quadrivium
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. It was developed by Martianus Capella. 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.
About the quadrivium, Proclus Diadochus said in In primum Euclidis elementorum librum commentarii:
Arithmetic is the Discrete At Rest
Astronomy is the Discrete In Motion
Geometry is the Continuous At Rest
Music is the Continuous In Motion
Medieval usage
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, and the B.Mus. remains a postgraduate qualification at Oxford and Cambridge universities).
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 practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised both in European and Islamic cultures.
Modern usage
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.[Morris Kline, "The Sine of G Major", Mathematics in Western Culture, Oxford University Press 1953]
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 often recovered through Islamic classical scholarship, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the classical education movement.
See also
 Andreas Capellanus
Degrees of the University of Oxford
Gutenberg College
References
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