- Quadrivium
The quadrivium comprised the four subjects, or arts, taught in
medieval universities after the trivium. The word isLatin , meaning "the four ways" or "the four roads": the completion of theliberal arts . It was developed byMartianus Capella . The quadrivium consisted ofarithmetic ,geometry ,music , andastronomy . These followed the preparatory work of the trivium made up ofgrammar ,logic (ordialectic , as it was called at the times), andrhetoric . In turn, the quadrivium was considered preparatory work for the serious study ofphilosophy andtheology .About the quadrivium, Proclus Diadochus said in "In primum Euclidis elementorum librum commentarii":Fact|date=February 2008
Arithmetic is the Discrete At Rest
Astronomy is the Discrete In Motion
Geometry is the Continuous At Rest
Music is the Continuous In MotionMedieval 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
harmonic s, in particular the study of the proportions between the music intervals created by the division of amonochord . 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 inspace , music number intime , 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 theclassical education movement .Fact|date=January 2008ee also
*
Andreas Capellanus
*Degrees of the University of Oxford
*Gutenberg College References
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