sions of the musical modes is found in these documents. The earliest extant tonary, found
in the Psalter of Charlemagne (B.N. lat. 13159), originated at the abbey of Saint-Riquier
in the late 8th century. A further crucial tonary is that of Metz, known as the Carolingian
Tonary, which was probably compiled ca. 830 in Metz (preserved in four manuscripts,
9th–11th c.). Perhaps the most important document of this genre is found in the
manuscript Montpellier, Bibliothèque de la Faculté de Médecine, H. 159, a source that
originated in the abbey of Saint-Bénigne in Dijon, probably under the influence of the
monastic reformer William of Volpiano (d. 1031). This source, employing both neumatic
notation and an alphabetic notation with roots in the musical system found in Boethius,
organized and recorded all the chants of the Mass according to their mode and liturgical
genre. Odoranus of Sens (d. 1046) compiled an important tonary, and the Tonale sancti
Bernardi documents the Cistercian chant reforms.
Monastic houses throughout France were the centers of musical thought during the
10th and 11th centuries. The abbey of Fleury, judging from the number of theoretical
works copied at that abbey around the time of Abbot Abbo (ca. 940–1004), played a
notable role in copying and transmitting theoretical works ranging from Boethius to
contemporary anonymous treatises. At Fleury, musica continued to be taught within the
context of the Quadrivium, and both the speculative and practical aspects of music were
addressed. Cathedral schools likewise became important centers for the study of musica.
The cathedral school of Reims, when Gerbert of Aurillac (d. 1003) was master, was an
important center for the study of mathematics in general and, within that context,
Boethius’s De institutione musica. But as musical theory became more directed toward
problems of musical practice, the intimate relation between music and the remaining
mathematical disciplines became strained, and ultimately the separation of music from
the other three disciplines forms one of the primary causes of the decline of the
Quadrivium during the 11th and 12th centuries.
Four broad topics form the core of musical theory in France from the 9th through the
11th century. (1) For an author, the definition of a tonal system or basic collection of
pitches within which music takes place sets the fundamental principles. The Greater
Perfect System of Greek antiquity, with the added pitch from the synemmenon tetrachord
(b-flat), emerges as the predominant system. The system of Musica enchiriadis
nevertheless remains in the background of musical thought throughout these centuries,
and basic terminology from this complex of texts became integrated into the system
inherited from antiquity. The basic systems were taught as abstract collections of pitches
and tetrachords, then demonstrated empirically in the division of the monochord. (2)
Explanation of the tonal organization of liturgical melodies within the system developed
into the medieval theory of the eight modes, four authentic and four plagal. Early
theoretical discussions of the modes were based largely on the vocabulary and
organization of tonaries. In the course of the 10th and 11th centuries, the theory became
more systematic and the modes were explained as species of the octave. (3) Elementary
theory of polyphony, that is, organum, formed a part of several treatises, although
polyphony never occupied as significant a place in medieval theory as description and
analysis of monophonic liturgical melodies. (4) Finally, speculative reflections
concerning nonempirical music, from musical mythology to pure mathematics to music
of the spheres, continued to form a significant portion of theoretical thought.
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