i. Voice Hierarchy and Structure

The genre in which the hierarchic structure of the polyphonic fabric is clearest is certainly the motet. Since its origin in the early thirteenth century, the motet was traditionally constructed departing from a borrowed melody with its words which, rhythmicized in large values, served as its lowest part, the tenor. In most motets this melody was a melismatic fragment from Gregorian chant. Such is also the case with Machaut’s contributions to the genre; in three works only did he use a secular song as basis, thereby following another thirteenth-century tradition which otherwise had no follow-up in the fourteenth. The tenor is not the only borrowed material; also in the upper voices, called motetus and triplum, verbal citations are often found, usually from thirteenth-century songs though normally not together with their melody as in the tenor. All these citations point to the fact that the motet was an intellectual genre: to unravel the deeper meaning of the work one had to recognize the quotations in the first place, next to understand their context and the reason why they were chosen, and thirdly to apprehend how they are used in their new context. Only the literate had the necessary culture to appreciate these references to the past.

Machaut’s works in this genre are transmitted exclusively with their music (with a small exception, his motet about Fortune, M8, which appears in one peripheral source as text only); this is unlike the other lyric genres where usually both versions with and without music appear in the manuscripts. It is an indication that text and music were considered to be inseparable in the motets.

The choice of the melisma that, with its text, was to serve as the tenor depended on the pre-defined subject of the work, usually a problem of some kind. Remarkably, Machaut always found a fitting melisma, having the right words and a melody which permitted the composition of a polyphonic work. This is not as obvious as it may seem: the melisma had to offer possibilities for cadences and certainly for a satisfying closure. Not any melodic fragment will do, and Machaut must have known the Gregorian repertoire extremely well to make the choices we find in his works. Most but not all of his tenors have been identified; of the identified ones it is amazing how well not only the words but also the original context fits the subject and how each melody permitted the composition of an exciting piece of music.

Machaut’s original corpus of motets consisted of a series of 20 pieces, all but one for three voices and probably all finished at a fairly early stage, to which in the late 1350s three four-voice motets were added. Typical is his preference for subjects of courtly love and for the French language whereas his contemporaries more often chose political or ceremonial subjects with texts in Latin. In six of Machaut’s 23 motets, including the late ones, comparable subjects are dealt with, indeed in Latin. In the majority of his works, however, a parallel is drawn between the religious plane of the biblical world evoked by the tenor and the courtly world in the newly composed upper voices which each present the problem in a different manner or from different angles. This parallel can give rise to very different interpretations, depending on how much weight one assigns to each of the two spheres.

M1, Quant en moy/Amour et biauté/Amara valde, was probably meant as an exemplary work: in all but one of the main manuscripts this work is placed first, and in his ordering of his works per genre Machaut always placed a special work in the front position. Its texts as well, namely in the triplum, indicate a beginning. It may therefore serve as an illustration of the hierarchic structure of the motet.  The following discussions do not attempt to offer a complete interpretation of the piece, but rather illustrate selective characteristics of its hierarchical structuring, both as a representative of the motet genre and as relevant to its specific theme.[1]

The discussion is divided up into consideration of the choice and combination of text typifying the motet genre, the process of creating order using different musical parameters, illlustrated using M1, and the structuring use of counterpoint in this piece to highlight the central ideas of its text. Appended to the various explorations of this motet is a short overview of the differences in attitude to structure and hierarchy in the songs compared with the motet genre.

As reading through these discussions will make clear, M1 presents a reflection on the idea of perfection and the difficulty to reach it: perfection as a mensural idea; perfection in the sense of fulfilment as a goal of love and as the acceptation by the beloved; perfection as an ideal of comportment to strive after for a lover who wants to ‘perfect’ himself. This makes M1’s place at the head of the series of motets a well deserved one.

Not in all Machaut’s motets is the hierarchical structure as clear-cut as in M1; often the upper voices are more similar in movement, although the motetus is always slower than the triplum. In M11, the only other motet in which the lover addresses himself directly to his lady and which has a secular song for its tenor, the three voices are closest in movement, suggesting a greater degree of intimacy (this work is taken as a case study for the addition of ficta here). In other works the voices are more divergent, as when the tenor moves in maximodus, the very large values of maximae and longae, e.g. in M3. The prolatio level is the most formulaic and thus the least varied and interesting in rhythm; interesting problems of mensuration occur mainly in the larger values of tempus and modus. In this respect the motets differ from the songs where the modus level is often less important and rhythmic complications are found on the level of tempus and prolatio. M20, built on a rondeau and moving mainly in values of tempus and prolatio, is the exception, with some interesting rhythmic complications on the prolatio level. This work forms the transition between the genres of motet and song; in the earliest manuscript C it closed the series of motets. Interestingly, apart from M1, this motet alone has perfect mensuration overall. Thus in its original concept Machaut’s series of 20 motets began and ended with a motet in exclusively perfect values, suggesting that at least in the motets the traditional qualitative distinction between perfect and imperfect mensuration, whereby imperfect values were felt to need completion, was still in vigour.


Jacques Boogaart

[1] For a more extensive discussion of M1 with sometimes different interpretations and conclusions, see Alice V. Clark, ‘The Motets Read and Heard’, in Deborah McGrady & Jennifer Bain, eds, A Companion to Guillaume de Machaut (Leiden: Brill, 2012), pp. 185-208.


1. Creating a Constellation of Texts

M1 is based on a melisma from a chant belonging to matins of Holy Saturday, the day of expectation before Easter.

Sound and Score    ¦    Facsimile

Easter is the most important day in the Christian year, the celebration of the fulfilment of human salvation by Christ’s resurrection. The melisma itself, by its text Amara valde derived from the prophetic books of the Old Testament, points even further, to that ‘great and very bitter’ Day of Judgment that will come, on which the human soul will be accepted or refused by the supreme Judge. Thus the tenor evokes mixed feelings of expectation, joyful in the awaiting of the fulfilment of Easter, fearful when thinking of the final acceptance or refusal on the Day of Judgment. In the French texts of the upper voices the problem is also acceptance or refusal, but now of the lover by his lady.

Motet 1 Texts and Translations

In the motetus the lover vows to love ‘perfectly’ and asks his lady for grace, but on the express condition that it will not impair her honour. Since a lady of honour must never confess her love openly, this implies that the lover will have to wait endlessly for the fulfilment of his love. In the triplum the lover has just fallen in love for the first time and is uncertain about the outcome of his courtship, but also here he is kept waiting and must serve faithfully with only a faint hope of his love being fulfilled in the future. This makes him exclaim, sighing, that ‘amer’ (to love) is ‘amer’ (bitter), a classic wordplay in courtly poetry; the sound and signification of those words correspond with that of the tenor word ‘Amara’ which is so similar in sound to ‘Amare’ (to love). Thus the motet deals not only with the beginning of love but also with its possible outcome, its ‘perfection’. Waiting for fulfilment and striving for perfection are the feelings which the three texts have in common, but in opposed ways, positive and negative, as a fundamental tension.


Jacques Boogaart

2. Ordering through mensuration and range

After the choice of the basic melisma, called the color of the motet, the work was, musically speaking, as yet formless. By the rhythmicization of the color, in this case containing 30 notes, the composer gives a form to his motet; the resulting tenor constitutes ‘its bones’, as the theorist Johannes de Grocheio called it around 1300. On this foundation the upper voices are built.

A clear hierarchy exists in the movement of M1, which is at the same time a historical one. 

The tenor has the largest values, longae and breves, the oldest note types with which the whole development of mensuration began in the organum of the early thirteenth century; this mensuration level is called modus.



The motetus adds semibreves to these, such as appeared in the later thirteenth-century motet on the level of tempus.




The triplum also contains the most recent values of the fourteenth century, the minimae, on the level called prolatio (the motetus, too, has minimae but only six). 



Exceptionally, all the mensuration levels are perfect, i.e. ternary: the longa is worth three breves, the brevis three semibreves and the semibrevis three minimae (usually the mensural levels are mixed, with perfect modus, imperfect tempus and perfect prolatio being the most common combination). In the transcription these values are usually reduced by 4, i.e. the longa is transcribed as a whole note, the brevis as a half note, the semibrevis as a quarter note and the minima as an eighth note.

To make this element easier to follow, the following extract presents a different timbre for each voice, emphasising the tenor and therefore the way the other voices refer to it.

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When the tenor melody has been sung completely, a change in movement takes place: its melody is repeated but thrice as fast. This is the result of the so-called diminution: the original values, longae and breves, are replaced by the next smaller ones, breves and semibreves and thus the tenor’s movement becomes three times quicker.

Typical for motets from this time is their structuring in rhythmically fixed patterns, called taleae which are strictly identical in the tenor, less strictly so in the upper voices; the tendency is that the later motets have more such identical patterns in the upper voices than the earlier ones which may have very little of it. This is usually called isorhythm,[1] and it is found mainly in the larger values and in the hockets (a technique where notes in one part coincide with rests in another and then quickly are exchanged. A relatively slow use of this technique was included in the example above, b. 22-4). Especially in the diminution sections of a motet such hockets and isorhythmic patterns are more frequent. A few motets are pan-isorhythmic or nearly so, i.e. that each talea is isorhythmic in all three voices (M15 and M13 are examples of this development).

In M1 the 30 color notes are divided over six taleae of five notes and two rests each (see first facsimile extract above).

Sound and Socre

Recurring rhythmic patterns in the upper voices do occur, but only when two tenor taleae are combined the isorhythmic construction of the upper voices becomes clear; the audibly most obvious signs of it are the slow hockets mentioned above which appear in the 22nd to 24th measures of each double talea, and marked in the poems by very short verses of two syllables. Thus the motet consists of three double taleae of 36 breves and three diminished ones of 12 breves, adding up to the symbolic number of completeness and stability, 144. These taleae correspond with the strophic form of the upper voice texts. The increase of intensity by the tenor diminution can also be seen in the texts, where, from this point on smaller strophes appear.

In intervallic structure a motet is also hierarchically built, although less strictly so. Generally the tenor proceeds in small intervals like seconds or thirds, with the occasional leap of a fourth or a fifth. In the four motets where a contratenor is added (M5 and 21-23) it stays in the same register and is set in the same large time values as the tenor, but usually has larger intervals and leaps. The motetus sings at a distance of, generally, a fifth above the tenor, but may range from unison to an octave above the tenor. On special occasions, though, it can rise above the triplum or descend below the tenor. The triplum sings mostly at an octave above the tenor but may descend to a fifth or even less above it or rise to an octave plus fifth. Whereas the triplum usually follows the tenor in a gradual melodic movement with only few leaps, the motetus is often the unruly voice, jumping to and fro in very large leaps and register changes, and in some cases causing conflicts.  


Jacques Boogaart

[1] For a qualification and relativation of the term Isorhythm, introduced only at the beginning of the twentieth century, see Margaret Bent, ‘What is Isorhythm?’, in David Cannata [et al.], eds, Quomodo cantabimus canticum? Studies in Honor of Edward H. Roesner. Middleton WI: American Institute of Musicology, 2008: 121-43. 


3. Tension through counterpoint

Exemplary as it is in structure and mensuration, M1 also contains an exemplary contrapuntal problem. In the tenor melisma tension exists between the notes F and G, the basic notes of the soft and hard hexachords.

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They form a polarity which is played out in the course of the motet. Machaut may well have manipulated the melisma a little in order to enhance this opposition since no existing chant source has a melody which is identical to the color of the motet; especially in the middle part, notes 11-20 (talea II), Machaut’s version is rather different and shows more opposition between the soft and the hard hexachord.

Sound and Score    ¦    Facsimile

In the undiminished taleae the emphasis on F and G is more or less in balance (F is the final of taleae I and III, G of talea II) but in the diminution section the tension between the two poles becomes stronger by a preference for cadences on G, first in bars 110-4 in the motetus, then in the triplum in bars 118-21. In bar 119 where the tenor cadences on F the triplum even sings a dissonant f-sharp leading to g in the next bar. As a general rule tenors, and especially liturgical tenors, are not to be inflected, so the tenor’s F must stand, against the f-sharp in the triplum. The conclusion is that Machaut deliberately steered the music into a clash at this point, perhaps as a parallel of the word folettement (‘foolishly’) in the text; the word is also highlighted by its ‘wrong’ accentuation ‘fòlettèment’ whereas elsewhere in this motet the text declamation follows the natural accents. The growing tension in the counterpoint between G and F has a meaning for the text but also purely musically it can be explained as a play with two poles of contrapuntal attraction in order to create musical tension. In bars 133-4 the two even succeed each other in parallel octaves. Towards the end of the piece the attraction of G becomes still stronger and from bar 140 the listener expects a final cadence on G, so that the following real cadence on F has the effect of a surprise. Thus in this work there is not, as has been shown for several other of his motets, a gradual reinforcement of the final towards the piece’s ending.On the contrary: the closure on F comes as a surprise. Interpreting the opposition of the soft and hard hexachords as a parallel with the pun amer-amer in the texts, this surprise may well have meant as: in the end the sweet (soft) tastes bitter (hard).


Jacques Boogaart

4. Hierarchical order in the song

Even when songs contain pre-existing materials, these are most commonly reserved for single locations rather than as an underpining device streatching the entire length of the work. As a result, the songs do not have an established melodic basis, internalised by composer, performer and audience upon which to implement the kinds of processes applied to Chant in the motets. Structuring tools such as a degree of isorhythmic behaviour or the use of hockets do sporadically appear in the songs, but in drastically reduced frequency.

Most typically, only one voice carries a text, and textless voices do not offer any kind of implied texts as do the motet tenors. This changes the hierarchical designation of a work’s basis. In the motets, the (unordered) tenor is the only voice which has an independent meaning separate from the others through its performance as chant. In the songs, the only voice with the potential for being appreaciated independently of a polyphonic texture is the texted cantus (there is later evidence of use of some song tenors as dance accompaniment, but in such a functional shift one may ask whether any of the original meaning of the song is transferred onto the melody’s new use).

In this new hierarchical constellation, it does not make sense to order the central voice into a slow moving, regular rhythmic pattern as this would get in the way of the text declamation. Instead, it is the text structure that dictates the form, both in terms of the large-scale combination of repeating form-parts, and the common mirroring of musical phrases with lines of text. These, though, do not prescribe an exact length, as the speed of declamation is not constant, and melismas of different lengths can be inserted, most commonly at the beginning and / or the end of poetical lines.

In polyphonic settings, the second voice in the hierarchy is always the tenor. As with the motets, it tends to move more slowly and regularly than the cantus, and to the most part its total range sits a fifth lower than that of the texted melody. By aligning itself with or subverting the phrase structure and cadence locations of the cantus, it comments on and supports the melody. In providing a harmonic structure it can highlight and weaken points in the melody of the upper voice, bolster the expectations it creates or build surprises undermining the cantus. Whatever the setting, the contrapuntal duet between cantus and tenor has to be correct. Even when the tenor is in the middle of the harmonic texture, the interval between it and the cantus should be consonant. Only on very rare occasions would the tenor and a contratenor swap roles.

The addition of a third voice can involve either a triplum, moving in the same range as the cantus, or a contratenor, sharing the range of the tenor. Earlier three-part settings tend to incorporate a triplum, while the second part of the fourteenth century saw the establishment of the contratenor as the standard third voice. Both these voices can be more flexible in their rhythmic, harmonic and melodic behaviour, and offer a second layer of commentary on the central duo. In such constellations, the tenor tends more often to support the cantus and the third voice to destabilize the structure, but the degree to which each voice sticks to this expectation is one more tool in the composer’s arsenal of individualising a setting. Four-part settings incorporate both contratenor and triplum.

For other typical behaviour patterns of the different voices, see the discussion of their roles in medieval cadence formulae.


Uri Smilansky