In recommending songs to users, various types of relationships can be considered, such as songs liked by users with similar preferences or songs that are acoustically similar to those the target user already likes. Providing explanations for recommendations based on such relationships improves transparency and trust, but users currently have no control over which relationships are emphasized. To solve this problem, we extend an existing recommendation method based on a graph convolutional network (GCN) by representing each relationship as a separate graph layer with adjustable weights. By applying this method, we implemented a song recommender system with three types of relationships (user preference similarity, acoustic similarity, and creator commonality) on a music web service called “Kiite.” On the service, four types of recommendation results are displayed, depending on which relationships are emphasized and to what degree. The recommender system offers both transparency and controllability in that users can freely switch between the four recommendation result types. An analysis of over two years of usage logs demonstrates the effectiveness of combining transparency and controllability in music recommendation.