Unofficial Hatsune Mix and Fairy Idol Kanon are both manga with a large focus on music and a female protagonist's passion and talents for singing. While Unofficial Hatsune Mix is an anthology of stories and Fairy Idol Kanon is a story with a main narrative, they both provide a couple of comedic scenes.
When I first saw this, immediately thought, Cyber Idol Mink - Hatusne Miku;; Besides that Cyber Idol Mink are kind of like real people and stuff. They both go through a CD that makes them become a singer. You have to read both of them to get what i'm thinking of.