The basic note values of mensural notation are essentially identical to the modern ones. Mensural notation uses the Breve, nominally the ancestor of the modern breve or double whole note; the Semibreve (whole note), the Minim (half note), Semiminim (quarter note / crotchet), Fusa (eighth note / quaver), Semifusa (sixteenth note / semiquaver), and very rarely smaller ones. There were also two larger values, the Longa and the Maxima (or Duplex longa).
|White notation (15th–16th cent.)|
|Black notation (14th–15th cent.)|
|Franconian notation (13th cent.)|
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 it was first used for. 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 (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:
At the 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.
Just like the notes, the rest symbols already had the same shapes that were later to develop into the modern symbols (with the smaller values being successively introduced in the course of the period of Mensural notation). Unlike the notes themselves, rests had a fixed, invariable duration and could not be perfected, imperfected or alterated; however, they could in turn induce imperfection on a neighbouring larger note. For longa rests, there were two separate forms for the perfect (triplex) and for the imperfect (duplex) longa. As a consequence of their invariant duration, a sequence of rests could be used as an indication of the prevailing meter of a composition (in the absence of modern bar notation). This is often found at the beginning of the tenor voice of a composition.
Ligatures are groups of notes written together. They were a holdover from the modal rhythmic system which preceded mensural notation, and they retained some of the original rhythmic meaning they had had there.
The origins of ligature semantics can be found in a rhythmical re-interpretation of the ligature neumes used since much earlier in the notation of Gregorian plainchant. In modal notation, ligatures had been used to represent stereotyped sequences of short and long notes, grouping notes together in much the same way as metric feet are used to group short and long syllables in Latin poetry. The most basic rhythmical unit was felt to be a group of one short and one long note (brevis-longa), like an iamb in poetry, filling an upbeat pattern in the typical 6/4 meter mentioned above. All other two-note groups were classified in terms of deviation from this basic pattern. In medieval terminology, a two-note ligature possessed "propriety" (proprietas) if and only if its first note was short; and it possessed "perfection" (perfectio) if and only if its second note was long. (Note that this sense of perfection is unrelated to the issue of perfect vs. imperfect in the sense of triplex vs. duplex duration of the long note as discussed above.)
|Value||Medieval terminology||Descending||Ascending||Alternative ascending|
|1.||BL||cum proprietate, cum perfectione|
|2.||LL||sine proprietate, cum perfectione|
|3.||BB||cum proprietate, sine perfectione||()|
|4.||LB||sine proprietate, sine perfectione||()|
|5.||SS||cum opposita proprietate|
In the course of time, some alternate versions of the ascending ligatures were developed (last column). Thus, the basic ascending podatus shape was replaced by one where the second note was both folded out to the right, and marked with an extra stem (two alterations cancelling each other out, as it were). The ascending L-L (sine proprietate) was modified accordingly. Some confusion consequently arose about how to write an ascending L-B or B-B (sine perfectione). This, in the end, was the only area of ligature notation that was controversial among contemporary theoreticians, with some authors prescribing one set of values to two ligature shapes, and other authors just the reverse.
For ligatures of more than two notes, the following rules hold:
By the late 15th century, the most common ligatures by far were those cum opposita proprietate (S-S), but all were still in routine use.
Unlike the original system of Franco of Cologne, which was geared towards the invariant metric pattern of 6/4 (with inherently triplex longa), later compositions from the 14th-century Ars nova onwards could display a greater variety of basic metric patterns. They can be defined as different combinations of duplex (imperfect) and triplex (perfect) subdivisions on successive hierarchical levels:
|1 maxima = 3 longae||1 maxima = 2 longae|
|1 longa = 3 breves||1 longa = 2 breves|
|1 brevis = 3 semibreves||1 brevis = 2 semibreves|
|1 semibrevis = 3 minimae||1 semibrevis = 2 minimae|
The perfect modus and maximodus were rare in practice. Of most practical importance were the subdivisions from the brevis downwards (by that time, the semibreves and no longer the breves had taken over the function of the basic counting unit). The four possible combinations of tempus and prolatio could be signaled by a set of mensuration signs at the beginning of a composition: a circle for tempus perfectum, a semicircle for tempus imperfectum, each combined with a dot for prolatio maior, or no dot for prolatio minor. These correspond to modern 9/8, 3/4, 6/8, and 2/4 meters respectively.
|Tempus perfectum||Prolatio maior||9/8|
|Tempus perfectum||Prolatio minor||3/4|
|Tempus imperfectum||Prolatio maior||6/8|
|Tempus imperfectum||Prolatio minor||2/4|
An individual composition was not limited to a single set of tempus and prolation. Meters could be shifted in the course of a piece, either by inserting a new mensuration sign, or by using numeric proportions. A "3" indicates that all notes will be reduced to one-third of their value; a "2" indicates double tempo; a fraction "3/2" indicates three in the time of two, etc. The proportion "2" could also be expressed by a vertical stroke through the mensuration sign (the root of the modern "alla breve" signature).
The use of numeric proportions can interact with the use of different basic mensurations in fairly complex ways. This has led to a certain amount of uncertainty and controversy over the correct interpretation of these notation devices, both in contemporary theory and in modern scholarship.
Another way of altering the metrical value of notes was coloration. This refers literally to the device of writing a note in a different color. In (earlier) Black Notation, colored notes were written in red. In (later) White Notation, coloring involved a switch between hollow and filled-in shapes. Colored notes are understood to have 2/3 of their normal duration, and are always imperfect with respect to their next smaller sub-divisions. Coloration was variously used to notate shorter passages of triplet or hemiolic rhythms. Coloration of single notes could also be used to override rules of perfection/imperfection that would otherwise have been called for. The use of red notation flourished in the so-called ars subtilior. Perhaps the most famous example is a heart shaped manuscript by Baude Cordier, which uses the notation for its symbolic effect to set down a line of music all in red within the larger heart.
Whereas the rules of notating rhythm in Mensural notation were in many ways different from the modern system, the notation of pitch already followed much the same principles. Notes were written on staves of five (sometimes six) lines, prefixed with clefs, and could be alterated by accidentals.
Mensural notation generally uses C-clefs and F-clefs, on various lines; G-clefs, while used infrequently throughout the period, did not come into completely routine use until the later 16th century. Clefs originally bore shapes more or less closely resembling the letter they represented, but in the course of time they developed more ornamental shapes like these 15th century examples:
Accidentals in mensural notation look essentially identical to those of today, and include both sharps and flats, of which flats are somewhat more common. Key signatures appear from the 14th century on, with one flat (always B-flat) the most common, and two flats (with the addition of E-flat) becoming increasingly common through subsequent decades; these are, in fact, the only flat key signatures which appeared prior to the mid 16th century. Much rarer are sharp key signatures, which never move beyond F- and C-sharp. Occasionally, flats appeared without the presence of a clef; in these cases, the flats essentially serve as a clef, since as we have seen, they are always B and E-flats, respectively.
The most significant difference between Mensural and modern notation in the area of pitch is the use of musica ficta: while some accidentals were written out, most routine chromatic alterations were not notated and left to be supplied by the performer.
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.