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Musical notation system used for Renaissance vocal polyphony

Mensural notation is the musical notation system used for polyphonic European vocal music from the late 13th century until the early 17th century. The term "mensural" refers to the ability of this system to describe precisely measured rhythmic durations in terms of numerical proportions between note values. Its modern name is inspired by the terminology of medieval theorists, who used terms like musica mensurata ("measured music") or cantus mensurabilis ("measurable song") to refer to the rhythmically defined polyphonic music of their age, as opposed to musica plana or musica choralis, i. e., Gregorian plainchant. Mensural notation was employed principally for compositions in the tradition of vocal polyphony, whereas plainchant retained its own, older system of neume notation throughout the period. Besides these, some purely instrumental music could be written in various forms of instrument specific tablature notation. Mensural notation grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so called rhythmic modes, which were developed in France around 1200. An early form of mensural notation was first described and codified in the treatise Ars cantus mensurabilis ("The art of measured chant") by Franco of Cologne (c. 1280). A much expanded system allowing for greater rhythmic complexity was introduced in France with the stylistic movement of the Ars nova in the 14th century, while Italian 14th century music developed its own, somewhat different variant. Around 1400, the French system was adopted across Europe, and became the standard form of notation of the Renaissance music of the 15th and 16th centuries. Over the course of the 17th century, mensural notation gradually evolved into modern measure (or bar) notation. The decisive innovation of mensural notation was the systematic use of different note shapes to denote rhythmic durations that stood in well defined, hierarchical numerical relations to each other. While less context dependent than notation in rhythmic modes, mensural notation differed from the modern system in that the values of notes were still somewhat context dependent. In particular, a note could have the length of either two or three units of the next smaller order, whereas in modern notation these relations are invariably binary. Whether a note was to be read as ternary ("perfect") or binary ("imperfect") was a matter partly of context rules and partly of a system of mensuration signs comparable to modern time signatures. There was also a complex system of temporarily shifting note values by proportion factors like 2:1 or 3:2. Mensural notation used no bar lines, and it sometimes employed special connected note forms (ligatures) inherited from earlier medieval notation. Unlike in the earliest beginnings of the writing of polyphonic music, and unlike in modern practice, mensural notation was usually not written in a score arrangement but in individual parts. Mensural notation was extensively described and codified by contemporary theorists. As these writings, like all academic work of the time, were usually in Latin, many features of the system are still conventionally referred to by their Latin terms.

Sometimes, music was written in such a way that the same line of music had to be performed under two or more mensuration schemes, typically leading to slower (augmented) and faster (diminished) versions of the same passage. In such cases, the music was typically notated only once, and several different mensuration signs were placed in front of it together, often supplemented with a verbal instruction of how it should be executed (called a "canon"). This technique could be applied both successively and simultaneously. Successive mensural canons were a characteristic feature of late 14th and early 15th century isorhythmic motets. A famous example is Nuper rosarum flores by Guillaume Dufay, where the tenor (notated all in longa and a few breve values) is performed first as tempus perfectum , then tempus imperfectum , then tempus imperfectum diminutum , and finally tempus perfectum diminutum , leading to length relations of 6:4:2:3 between the four repetitions. Pieces that demanded simultaneous execution of versions of the same music, i. e., contrapunctal canons, were written by several composers of the Franco Flemish school in the late 15th and early 16th century, such as Josquin des Prez, Johannes Ockeghem or Pierre de la Rue. Ockeghem's Missa prolationum is famous for systematically exploring different ways of combining pairs of voices in mensural canons. In the example given below, from the first "Kyrie" of this mass, both upper voices sing the same notated line, one reading it as "tempus imperfectum" and the other as "tempus perfectum". The two lower voices are similarly coupled with each other. Each of the four voices thus starts the piece in a different mensuration, leading to different bar length in the modern transcription. (The lower voices, which are written in prolatio maior, later shift to a meter where all semibreves are imperfected through black coloration, which means they end up having the same length as those of the upper voices after all.)

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 altered by accidentals.

The use of accidentals in medieval and renaissance music differs significantly from modern practice. Medieval notation used two accidental signs, the "b molle" and the "b durum" While the former was identical in form to the modern flat sign , the latter could be written in forms that resemble either the modern sharp or the modern natural , but these functions were not distinguished from each other as they are today. The b molle served to pick out the lower of two alternative semitone steps for a given note (e. g., a B as opposed to a B), while the b durum served to pick out the higher one (e. g., B as opposed to B, but also F as opposed to F, etc.). The meanings of both signs thus overlaps with that of the natural sign today. Until the 16th century, only the flat signs regularly occurred as key signatures at the beginning of a staff (one or at most two flats). Both forms of accidentals could occur as temporary accidentals elsewhere; however, in practice they were often not written but left to the performer to infer according to the rules of counterpoint and musica ficta.

Mensural notation may contain a number of other symbols.

The custos (pl. custodes, from the Latin for guard) appears at the end of the staff on or between the staff lines. It indicates the pitch of the first note that occurs on the following staff that belongs to that part relative to the clef of the current staff. This helps performers to prepare to sing the next note without having to look away from the current passage (analogous to the catchword in older printed books). If the next staff for the part occurs on the following page, two custodes may appear immediately next to each other. In the earliest manuscripts, custodes appear as thin or small notes (somewhat like modern cue notes). By around 1500 a separate sign resembling a 'w' with a long upward tail had been developed, which briefly survived into the more modern musical notation of the early Baroque period (early 17th century).

The corona appears above the last note of the piece (or section). It is similar to the fermata in modern notation. It typically appears above the last note at each part of a piece to indicate the note should be held longer that its value indicates. If it appears somewhere other than at the end of a piece, typically a short pause is expected before proceeding with the notes after the note with the corona.

The signum congruentiae indicates the position of entry of another voice. This is used to denote canons and rounds. Instead of writing out all parts, only one part is written out. The signum congruentiae indicates the point in each part where the following part must start from the beginning. There is some variation in the way signa congruentiae are denoted.

The most important early stages in the historical development of mensural notation are 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 rhythmic modes. He also refined the use of semibreves:, while in earlier music, one breve could occasionally be replaced by two semibreves, Franco described the subdivision of the breve as ternary (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 breve into even more short notes. However, he did not yet define these as separate smaller hierarchy levels (minim, semiminim etc. ), but simply as variable numbers of semibreves. The exact rhythmic interpretation of these groups is partly uncertain. The technique of notating complex groups of short notes by sequences of multiple 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 metric 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 and imperfection across all levels, down to the minim, and it introduced the devices of proportions and coloration. During the time of the Franco Flemish school in Renaissance music, use of the French notation system spread throughout Europe. This period brought the replacement of black with white notation. It also brought a further slowing of the duration of the larger note values, while introducing even more new small ones (fusa, semifusa, etc.). Toward the end of this period, the original rules of perfection and imperfection became obsolescent, 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, ultimately leading toward the modern notation system.

[=Apel 1961, in German.]