The PhD, which is required for students who want to work as university professors in musicology, music history, or music theory, takes three to five years of study after the master's degree, during which time the student will complete advanced courses and undertake research for a dissertation. The DMA is a relatively new degree that was created to provide a credential for professional performers or composers that want to work as university professors in musical performance or composition. The DMA takes three to five years after a master's degree, and includes advanced courses, projects, and performances. In Medieval times, the study of music was one of the Quadrivium of the seven Liberal Arts and considered vital to higher learning. Within the quantitative Quadrivium, music, or more accurately harmonics, was the study of rational proportions.