After decades of black-boxing the existence of algorithms in technologies of daily need, users lack confidence in handling them. This thesis study investigates the use situation of intelligent music recommendation systems and explores how understandability as a principle drawn from sociology, design, and computing can enhance the algorithmic experience. In a Research-Through-Design approach, the project conducted focus user sessions and an expert interview to explore first-hand insights. The analysis showed that users had limited mental models so far but brought curiosity to learn. Explorative prototyping revealed that explanations could improve the algorithmic experience in music recommendation systems. Users could comprehend information the best when it was easy to access and digest, directly related to user behavior, and gave control to correct the algorithm. Concluding, trusting users with more transparent handling of algorithmic workings might make authentic recommendations from intelligent systems applicable in the long run.