4.4

# Ligatures as rhythmic figures: mensural rules II

As we showed last week, ligatures are the central means to convey rhythm in the modal notation of the 12th and early 13th centuries. We have learned that in modal notation they represent some sort of ‘code’ that was used to indicate pre-existent rhythmic patterns. In the course of the 13th century, however, different forms of ligatures increasingly came to signify fixed rhythmic sequences. The notational signs of the ligatures gradually lost the semantic ambiguities they had had in modal notation. As a consequence, the exact form of the ligatures gained crucial importance. In this article, we want to introduce you to these ligature forms and their uses and meanings in the second half of the 13th century. This development culminated in the ligature rules of Franco of Cologne which remained valid until ligatures became obsolete around the end of the 16th century.

While ligatures of two notes in modal notation mostly translated into the sequence brevis-longa, three-note ligatures were ambiguous in their meaning which depended on the given mode. This changed with the great motet manuscripts of the 13th century, Codex Bamberg (Staatsbibliothek, Lit. 115) and Codex Montpellier (Faculté de Médecine H 196). While the tenors were still mostly notated in modal notation in the older parts of these manuscripts, for the upper voices ligatures were used in a new way. Two-note ligatures were now read in the context of the neighbouring notes. Depending on whether they stood for a perfect longa (three tempora), an imperfect longa (two tempora) or a breve (one tempus), they could now signify different rhythms. The same applied to three-note ligatures. The following table shows the different forms of ligatures and their corresponding values in place of one, two or three tempora.

Table 1: Ligatures before Franco of Cologne. The same ligatures could have different values depending on their context. (Click to expand)

Whereas two-note ligatures could signify different rhythms depending on their form, three-note ligatures mostly meant the same rhythm, regardless of their form but depending on their relative position. Three-note ligatures in place of an imperfect longa represent the sequence semibreve-semibreve-breve, and in place of a perfect longa mostly three breves. Please note that an upward stem in the beginning of a ligature always indicates two semibreves.

As can be seen in our table 1, the ligatures used in the earlier parts of Ba and Mo still remain slightly flexible in their meaning, allowing different readings depending on their contexts. Looking back, they can thus be considered some sort of transition towards the fixed ligature rules which were set by Franco of Cologne in his treatise Ars Cantus Mensurabilis (around 1280) and which, in their strictness and clarity, brought a new notational flexibility that ended the constraints of the modes.

Francos ligature rules took as their starting point the ‘standard’ square notation appearance of two- or three-note neumes (pes, clivis, torculus, porrectus, climacus, scandicus –> see Step 2.4). He established that a ligature has a beginning and an end (its first and last note). The beginning could be cum proprietate (‘with property’) and sine proprietate (‘without property’), the end of the ligature could be cum perfectione (‘with perfection’) and sine perfectione (‘without perfection’). If the ligature had the standard neume appearance, it was deemed cum proprietate and cum perfectione and the first and last notes were translated as brevis-longa. The standard appearance could be modified by either adding or removing stems, turning note heads or replacing square with oblique note forms.

Table 2: Ligatures written according to the rules of Franco of Cologne. Signs become distinct. (Click to expand)

Let us take the pes as an example. If the second note was turned right, the ligature lost its perfectio and had to be read brevis-brevis. If one added to this modified pes a stem on the right side of its first note, it also lost its proprietas and was thus read longa-brevis. If such a stem was added to the right side of the first note of an unmodified pes, the ligature lost its proprietas but kept its perfectio and hence signified longa-longa. An upward stem at the beginning of the ligature indicated opposita proprietas (‘opposite property’) and, like in pre-Franconian ligatures, produced two semibreves.

The clivis could undergo similar modifications. While in its standard form it meant brevis-longa (cum proprietate et cum perfectio), it lost its proprietas when the stem on the left side of the first note was removed and was then translated as longa-longa. If the stem was kept but the second note was transformed into an oblique form, it lost its perfectio (making brevis-brevis). If the stem was removed from this oblique ligature, it was regarded as sine proprietate et sine perfectio and thus read as longa-brevis. Again, the upward stem produced two semibreves.

Ligatures with three or more notes functioned according to the same principles that are shown in our table 2. Middle notes were always regarded as brevis unless a downward stem was drawn on the right side of any note within the ligature. The upward stem at the beginning of a note (opposita proprietate) was only applied to the first two notes in the ligature, turning them into semibreves.