Recently I have been thinking again about the Missa L’Ardant desir, an anonymous polyphonic mass that was at the centre of a previous piece of research on the use of unusual signs in fifteenth-century music notation. The remarkable Confiteor from the Credo of this mass is but one of a number of distinctive features in this mass. Like many polyphonic settings of the Ordinary of the Mass from the middle of the fifteenth century (or slightly later, perhaps the 1460s, in the case of the Missa L’Ardant desir) this setting repeatedly uses a preexistent tune, mostly in the Tenor, throughout its settings of the five items of the Ordinary of the Mass, the Kyrie, Gloria, Credo, Sanctus and Agnus dei. This preexistent tune, called the cantus firmus meaning ‘the fixed song’, could be drawn from either a liturgical chant (a chant sung in the Mass or the Holy Office) or a secular song, both courtly and also popular street songs. In the case of the L’Ardant desir melody, there is no surviving court song that corresponds to the L’Ardant desir text incipit or melody used in the Mass, although the tenor survives in two settings (nos. 133 and 134) from the Buxheimer Organ Book, a mid-fifteenth century book of early organ or keyboard tablature now in the Bavarian Library at Munich.
Some years ago Rob C. Wegman argued persuasively that the Missa L’Ardant desir as it survives solely in the manuscript Cappella Sistina 51 in the Biblioteca Apostolica Vaticana (Rome) represents a subsequent phase in the transmission of this mass. (The article is available here; log-in access/a subscription is required.) By transmission, I refer to the process by which a piece of music is copied and distributed in a culture before the invention of the movable type music printing press by Ottavio Petrucci at the dawn of the sixteenth century. Before this time (apart from some interesting experiments with woodcuts in the second half of the fifteenth century), all music was copied by hand, a painstaking and often expensive undertaking. Wegman pointed out that many of the unusual transformations of the rhythms and indeed melody of the L’Ardant desir tune found in the CS 51 transmission of this Mass can be explained as straightforward and some not-so-straightforward manipulations of the original melody. For example, the note values of the melody are sometimes doubled. Sometimes the melody is sung in duple meter, sometimes triple and even in quadruple meter operating a particular proportion with respect to the other voices in this four-part composition. Because certain elements of late medieval musical notation operate contextually, changing the meter of the melody also changes the value of some notes. But this is not the end of the story. As the mass progresses, the anonymous composer reaches into a grab-bag of notational tricks and subjects the melody to several unusual transformations. Sometimes the rhythms of notes are changed by simply reading the original tune’s notation as if all note stems have been erased. At one point, the melody is sung upside down, in the sense that when the original melody rises, its transformation falls, and vice versa. At the very end of the Mass, in Agnus dei III, the composer reaches further into his bag of tricks and modifies the melody’s rhythm by changing the longest note, called the maxima in medieval music theory, into the shortest note, called the minima, and vice versa. (In practice, composers and scribes actually use notes smaller than the minima, but none of these appear in the L’Ardant desir tune. Note that the minima of late medieval notation is the ‘ancestor’ of the minim or half-note in present-day traditional music notation.) Similarly the second shortest note (the semibreve) is swapped for the second longest note (the long), and vice versa, but the middle note, the breve, stays the same, as shown here.


As Wegman explains, and as Emily Zazulia as recently demonstrated in her dissertation, these various transformations could have been readily achieved by taking the one version of the written L’Ardant desir tune and simply instructing the singer of the tenor to change the melody in various ways, whether simply by changing the time signature/meter, omitting rests, or more complex transformations like inverting the melody or swapping one rhythm for the other. By the time that the Missa L’Ardant desir was created, this process of musical transformation wasn’t so unusual; indeed it had already been used in the late fourteenth-century motet and seems to have been transferred to Mass composition around the middle of the fifteenth century as other examples discussed by Wegman indicate.
So there’s nothing new here in terms of what is already known about the Missa L’Ardant desir, although the following table offers some refinements to our understanding of some of the devices causing rhythmic transformations, particularly in the Et resurrexit.

While some of these transformations are similar to those found in other contemporary settings, others like those in the Credo and Agnus dei foreshadow bolder treatments of the cantus firmi in the Mass settings by late fifteenth-century composers like Jacob Obrecht and Josquin des Prez. The question that I soon began asking myself was why might the composer have chosen these transformations at particular points throughout the Mass, and might they actually ‘mean’ something, or at the very least symbolise some aspect of the liturgy in general or in particular?
Two aspects of the treatment of the cantus firmus stand out in the Missa L’Ardant desir, although more could be said elsewhere about several other tenor transformations, cantus firmus quotations in other voices and use of other musical devices like melodic repetition or sequences. The setting of the Confiteor stands out for the absence of any type of transformation of the cantus firmus, despite the fact that the other three non-tenor voices constitute one of the most complex examples of proportional notation outside pedagogic sources. Secondly, so far as I have been able to determine, the swapping of the maxima for the minima in the Agnus dei III is found anywhere else in the polyphonic mass repertoire in the fifteenth century. (Wegman must be credited once again with recognising rhythmic transformation in the Agnus dei III.)
The text of the Confiteor contains the article of faith from the Nicene Creed that professes the Christian belief in unique baptism for the remission of sins and the promise of everlasting life. The Agnus dei occurs in the Mass at the point that the consecrated communion bread is broken, symbolising the break of bread at the Last Supper. Its text acknowledges the agency of Christ’s sacrifice for the salvation of Christian souls: Agnus dei qui tollis peccata mundi, miserere nobis, ‘Lamb of God who takes away the sins of the world, have mercy on us’. Thus the Confiteor and the Agnus dei are linked through their reference to the remission or removal of sin through baptism and salvation. This linking of baptism and Christ’s sacrifice comes as no surprise, given the same emphasis is accorded to both elements in religious painting in the fifteenth century. Hubert and Jan Van Eyck’s Adoration of the Lamb from the Ghent Altarpiece (1432) visually represents this relationship between baptism and salvation by placing an eight-side baptismal font in the foreground, immediately before an altar on which stands the Lamb of God whose blood spills symbolically into a communion chalice. Just in case the viewer is in any doubt about the symbolism in this panel, Van Eyck painted in the words ‘Here is the font of the water of life proceeding from the throne of God and the Lamb’ on the baptismal font, and the text of the Agnus dei on the altar upon which the pascal Lamb stands. (Note: there is a slight problem with the last word in the first inscription which seems to read homi or homini, which makes no sense theologically.) What is perhaps surprising is the emphasis the composer of the Missa L’Ardant desir places on this relationship and what musical symbols are used to represent this.
One possible explanation of the musical symbols in the Missa L’Ardant desir might lie in the writings of an important fifteenth-century prelate and thinker, Nicholas de Cusa (1401–1464), sometimes called Cusanus. Although he was an important canon lawyer (who distinguished himself at the Council of Basel), papal envoy and administrator, Cusanus also wrote prolifically on theology, philosophy, mathematics and the sciences. I believe that one of his earliest books, ‘On learned ignorance’ (De docta ignorantia) holds clues to a new reading of the Missa L’Ardant desir. (The philosopher Jasper Hopkin’s has generously provided a wealth of free online resources, including a translation of De docta ignorantia on his website. This research is very much indebted to his scholarship.) In ‘On learned ignorance’, Cusanus expounds upon the finiteness of human knowledge in relation to God. This strand of mystic theology is nothing new in itself since the same argument had been articulated by the sixth-century Neoplatonist Pseudo-Dionysius the Areopagite and closer to Cusanus’ time by the Dominican mystic Meister Eckhard von Hockheim (c.1260–c.1327). The novelty of Cusanus’ approach rested with his use of numbers—including the ‘unreal’ number infinity—and geometry to illustrate and support his argument. While it would require several paragraphs to describe fully several important principles of Cusanus’ theology in ‘On learned ignorance’, the following points sum up in a potted fashion those relevant to this discussion:
1. Because God is all things and there can be nothing greater than God, God is the Absolute Maximum (DI I.3). The Absolute Maximum is incomprehensibly infinite in its magnitude and nature, and eternal. Because it is all things, there is only one Absolute Maximum.
2. Because the Absolute Maximum is all things in and of itself, nothing can be lesser that it and therefore it is also the Absolute Minimum (DI I.2). The Absolute Maximum is equal to the Absolute Minimum. This is an example of Cusanus’ peculiar mode of reasoning known as the coincidence of opposites.
3. The Absolute Maximum’s infinite being can only be equated to infinity. Cusanus demonstrates this with the figure of a triangle (DI I.14). If any one side of the triangle is of infinite length, then he reasons that the other two sides must also be of infinite length, both separately and together. The triangle also serves to illustrate the Christian doctrine of the Trinity, the triune being of God, Jesus Christ and the Holy Spirit.
4. As a consequence, this infinite Oneness only begets itself (a concept that will be crucial in the third book of ‘On learned ignorance’ concerning the God-Man), and is therefore eternal. Plurality arises from Oneness (by multiplication), and is derivative and therefore transient. In other words, God is eternal and infinite, creation is transient and finite (DI I.8).
5. According to Cusanus’ Neoplatonic theology through the gradual mortification of the flesh through faith, the believer progressively ascends from a state of plurality to oneness with Christ (DI III.2). Ascent towards God, starting with baptism is not a new idea, but Cusanus symbolises this spiritual transformation through numbers and their relationship to one another.
I have already argued elsewhere that cessation of complex proportions in the Confiteor from the Missa L’Ardant desir symbolises the remission of sins described in the text of this article. In terms of a Cusanan reading of this section of the Missa L’Ardant desir, the imitative entries in the non-tenor voices in the first 14 bars are sung proportionally in relation to the tenor voice. In most cases these voices use a four to three proportion or compounds of it. Interestingly Cusanus states that inequality, symbolised by proportions like 4:3, is the mark of transience and plurality, that of this world, while equality symbolises eternity (eg. 1:1). After 14 bars, the non-tenor voices all stop singing proportionally and fall back into same meter as the tenor voice. In this sense the non-tenor voices attain equality or oneness with the musical meter as the tenor voice, which up until this point they have been struggling against that complex proportions. Moreover, the tenor voice only enters after six bars of rest. Could the eight bars of melody in the tenor sounding against the proportions in other voices correspond to the eight sides of the baptismal font, the highly recognisable physical symbol of baptism found in many churches and in Van Eyck’s Adoration of the Lamb? I don’t believe the music symbology is coincidental. But, even in light of the fact that the Ordinary items of the Mass set polyphonically are interspersed with other items sung to plainchant, intoned or spoken silently, the Confiteor might be seen as the figurative centrepiece in the spectacle of this Mass, coming at the end of the first item of the Liturgy of the Eucharist, the most sacred liturgy of the church. As the first and unique sacrament of the faith, baptism takes centre stage.
Reading Cusanus in conjunction with the Confiteor of the Missa L’Ardant desir provides one way of understanding its use of wayward proportionality at the beginning of the Confiteor. However, the influence of Cusanus’ ideas also explain the rhythmic transformations of the Agnus dei III. The equating of maximas with minimas and vice versa in this section of the mass presents itself as an uncanny musical representation of Cusanus’ coincident opposites, the Absolute Maximum and Absolute Minimum, symbolising for feeble human minds the incomprehensible God. In this sense, the symbolic imagery of the Missa L’Ardant desir resembles that of Van Eyck’s Adoration of the Lamb. In The Adoration of the Lamb, the viewer must visually negotiate the symbolic space of this painting by proceeding past the eight-sided baptismal font towards the symbol of the paschal Lamb who takes away the sins of the world. In the Missa L’Ardant desir, because it is a musical event, the listener must progress within a linear timeframe, proceeding past the symbol of the baptism in the Confiteor before approaching the Agnus dei. But the symbolic representation of God’s incomprehensibility at the very end of the polyphonic setting of the Mass in the third Agnus dei serves as a poignant reminder of the Lamb of God’s agency in the salvation of all believers.
The question that I have already asked myself is whether it is plausible to suppose either a Cusanan influence upon the composer or at the very least upon some of those that might have sung or heard this mass. The Mass’s anonymity posses a some obstacles to the first part of this question, although Cusanus’ status in the mid fifteenth-century church would have made it more likely that his views and writings were known in Germany and Italy during this time. Cusanus in many respects marks the end of a late medieval tradition. However his ideas influenced a small number of subsequent thinkers so some extent, including Marsilio Ficino and Giordano Bruno, and German humanists. Clearly further work is required concerning the permeation of Cusanus’ ideas into artistic and musical circles (and I would like to hear what readers think in this respect), although I suspect that revival of Neoplatonic thought during the fifteenth century makes this task a difficult one.
This post is based upon a paper that I delivered during the ‘Transformations’ Symposium of Arts New England at the University of New England, Australia, 12-13 November 2012. To my knowledge there is no recording of the Missa L’Ardant desir to date, something I am keenly interested in working to remedy in the future. A synthetic recording many be found on Rob C. Wegman’s Renaissance Masses 1440–1520 website, although his reading of the Confiteor differs from my own interpretation in several respects.