Voice function and polyphonic cadence formulae

To recap, a full, standard polyphonic cadence of the middle and later fourteenth century is basically a three-part affair. It has an ‘authentic’ and a ‘plagal’ version, both witnessing the stepwise expansion of a combined major third and major sixth towards a combined fifth and octave. The authentic form sees the tenor descending by a tone and the cantus and contratenor ascending by a semitone, while the plagal form has the tenor descend by a semitone and the other two voices ascend by a tone. By the later fourteenth century, it is very common for final, clos cadences to be authentic, and for intermediate, ouvert cadences to be arrived at using plagal progressions.

In a two-part setting the contratenor function is removed. In a four-part setting the contratenor progression is doubled by the triplum and octave up, which is the same progression expected for this voice if it rather than a contratenor appears in a three-part setting. Examples of this kind of progression can be seen and heard in many of the extracts presented throughout this section of the website.

As can be surmised from these patterns, it is important to take into consideration both the general function and the local behavior of the voice to which unnotated ficta is being added. In the context of a D piece, for example, arrivals at an A sonority for a cantus and tenor performer are likely to be part on an unstable progression if not the work’s official ouvert sonority. As a result, they may well expect a plagal arrival, and the use of G and B-flat. Within the same piece, contratenor arrivals on A are likely to form part of clos cadences, moving towards the fifth a strong sonority. As such, the expectation for an authentic cadence is strong, which will in turn calls for G-sharp (to match the expected sixth E/C-sharp between tenor and cantus) and perhaps also F-sharp as part of its melodic preparation.

Personally, I recommend keeping both components of cadence structure in mind also in contexts such as this. Even if a B-flat was signified in the key signature, I would suggest a contratenor or triplum arrival to an A via G-sharp as part of a strong D cadence should take B-natural to be part of the same gesture and treat it as part of their cadential ficta. Especially when playing from parts, I would consider melodic cadential progressions such as B-flat : A : G-sharp : A to be very counterintuitive. If the first B-flat is indispensible or notated specifically, this can be a sign that the following G should not be inflected, weakening the approaching cadence. Such effect are treated below, but an interesting cases of such a procedure could be seen in the two three-part versions of R10 found in MS C, or the new contratenor given to R7 in MS E. In R10, the later contratenor added at the bottom of the page follows normal expectations and can easily accommodate a G-sharp as part of the ouvert cadence at the middle of the song (no B play a part in the progression).

Sound and Score     ¦     Facsimile

It is interesting that the original contratenor, which is maintained in the later, four-part version of this song, specifies a B-flat as part of this progression. This surprises the ear and ‘forces’ a weakening of the ouvert cadence, creating the sense that the music has to continue directly into the B-part.

Sound and Score     ¦     Facsimile

The opposite is found in R7. Here, the original two-part final cadence is a completely standard progression between cantus and tenor. The added contratenor of MS E behaves in the expected contrapuntal manner, but weakens the cadence through the insistence on B-flat and the implied G-natural. This is further highlighted by the likely performance of B-natural and C-sharp in the cantus while the B-flat in the contratenor is sounding.

MS A:   Sound and Score     ¦     Facsimile

MS E:   Sound and Score     ¦     Facsimile

 As basic behavioral guidelines, the combination of cadential expectations and common modal frameworks suggest the following patterns:

  • The cantus is likely to add more sharpening ficta in cadential progressions and more flattening ficta in other places.
  • The tenor tends to add relatively few extra inflections, and these tend to be flattening towards open cadence.
  • The contratenor (or triplum) is likely not only to have many additions, but also to use the most varied inflected pitches. Especially common are sharpenings a fourth below (or fifth above) cadential progressions in the cantus.

Even while maintaining the standard contrapuntal cadential relationships, manifestations of full cadences can vary greatly, as melodic elaborations and rhythmic play can cause the actual full leading sonority to be very short. In the following extract, taken from B41, the tenor and contratenor progress in a regular, stable way towards the cadence at its end. The early arrival on the triplum to its leading note and the late, ornamented arrival of the cantus, pepper the progression with some strong dissonances, such as brief sounding E-flat/g/d/f-sharp on the second beat of the second bar.

Sound and Score     ¦     Facsimile

Still, musicians hearing the progression and seeing the direction of travel of their voice would have no difficulty in adding the necessary F-sharp (and maintaining the B-natural after hearing an E-flat in the tenor) for the full cadence. Looking ahead at the direction of travel is especially pertinent to the medieval context as manuscripts presents the voices separately rather than in score. This also gives yet another reason to have strong expectations for the way your voice is likely to behave in a polyphonic context.

It is not obligatory to create a full cadence at every possible opportunity. Indeed, some works do not use the standard cadential progressions even in their final cadences. Still, when the notes allow, one is perhaps expected to strengthen arrivals at major resting points such as the ends of musical sections, or before a particularly strong cadence within a form part. Allowing for some cadences to remain partial can give different strengths to different arrivals and amount to another tool in a performer’s expressive and structuring arsenal. When doing so, the efficacy of this tool with its strong audible consequences should be kept in mind. There are a number of techniques for weakening cadences. Some involve the substitution of cadence notes with rests, supplying an unexpected sonority in place of the cadential perfection, or using a non-standard melodic progression to get to the cadence note. While present in many of the examples given, these are not relevant to the current discussion. As far as the addition of accidentals and ficta are concerned, weakened cadences involve the avoidance of one or both of the leading tones (semitone progression) presented as part of a full cadence above. At times, weakened cadences are explicitly notated. More often, the lack of notated accidentals in the source leaves the readers with a weak cadence which they can leave as it stands or add ficta in order to strengthen. It is, of course, also possible for ficta additions to weaken a cadence that is notated as a strong one in the source, or to change the strength of arrival between repetitions.

The different options are demonstrated by another extract from B41, taken from two different sources. This is the first ending of the A-part, complete with ouvert cadence on D (in the context of a C piece), and has four cadential progressions. These point towards the beginning of bars 8, 10, 11 and 12 of the song. The progressions towards b. 8 and 11 fulfill the melodic criteria for full cadences (even though the triplum avoids the cadence note in b. 8). The progression to b. 10 is more complex. It can be read either as a C cadence in which the tenor and contratenor swap voices and the triplum avoids its standard progression, or as a combination of two duets, the cantus and contratenor leading towards C and the triplum and tenor towards G with both higher voices avoiding melodic fulfillment through the insertion of a rest (triplum) or an unexpected sonority (G rather than C in the cantus). The ouvert arrival sees a normal progression (even if very quick) in the tenor and contratenor, but with the cantus doubling the contratenor and the triplum taking on the traditional cantus final note D, but avoiding the melodic progression via C.  This phrase allows for varied decisions to be taken about the required strength of these cadences.

Sound and Score     ¦     Facsimile

The version in MS A does not have flats in the key-signature. Instead, the first B7 in the cantus explicitly weakens the first cadential progression, even though both contratenor and triplum are instructed to create the lower leading tone by performing F-sharp. It seems clear that the triplum should raise also the second F of the bar, as it is also part of the leading figure to G. The cantus’ return to B-natural in b. 9 strengthens the pull towards C, matching the F-sharp in the tenor and emphasizing the surprising transition to G instead. Its repetition in the next bar is then fulfilled with the arrival on C at the beginning 11. As this is so close to the ouvert ending, I have decided to weaken this cadence, maintain F-natural in the triplum and contratenor and leave it with only one (upper) leading tone. The cantus’ signaled B-flat in this bar leads to the final A sonority of the ouvert and should be repeated a couple of notes later. Here again I kept the cadence week (as suggested by its extreme brevity of its rhythmic preparation), and avoided the possibility of adding an E-flat in the tenor. The structural clarity of final cadences of the different form parts is usually clear enough also when weakened, and doing so can help bind together  sections that are very often syntactically connected.

Sound and Score     ¦     Facsimile

The version in MS C has a B-flat in the signature of the cantus. In this case, it is rather tempting to fulfill the cadential expectation in b. 8 and add a B-natural as ficta. Its return to B-flat for the rest of the extract points more clearly towards its eventual arrival on the ouvert A, muddying the cadential progression to b. 10 and weakening further that of b. 11. As compensation, I added the E-flat in the progression to b. 12, making the final cadence of the section stand out from all the previously unfulfilled cadences.

Together, these two extracts demonstrate the five sonority possibilities of cadential progression: full authentic cadence (double leading tone); full plagal cadence (lower leading tone); two single leading tone cadences (upper only and middle only); and no leading tone.


Uri Smilansky


***********************STOP PRESS!!!!!!!!************************

The Complete Poetry and Music of Guillaume de Machaut Volume 1 is out now!!!!

Volume 1: The Debate Poems is now available in print.

You can also enjoy the entire volume online via the Middle English Texts Website.

Edited and translated by R. Barton Palmer, with art historical commentary by Domenic Leo, and musical commentary by Uri Smilansky, the volume contains  Le Jugement dou Roy de Behaigne, Le Jugement dou Roy de Navarre, and Le Lay de Plour.




The Ferrell-Vogüé Machaut Manuscript

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