It's simple and a bit of a miscellaneous grab-bag of puzzles and story ideas. It's just another high school anime, with an episodic structure and not much of an overall story. It makes some choices that will disappoint a fair chunk of the audience. However I enjoyed it. It's fun, imaginative and blessed with lively characters. I'm not surprised to learn that it's also got a live-action movie adaptation
Chika is a brash, loud girl with lots of physical strength and the doomed goal of becoming refined and ladylike. To achieve this, she's started playing the flute. If she joins her new high school's band club, she'll become a blushing maiden, loved by all!
Haruta is a super-intelligent boy who doesn't get on with his family and is staying in rented accommodation, or occasionally a sleeping bag at school. He's also Chika's childhood friend, although they haven't seen each other in nine years and they clearly don't see eye to eye. He'll point out that she's an idiot whose only redeeming feature is that she's brazen, pig-headed or whatever. She might respond with violence. They bicker all the time, but they're also practically joined at the hip and it's rare to see them apart. Their classmates sometimes wonder if they're dating, but as it happens Haruta's gay and they're both in love with the teacher who leads their band club. (Apparently the live-action film decides to make them romantically involved anyway, which sounds dodgy to me even if they're clearly soulmates in an "opposites attract" sort of way. You can see why audiences might ignore everything the show keeps saying and assume they'd end up together, which is probably a factor in this being a comparatively obscure franchise in the West.)
This show has various elements. They don't really fit together, but it has them all.
1. BAND CLUB. Everyone in the cast is either doing band club, protesting loudly that they refuse to do band club even though they'd be ideal for it or a candidate for a career as a professional musician. The show's building up to a national band competition. Music is important and everyone takes it seriously... but on closer examination, this isn't really a music show. We never watch their rehearsals. We never see Kusakabe-sensei's teaching style. Instead of being the show's dramatic engine, think of it more as a setting.
2. RELATIONSHIPS. There are various potential romances, although the only non-subliminal one is the Haruta-Chika-Kusakabe triangle. However this doesn't really drive episodes either. Haruta and Chika are love rivals, but this mainly manifests as mild love plan sabotage and squabbling. It doesn't colour their scenes with Kusakabe-sensei himself, who oddly enough remains a fairly one-dimensional background character throughout. (Theoretically there's also the possibility for Haruta-Chika romance, which the show isn't afraid to tease gently... but no.)
Much more important are all the new characters. Any episode is likely to be about helping someone get over their unusual personal problems and eventually having them join the band club, or occasionally refusing to join but hanging out with them anyway. The club goes from having four members (ep.1) to twenty-something (the end of the season), although most of those join by themselves in the ordinary way.
3. PUZZLES. This is the main one. It's a detective show, for a broad definition of "detective". Why did a dead boy paint his Rubik's cube white and what would it mean to solve an all-white cube? Why did a teacher change his class's seating three times? Why did a hospitalised grandad paint jungle elephant pictures and what's that got to do with a colour called Elephant's Breath? (There really is such a colour, by the way. It's a sort of mid-grey beige.) I liked this a lot. These are imaginative puzzles and a good deal more distinctive than I'd expected before I started watching the series. The old folks' radio station is a lovely idea. The First Love Sommelier is a deranged notion, although the story he's being used to tell in ep.8 is quite sad underneath. There's one horrible bit of historical background that made me swear and start googling to see if that really happened. (I couldn't verify it, but that's not to say that it didn't.)
Occasionally these puzzles lead to some odd conclusions. Ep.9 presents a scenario that one hopes wouldn't have happened that way in the West, even if you know that tattoos have a different cultural significance in Japan. (That episode also gets some physics wrong.)
It's a lumpy show. It has major elements that you'd expect to be pulling the show in completely different directions. It's not surprising that the live-action film actually took one of those directions. However I liked the characters and I enjoyed the imaginative stories. Ep.8 has flashbacks with animal people and I'm still not sure whether that was unreliable narration or a club of people who really did dress up as teddy bears. Haruta and Chika made me laugh and I've come to like the fact that their relationship stays platonic. (That should be allowed sometimes, surely? They're still friends.) I think it's underrated.