Music is highly complex and provides a rich variety of insights into the human mind, its mental structures, and processes. Experienced musicians are able to create complex structures in real time effortlessly, yet there is at present no successful model of full musical structure. The integration of different musical aspects such as melody, rhythm, voice leading, and form as well as the representation of long-term structure are particularly challenging. To open new possibilities for the study of higher-order structure in music and its perceptual correlates, cognitive music research would benefit from further mutual integration of theoretical, mathematical, computational, and psychological research, similar to advancements in linguistics. This symposium therefore focuses on the formal understanding and empirical investigation of music-theoretically motivated research questions in music cognition. It connects perspectives from music theory, behavioral research, corpus research, and computational modeling, and aims to initiate interdisciplinary discussions about the currently most challenging topics related to the cognition of higher-order structures in music.