To study the rhythmical and social synchronization, also known as entrainment, that occurs when people move to music in a social context, novel applications that motivate and measure this behaviour are needed. In this paper, we describe the development of such an application, BeatLED, a social game that uses music, movement and luminescent textile. We analyse the requirements of such a musical social game, as well as the possible application fields, such as musicology research, team-building and health care. We developed novel game dynamics and integrated them into a proof-of-concept implementation, which was evaluated positively by 84% of the test users.