I wrote a preview for this series earlier. You can read it here.
Kids on the Slope is a much antecipated anime because it's the first time Yoko Kanno and Shinichiro Watanabe work together since the famous Cowboy Bebop. Let's start with the synopsis from wikipedia:
The beginning of summer, 1966. Because of his father's job situation, freshman high school student Kaoru Nishimi moves by himself from Yokosuka to Kyushu to live with relatives. Until then, Kaoru was an honor roll student who tended to keep to himself, but meeting notorious bad boy Sentaro Kawabuchi starts to change him. Through his devil-may-care classmate, Kaoru learns the attractions of jazz and finds the first person he can call a “friend.” He also discovers how much fun it is to play music with a pal. Other characters include Sentaro's kind childhood chum, Ritsuko, who is the daughter of a record shop owner; the mysterious upperclassman, Yurika; and Brother Jun, the much-admired leader among their peers.
The visual part of the anime is excellent. The backgrounds and the animation... Everything is good. This is clearly visible in the parts in which they play the instruments. You can see the animation quality there. The use of 3D in Kaoru's hand whil he plays the piano is very good and they did a perfect job joining that with the his drawn body. The soundtrack is composed of songs normal BGM songs and lots jazz for the normal scenes., including the songs the characters play. All according to the quality expected of Kanno. The OP and ED themes are also good and different from the usual anime songs.
Kaoru was born in a rich family and he spent his life moving from one place to another, making him grow up without friends. At first he gave me the impression that he was a character like Holden from Catcher in the Rye (or Kyon from Haruhi, to the otaku). But he stops being boring and cynical pretty fast and ends up being a very reasonable guy. Unlike most male leads, he's very mature and perceptive of other people's feelings. But he has the annoying habit of throwing fits when he's frustrated. Sentaro is a kind-hearted rebel who is pretty much the opposite of Kaoru in terms of personality. Ritsuko fills the role of the nice childhood friend that takes care of the troublemaking protagonists. We have also Yurika, a rich girl with a very cool and intense personality and Junichi, called brother Jun by Sentaro and Ritsuko, the super cool guy that goes to university in Tokyo. He's the only character I didn't like, because he's made to be so cool, handsome, strong, smooth and other stuff and I don't like those characters.
The anime is about friendship. Is about how Kaoru and Sentaro, bond because of jazz. And no, there's nothing gay about it, though it gets weird sometimes. But it's like the "It's me, your Sam." line from LotR. The problem is mostly on our end. It also has a lot of romance, including love triangles, and the usual teenage drama expected in a series set in a school, though it doesn't really focus on it.
What I found very nice in this anime is that relationships proceed fast. They don't spend ages delaying confessions and stuff like that. It's very rare to see that in anime. Yet it isn't really rushed because while things tend to be solved in 2 or 3 episodes, the anime covers 3 years, so, for the characters, sufficient time has passed. The characters' reactions also feel very real and the anime doesn't try to be more dramatic than it needs to be. It also gives attention to all 5 main characters, even if some have smaller roles.
The biggest problem in this series is the end. There's a time skip in the last episode that just makes you feel like a lot has been left out. And it has, because the manga shows what happens in those years. It's a pity. If they had one more episode they could've showed it and this problem wouldn't exist.
Kids on the Slope is a good anime. It's visual and musical quality are top notch, the pace is very good and the characters are very well written. It's recommended to all who want to see a good slice of life anime. But if you want an anime about music, you might get frustrated. Jazz has a very important role in the plot and there are many awesome jam sessions. But it's far from being the main focus of the anime.
After that time skip in the end of the anime series, I had to read the manga. The anime followed the manga very closely, so there's only one important difference, but it isn't really important in the end. But there are some details that were cut from the anime that explain things more. For instance, they show how Sentaro learned to play the drums and that explains what happens in the bar. Junichi's situation is better developed and after reading the manga I started to have sympathy for him.
But what's most important is that the author shows what happens during the time skip, which is very important and makes Kaoru grow a lot. The end is also longer and more detailed, leaving things less to the imagination of the reader and erasing the incredible coincidence that leads to the end in the anime, since the manga shows that the character wasn't there by chance.
The character design, which is the same from the anime is good, specially for a josei, and the backgrounds are competent, even though they're simple.
If you didn't watch the anime, it's a good read. If you watched the anime, you should read at least the last volume, so that you can see what the ending should've been.