Music theory has enjoyed a ubiquitous association with mathematics from its earliest beginnings. Among the abundant mathematical models that have inspired theories of music, combinatorics has played a continuous role since the seventeenth century, articulating musical spaces in which relations between elements of a discrete system can be articulated and quantified. This paper explores some representative theories of musical relations expressed in spatial terms using combinatorial techniques, revealing the abstract and profound ways in which mathematics, specifically combinatorics, informs music theory.