Nabokov, Nicolas [Nikolay]

(iii) The system of modal rhythm.

At some point between the composition of the early part of the Discantus positio vulgaris and the treatise ascribed to Johannes de Garlandia (c1240–60) the diverse rhythms of Parisian polyphony were abstracted into a series of repetitive patterns, analogous perhaps to the modern function of a time signature. These underlying patterns, termed ‘modes’ (Lat. modi, sing. modus; Garlandia: manieres), formed the principal means of signifying ligature rhythms until the advent of mensural clarifications to their shapes (see Rhythmic modes). The following list names authors whose works include discussions of modal rhythm. However, it is important to realize that mensural doctrines appear in treatises as early even as Garlandia's text. Furthermore, occasional inconsistency exists in these theoretical works as to the number of the modes, their ordering and the depiction of particular ligature shapes.Anonymous: Discantus positio vulgaris (c1230–40: survives only in a partly revised form; see Reckow, AcM, 1976, p.137, n.81); ed. Cserba, 1935, pp.189–94
Johannes de Garlandia: De mensurabili musica (c1240–60: portions may stem from an anonymous earlier treatise; the final chapter of the work as it survives in F-Pn lat.16663, ed. in CoussemakerS, i, postdates Franco); ed. Reimer, 1972
Bruges Organum Treatise (possibly earlier than Garlandia); ed. Pinegar, 1992
Anonymus 7 (certain portions identical to the Bruges treatise; others may postdate Franco; see Reimer, 1972, i, p.31, n.20); CoussemakerS, i, 378–83, and CSM, xxxvi
Amerus/Aluredus: De musica libellus (1271); ed. Kromolicki, 1909, and CSM, xxv
Anonymus 4 (after 1272); ed. Reckow, 1967
Dietricus: Regule super discantum (c1275); ed. Müller, 1886
Magister Lambertus: Tractatus de musica (c1275); CoussemakerS, i, 251–81
Anonymus of St Emmeram (1279); ed. Sowa, 1930, and Yudkin, 1988
Franco of Cologne: Ars cantus mensurabilis (c1280: see Frobenius, 1970); CSM, xviii
Walter Odington: Summa de speculatione musicae (before 1300); CSM, xiv

Table 6 shows the six commonest rhythmic modes in their most conventional numerical ordering together with their associated ligature patterns (indicated by brackets over the notes). Each has a fundamental recurrent pulse equivalent to the ultra mensuram long (= dotted crotchet), and each pulse divides into three smaller time units (tempora/breves = quaver). Several important distinctions among the patterns are defined by whether the main pulse falls on the last note of the ligature (i.e. 1, 3a–b, 6a–b) or on the first (2, 4, 6c), whether the pulse is divided L–B (1a–b, 3b, 6b) or B–L (2, 3a, 4, 6c) and whether a ternary ligature extends over one, two or three pulses. (The value of the three-note ligature is the most equivocal and in the 5th mode is restricted largely to the tenor part in discant passages; the 4th mode, curiously, appears to be a theoretical construction not encountered in practice.) In all these important distinctions, the note shapes as they appear in the manuscript sources remain ambiguous; harmonic consonance, the succession of ligatures and the proportions between parts all contribute to define (or confound) the intended rhythm. This ambiguity appears to have prompted the writing of many of the treatises listed above, as their authors tried to clarify the intended durations by modifications to the standard, chant-based notational figures.



Notation, §III, 2: Polyphony and secular monophony to c1260

(iv) Coniuncturae, plicae and strokes.

One of the most ambiguous of all modal figures was the climacus, which was drawn with lozenges in square notation. These were called currentes (Lat.: ‘running’) by Anonymus 4, probably as an extended use of a term that originally referred to the descending scales found in Aquitanian as well as Parisian polyphony. Johannes de Garlandia did not mention them at all, possibly because they could be confused with the rhomboid semibreve. Franco of Cologne called the figure the coniunctura (Lat.: ‘joined [note]’), and even in his most rational system it eluded rhythmic codification.

Liquescent forms of neumes also appeared in melismatic polyphony in modal rhythm. Usually they indicated an added breve on a weak beat (see modes 6b–c), although other values were possible according to the prevailing rhythmic framework and the length of the host note. Because a single liquescent note was usually written like a ‘U’ or an inverted ‘U’, it was termed Plica (Lat.: ‘fold’). A vertical stroke added to the end of ligatures made them ‘plicata’. The liquescent neume, however, did not abandon its original function in such texted music as conductus, secular monophony and in chant settings if the cantus firmus demanded it.

Vertical strokes were used for two different purposes: as indications of changes of syllable and to signify rests. For the first purpose 12th-century scribes drew a roughly vertical line through both staves, although in Parisian sources this shrank to a small stroke through one or two lines only. Where a rest was intended its duration was not specified, although it frequently corresponded to the penultimate value of the modal pattern.

Whereas former repertories tended to preserve the ligatures of cantus firmi, undifferentiated single notes were typical for tenors in the early Parisian corpus, whether the tenor held long notes in Organum or moved with the pulse in discant (see Discant, §I). Only in the later layers of discant did tenors include ligatures with breves. Although a stroke generally appears after each note of the tenor in organum, the pitch seems to have been sustained beneath the continuing organal voices. Anonymus 4 called this a burdo (Lat.: ‘support’, ‘drone’).

Notation, §III, 2: Polyphony and secular monophony to c1260