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. 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.
The quadrivium is implicit in early
Pythagorean writings and in the
De
nuptiis of
Martianus Capella,
although the term was not used until
Boethius early in the sixth century. As
Proclus wrote:
The Pythagoreans considered all mathematical science to
be divided into four parts: one half they marked off as concerned
with quantity, the other half with magnitude; and each or these
they posited as twofold. A quantity can be considered in regard to
its character by itself or in its relation to another quantity,
magnitudes as either stationary or in motion. Arithmetic, then,
studies quantities as such, music the relations between quantities,
geometry magnitude at rest, spherics [astronomy] magnitude
inherently moving.
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 music 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.
This schema is sometimes referred to as
classical education, but it is more
accurately a development of the 12th and 13th centuries with
recovered classical elements, rather than an organic growth from
the educational systems of antiquity. The term continues to be used
by the
classical education
movement.
See also
References
- Henri Irénée Marrou, "Les Arts Libéreaux dans l'Antiquité
Classique", pp. 6-27 in Arts Libéraux et Philosophie au Moyen
Âge, (Paris: Vrin / Montréal: Institut d'Études Médiévales),
1969, pp. 18-19.
- Proclus, A commentary on the first book of Euclid's
Elements, xii, trans. Glenn Raymond Morrow (Princeton:
Princeton University Press) 1992, pp. 29-30. ISBN 0691020906.
- Morris Kline, "The Sine of G Major", Mathematics in Western
Culture, Oxford University Press 1953