Mensural notation
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 amongst note values. Its modern name is derived from the terminology of medieval theorists, who used terms like musica mensurata or cantus mensurabilis 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 solely 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 by Franco of Cologne. 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 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 or binary 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 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.
Note values
The system of note types used in mensural notation closely corresponds to the modern system. The mensural brevis is nominally the ancestor of the modern double whole note ; likewise, the semibrevis corresponds to the whole note, the minima to the half note, the semiminima to the quarter note, and the fusa to the eighth note. Very rarely, mensural notation also used yet smaller subdivisions, such as the semifusa. There were also two larger values, the longa and the maxima, which are no longer in regular use today.Despite these nominal equivalences, each note had a much shorter temporal value than its modern counterpart. Between the 14th and 16th centuries, composers repeatedly introduced new note shapes for ever smaller temporal divisions of rhythm, and the older, longer notes were slowed down in proportion. 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, to semibreve–minim by the end of the 15th, and finally to minim–semiminim in modern notation. Thus, what was originally the shortest of all note values used, the semibreve, has become the longest note used routinely today, the whole note.
Originally, all notes were written in solid, filled-in form. In the mid-15th century, scribes began to use hollow note shapes, reserving black shapes only for the smallest note values. This change was probably motivated by the change from parchment to paper for the most common writing material, as paper was less suited to holding large dots of ink.
Rests
As with the notes, the shapes of the rest symbols in mensural notation are already similar to their modern descendants. The rest symbols of the larger values had a clear visual logic reflecting their time durations, based on the breve rest being a vertical stroke the length of one staff space. For the longa rests, a visual distinction was made depending on whether the longa was imperfect or perfect. Accordingly, their signs were visually twice or three times the length of a breve rest respectively, while the semibreve rest was half that length. Maxima rests, in turn, were groups of two or three longa rests combined. If several longa rests followed each other, groups of either two or three of them were written together on the same staff line to indicate whether they were supposed to be grouped into perfect or imperfect maxima units.Ligatures
| value | proprietas perfectio | desc. | asc. |
| B–L | cum propr. cum perf. | ||
| L–L | sine propr. cum perf. | ||
| B–B | cum propr. sine perf. | ||
| L–B | sine propr. sine perf. | ||
| Sb–Sb | cum opposita p. |
Ligatures are groups of notes written together, usually indicating melismatic singing of the same syllable over several notes. Ligature forms exist only for the larger note values from the semibreve upwards. Their use in mensural notation was a holdover from the earlier modal rhythmic system, of which they inherited some of their rhythmic meaning.
The rhythmic values of ligatures in modal notation had been based on a metric reinterpretation of the ligature neumes used since much earlier in the notation of Gregorian plainchant. In modal notation, ligatures represented stereotyped rhythmic sequences of short and long notes, typically involving groups of one or more initial short notes and one final long note. In mensural notation, this rule was generalized, with all other rhythmic combinations being classified in terms of deviation from this basic pattern. In medieval terminology, a ligature possessed perfectio if its final note was a longa, and it had proprietas if its first note was a breve.
Accordingly, a note pair of B–L ' could be written with the most basic of ligature shapes, those inherited from plainchant, namely the descending clivis and the ascending podatus. Likewise, three-note groups of B–B–L could be written with some of the inherited ternary neumes, such as the porrectus, the torculus, or the scandicus.
If, by way of exception, the first note was to be a longa ', this was indicated by a reversal of initial stems: the descending clivis had its downward stem removed, while, conversely, the ascending podatus had one added to it.
On the other hand, if the final note was to be a breve ', this was signaled by a change in the noteheads themselves: the descending sequence of square heads was replaced with a single diagonal beam, while the ascending podatus had its second note unfolded to the right. Both sequences correspond to the initial B–B segments of the ternary porrectus and torculus respectively.
If both exceptions concurred ', the corresponding alterations were combined.
In addition to sequences of longa and breve, ligatures could also begin with pairs of semibreves. These were called cum opposita proprietate, and always marked by an upward-pointing stem to the left of the note pair.
There were also some alternate versions of the ascending ligatures. Thus, the basic ascending B–L podatus shape was replaced by one where the second note was both folded out to the right and marked with an extra stem, as if these two modifications were meant to cancel each other out. The ascending L–L ' was modified accordingly.
Ligatures could contain any number of notes. In multi-note ligatures, the rules about initial and final values are applied in analogy to those in the binary forms. In addition, the following rules hold for notes in all positions:
- Any notehead with an upward stem to its left is the first of a pair of semibreves '
Mensurations
| Ternary | Binary | |
| Maximodus | perfectus 1 Mx = 3 L | imperfectus 1 Mx = 2 L |
| Modus | perfectus 1 L = 3 B | imperfectus 1 L = 2 B |
| Tempus | perfectum 1 B = 3 Sb | imperfectum 1 B = 2 Sb |
| Prolatio | maior 1 Sb = 3 Mn | minor 1 Sb = 2 Mn |
Mensural notation distinguished between several basic metric patterns of a piece of music, which were defined as combinations of ternary and binary subdivisions of time on successive hierarchical levels and roughly correspond to modern bar structures. The division of the semibreve into minims was called prolatio, that of the breve into semibreves was called tempus, and that of the longa into breves was known as modus. The division of the maxima into longas was called modus maximarum or modus maior; in the modern literature it is also sometimes called maximodus. Each of these levels could be either perfect or imperfect. The two types of prolatio were also known as "major prolation" and "minor prolation" respectively.
The perfect modus and maximodus became rare in practice after the 14th century. Of most practical importance were the subdivisions from the breve downwards, as by that time the semibreves rather than 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 measures of,,, and respectively, or alternatively,, and respectively. In each case, one breve corresponds to one modern bar. In addition, each of these basic patterns had a diminished variant, indicated by a vertical stroke through the sign. These so-called "cut signs" indicated a reduction of all temporal values by a factor of two. A reversed semicircle was usually understood to be the same as.
There were normally no special signs for indicating the higher divisions of modus and maximodus. However, groups of longa rests at the beginning of a piece could be used as an indicator of the intended meter. If longa rests were written across three staff spaces, they were perfect; moreover, if they occurred in groups of three written together on the same staff line they indicated perfect maximodus. Occasionally, if no voice happened to have a sufficiently long rest at the beginning of the piece, a dummy rest symbol of one maxima's worth of longae would be written to the left of the mensuration sign; in that case it was understood as part of the time signature and not actually executed as a rest.