History
The most important early stages in the historical development of Mensural notation are found in the works of Franco of Cologne (c. 1260), Petrus de Cruce (c. 1300), and Philippe de Vitry (1322). Franco, in his Ars cantus mensurabilis, was the first to describe the relations between maxima, longa and breve in terms that were independent of the fixed patterns of earlier Modal notation. He also refined the use of semibreves: while in earlier music, one brevis could occasionally be replaced by two semibreves, Franco described the subdivision of the brevis as triplex (perfect), dividing it either into three equal or two unequal semibreves (resulting in predominantly triplet rhythmic micro-patterns.)
Petrus de Cruce introduced subdivisions of the brevis into even more short notes. However, he did not yet notate these as separate smaller hierarchy levels (minima, semiminima etc.), but simply as variable numbers of semibreves. The exact rhythmical interpretation of these groups is partly uncertain. The technique of notating complex groups of short notes by sequences of semibreves was later used more systematically in the notation of Italian Trecento music.
The decisive refinements that made notation even of extremely complex rhythmic patterns on multiple hierarchical metrical levels possible were introduced in France during the time of the Ars nova, with Philippe de Vitry as the most important theoretician. The Ars nova introduced the shorter note values below the semibreve; it systematicized the relations of perfection/imperfection across all levels down to the minima, and it introduced the devices of proportions and coloration.
During the time of the Franco-Flemish or Dutch school in Renaissance music, use of the French notation system gradually spread throughout Europe. This period brought the replacement of Black with White Notation (due at least in part to the more widespread use of paper, rather than vellum, for music). It also brought a further slowing down of the duration of the larger note values while introducing even more new small ones (fusa, semifusa etc.). Towards the end of this period, the original rules of perfection/imperfection (as they dealt primarily with the larger members of the system) became gradually obsolescent together with the use of these note values themselves, as did the use of ligatures. During the 17th century, the system of mensuration signs and proportions gradually developed into the modern time signatures, and new notation devices for time measurements, such as bar lines and ties, were introduced, thus ultimately leading towards the modern notation system.
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