle to make it in the music business, and also to stay together. As well, they have to deal with personal issues, such as parental objections, and watching their old bands succeed ahead of them. Sakuya is the most troubled band member, as he has to deal with his tragic past, and his relationship with teenaged lyricist Aine.
You can watch it here
https://www.crunchyroll.com/showseriesmedia?id=572
Then I did a search and found these but I have not seen them:
Lemon Angel Project
Lemon Angel was once the greatest girl band of Japan, but then it broke up and most of its members vanished. When a music producer decides to put together a new Lemon Angel, average high schooler Tomo Minaguchi is approached to audition for the group. Little does she know of the mystery behind the original Lemon Angel...
All 13 episodes are on crunchyroll
https://www.crunchyroll.com/showseriesmedia?id=108
Beck
Tanaka Yukio, better known by his nickname Koyuki is a 14 year old who feels disconnected from life in general. Through the act of saving a mismatched dog, he meets guitarist Minami Ryuusuke, and becomes involved in Ryuusuke's new band BECK. Koyuki's life starts to change as the band struggles towards fame.
Lovedol ~Lovely Idol~
Lovedol, or Lovely Idol, is a girl group consisting of two generations of idols. The 3rd Generation is about to make its debut, but to their surprise, they have been delayed! The vague reason is only that "they lack something." The manager, and the 3rd Gen. girls too, must find the answer.
You can watch this here
https://www.crunchyroll.com/showseriesmedia?id=534
Edit:Oh and here is one I plan to watch
Nana
Komatsu Nana moves to Tokyo, following after her boyfriend Shouji to gain a life she has always dreamed of. On a train bound for Tokyo, she meets Osaki Nana, the vocalist for the punk rock band "Blast", also moving to Tokyo to achieve her dreams of becoming a professional. Sharing the same name, the two of them perhaps through a twist of fate, ended up becoming flat mates in Tokyo, where together they support each other through each of their love lives and careers. Based on the manga by Yazawa Ai.