Mensural Notation - Context-dependent Note Values

Context-dependent Note Values

In order to understand the principles by which notes had their triplex (perfect) or duplex (imperfect) value determined by context, it is necessary to look at the evolution of the notational system in the context of the rhythmic nature of the medieval music in which it was first used. Most music in the 13th and 14th centuries followed the basic pattern of a fairly swift 6/4 meter (in modern notation). Melodies therefore consisted mainly of three-beat notes (in modern notation, dotted half notes), or alternating sequences of half notes and quarter notes, or groups of three quarter notes. Beginning with Franco of Cologne in the late 13th century, all these were notated using the longa and breve notes. Simplifying somewhat, a longa was automatically understood to fill a whole triplex metric group (be perfect) whenever it was in the neighborhood of other notes that did the same, i.e. whenever it was followed by another longa, or by a full group of three breves. When, however, the longa was preceded or followed by a single short note, then they were understood to form one of the characteristic sequences of a simple half and a quarter note together. Thus, the longa had to be reduced to a value of two (be made imperfect). When, finally, there were only two breves in between two longs, then the two breves had to fill up a triplex metrical group together. This was done by lengthening (alterating) the second breve to a value of two, resulting in a syncopated short-long rhythm as opposed to the otherwise dominating long-short one.

This basic principle, of inherently perfect long notes being imperfected by adjacent short notes, or alternatively of short notes being alterated into longer ones, was elaborated into an intricate set of precedence rules by notation theorists. In order to avoid remaining ambiguities, a separator dot (tractulus) was introduced to make clear which notes were supposed to form a triplex group together. It could be placed between a long and a breve to enforce perfect (triplex) value on the former when the latter would otherwise have imperfected it (signum perfectionis). It could also be used to disambiguate the readings of sequences of more than three breves in a row (divisio modi). The following (adapted from "Notation" in New Grove Dictionary of Music and Musicians) shows some of the resulting possibilities:

In their earliest stage, the rules of perfection and imperfection were applied only to the relation between longa and brevis. Beginning from the mid-14th century (with Philippe de Vitry's theory of the Ars nova), the same principles were also applied to the next smaller note values, the semibreves and minims. All subdivisions further down remained inherently and invariably imperfect.