 If you liked
Coquelicot-zaka kara
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 ...then you might like
Sakamichi no Apollon
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Set in the '60s, lots of jazz/blues/swing music (although SnA is all about the jazz), three protagonists - two boys, one girl (Poppy Hill is mainly the main two though) and a sweet, slow nostalgic storyline with great world building and enchanting moments.
While both are very different anime, they contain very similar settings. The anime are both slice-of-life with a romance theme set in the 20th century. If you like artsy anime with some good romance, I recommend this.
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Recommended by josenewtype
Similar setting, school romance.
Both shows look amazing and have great music with it.
Sakamichi no Apollon is more serious.
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Recommended by TrueArcanum
Immediately thought of From Up on Poppy Hill when watching Kids on the Slope. The background and concept of the story are different but two things that are certain is that both have high school characters in the 60's, and somehow both anime give off the same vibe. The songs used in both are also really "light" and pleasant to hear, especially on Sakamichi because it is a music-themed anime. Worth to watch, worth to try!
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Recommended by hanakocheeks