"H" received favorable reviews from most music critics. Adam Greenberg from Allmusic reviewed the parent album "Rainbow" and favoured "Independent" and "Hanabi", but failed to mention "July 1st". He felt that "Hanabi" "focuses strongly on her vocal qualities as well as some interesting phrasing [...]", while he concluded that the song "Close to You" "[...] never quite gets off the ground, especially when compared to the ending track, ["Independent",]" Greenberg, who had written the extended biography of Hamasaki on the same website, had listed "Hanabi" as one of her career standouts. "CDJournal" had reviewed each track on their mini-review. For "Independent", the reviewer called it an "upper dance tune" and felt the song sounded "aggressive." For the second track, the reviewer commended the song's composition and production and called it a "summery, refreshing dance tune." However, slight criticism was directed on the chorus that needed "minor adjustment." For the third track, the reviewer felt that the song expressed the sadness of the end of summer through a Japanese fireworks motif, and praised her freely expressed world view.