 If you liked
Layton Kyouju to Eien no Utahime
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 ...then you might like
Lost Song
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The power of songs is important in both of the anime, and both anime also have people who want to abuse the powers and turn music into a weapon of mass destruction.
Additionally, along the way, the main characters of both the anime go on a journey to follow their destiny and make important friends along the way.
Therefore, if you like the plot and theme of one these, you'll surely like the other one too!