"Music Theory" means different things to different people. I see it as the study of musical possibilities. I prefer to articulate many of these possibilities in the in the terms laid out by the cognitive sciences (whereas many music theorists use mathematical terms), and I use the methods of history and cultural studies to show how many possibilities have in fact been carried out in music. I suppose I am largely interested in investigating the interfaces between mind, perception, technique/technology, and culture. Music Theory is fundamental to the practice of music--that's why music students nearly always study music theory early on. Theorists generally spend a lot of time analyzing musical artworks. While I see much value that, as a scholar I prefer to use such analysis as a means to a greater end. Our changing world confronts musicians as well as society with crucial issues having to do with the basic functions and definitions of music. Investigating those functions and definitions is the heart of my research.
In the Middle Ages music was one of the seven Liberal Arts that you studied if you fortunate enough to attend high school (roughly speaking). The liberal arts were Grammar, Logic, Rhetoric, Arithmetic, Geometry, Music, and Astronomy. Music had to do with the manifestation of numbers in music, which is why it came between Geometry and Astronomy. Present-day music theory is descended from that academic study of music. Today the study of music theory begins with courses in harmony, counterpoint, and other basic principles of musical composition. It can eventually lead to research in a variety of areas. Some of these areas concern music directly: for example, theorists analyze, contemplate, and criticize musical works, they study the history of music and its theories, and they compose. Other areas of music theory seem to use music only as a starting point: you'll sometimes find music theorists in psychology, philosophy, or computer-science departments, to name a few.
To find out about the institutions of music theory, check out the Society for Music Theory. Find out about other types of musical scholarship by looking up the American Musicological Society or the Society for Ethnomusicology.
Click here to find out how to study music theory at Pomona College.