Mensural notation

A manuscript page of early mensural notation, late 14th century. The Agnus Dei of the Barcelona Mass.

Mensural notation is the musical notation system which was used in European music from the later part of the 13th century until about 1600. "Mensural" refers to the ability of this system to notate complex rhythms with great exactness and flexibility. Mensural notation was the first system in the development of European music that systematically used individual note shapes to denote temporal durations. In this, it differed from its predecessor, a system of rhythmic modes, which had been the first way to notate rhythm. Mensural notation is most closely associated with the successive periods of the late medieval Ars nova and the Franco-Flemish school of Renaissance music. Its name was coined by 19th-century scholars with reference to the usage of medieval theory, going back to the treatise Ars cantus mensurabilis ("The art of measured chant") by Franco of Cologne (c. 1280).

Note values

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).

Modern notation
White notation (15th–16th cent.)
Black notation (14th–15th cent.)
Franconian notation (13th cent.)

Differences between Mensural and modern notation are partly superficial, but partly quite fundamental:

• Notes were written diamond- rather than oval-shaped, and they had their stems perched directly on top (or bottom, very occasionally) rather than to one side. Before the mid-15th century, all notes were written in solid, filled-in form (Black Notation), but after that the larger note values were written hollow, like today (White Notation).

• Each note had a much shorter temporal value than its nominal modern counterpart. This is because in the course of time, composers invented new note shapes for ever smaller temporal divisions of rhythm, and the older, longer notes were slowed down in proportion. Thus, the basic metrical relationship of a long to a short beat shifted from longa–breve in the 13th century, to breve-semibreve in the 14th and 15th, to semibreve-minim by the end of the 16th, and finally to minim–semiminim (i.e. half and quarter notes) in modern notation. What was originally the shortest of all note values used, the semibreve, has today evolved into the longest note used routinely, the whole note.

• While the relation of each note value to the next smaller one in modern notation is invariably 2:1 (unless indicated otherwise), the mensural system was more flexible. The principal members of the system – maxima, longa, breve, and semibreve – could all contain either two or three of the next smaller units. Whether a note was to be read as triplex (perfecta) or duplex (imperfecta) was a matter partly of context (see below) and partly of mensuration signs, a system comparable to modern time signatures (see below).

• Sequences consisting of the larger members of the system (maxima, longa, breve, and semibreve) could optionally be written together as ligatures.

• Bar lines and ties were not used.

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:

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.

Rests

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

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.)

1. Accordingly, a note pair cum proprietate et cum perfectione could be written with the most basic of ligature shapes, those inherited from plainchant, namely the descending clivis and the ascending podatus.
2. If, by way of exception, the first note was to be long (sine proprietate), this was signaled by a reversal of the use of stems: leave out the stem of the descending clivis; add a stem to the ascending podatus.
3. If, conversely, the second note was to be short (sine perfectione), this was signaled by a change in the noteheads themselves: replace the descending sequence of square heads with a single diagonal beam; fold out the second note of the ascending to the right.
4. If both exceptions co-occurred (sine proprietate et sine perfectione), both graphical alterations were combined accordingly.
5. In addition to sequences of a longa and a breve, ligatures could also contain a pair of semibreves (but never a single one). These were called cum opposita proprietate, and consistently marked by an upward-pointing stem at the left of the note pair.

	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:

• Any notehead with an upward stem to its left is the first of a pair of semibreves (cum opposita proprietate).
• Any medial notehead with a downward stem to its right is a longa.
• A prolonged, double-wide notehead with a downward stem to its right is a maxima.
• Any other notehead not covered by any of the rules above is a brevis.
• The perfect or imperfect duration of each note within a ligature is determined according to the same principles as for the standalone notes.

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.

Modes and mensuration signs

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:

Maximodus	perfectus	imperfectus
	1 maxima = 3 longae	1 maxima = 2 longae
Modus	perfectus	imperfectus
	1 longa = 3 breves	1 longa = 2 breves
Tempus	perfectum	imperfectum
	1 brevis = 3 semibreves	1 brevis = 2 semibreves
Prolatio	maior	minor
	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

Proportions and colorations

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).

A page of the heart-shaped manuscript by Baude Cordier, showing a rhythmically complex piece of ars subtilior.

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.

Pitch notation

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.

Clefs

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 and musica ficta

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.

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.

Examples

15th century

The following example shows the use of Mensural notation in the mid-15th century. It is a three-part English carol, Hail Mary full of grace, as contained in the manuscript Ms. Selden B.26, f.23, c.1450. The example illustrates the use of perfect and imperfect breves and alterated semibreves within a tempus imperfectum cum prolatione majore (6/8 time), as well as the use of some ligatures cum opposita proprietate, and the occasional use of coloration for the notation of hemiolic (3/4 instead of 6/8) patterns.

Example in Mensural notation (reset after original)

Example transcribed into modern notation

External links

• Raybro's Reading White Mensural Notation - an excellent compendium of information on mensural notation, with images.
• In the early music newsgroups, there have been some very interesting discussions in the past ten years of musica ficta in performance, featuring such illustrious scholars as Margaret Bent.
• Peter Urquhart’s ficta page
• Potato print - facsimile examples
• Extended introductions to ligatures, mensuration, and coloration

References and further reading

• Willi Apel, The Notation of Polyphonic Music, 900-1600, 5th edition, Cambridge, MA: The Medieval Academy of America, 1961.
• Roger Bowers, 'Proportional notation,' The New Grove Dictionary of Music and Musicians Online, accessed 4 June, 2005. (subscription access)
• David Hiley, Thomas B. Payne, Margaret Bent, Geoffrey Chew and Richard Rastall, 'Notation: III and IV,' The New Grove Dictionary of Music and Musicians Online, accessed 4 June, 2005. (subscription access)