Quadrivium

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The quadrivium comprised the four subjects, or arts, taught in medieval universities after the trivium. The word is Latin, meaning "the four ways" or "the four roads": the completion of the liberal arts.

At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA the student could enter for Bachelor's degrees of the higher faculties, such as Music. To this day some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt degrees are examples in the field of philosophy).

In medieval educational theory, the quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium, made up of grammar, logic (or dialectic, as it was called at the times), and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy and theology.^[1]

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the musical intervals created by the division of a monochord. A relationship to music as actually practiced was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practiced both in European and Islamic cultures.

In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered as the study of number and its relationship to physical space or time: arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number.^[2]

This schema is sometimes referred to as classical education, but it is more accurately a development of the 12th and 13th centuries, with classical elements oftened recovered through Islamic classical scholarship, rather than an organic growth from the educational systems of antiquity.