Antoine Busnoys's Missa L'homme armé commits one notational error after another—at least according to Johannes Tinctoris. As several scathing passages in his Proportionale musices attest, Tinctoris abhors Busnoys's mensural innovations. And yet Busnoys's notational choices, while certainly idiosyncratic, are also arguably justifiable: the composer was merely finding ways of recording novel musical ideas that had no agreed-upon notational solutions. In this article I argue that Tinctoris's response to Busnoys is not limited to the criticisms in his theoretical treatises. Tinctoris the composer responds far more comprehensively, and at times with far greater sympathy for Busnoys's practice, in his own Missa L'homme armé. He echoes Busnoys's mass notationally, in that he treats it as an example of what not to do; his response is also deeply musical, in that he tackles similar technical problems as a means of achieving analogous contrapuntal effects. Tinctoris's and Busnoys's settings need to be understood in the context of fifteenth-century masses, one in which composers were not necessarily content to work within the system but invented new ways of writing in order to create new sounds. In doing so, mere “composers” could sometimes achieve significance as “theorists.” Taken together, the L'homme armé masses of Busnoys and Tinctoris raise a range of historiographical issues that invite us to reassess the figure of the “theorist-composer.” This article thus not only contributes to the discourse on musical borrowing but also opens out to a broader framework, asking what it means for a late medieval musician to theorize—in music as well as in prose.

The Credo of Antoine Busnoys's Missa L'homme armé ends strangely. This strangeness, which stems from a nearly constant superimposition of duple and triple meter in the Confiteor, creates a soundworld uncharacteristic of even the most complex fifteenth-century polyphony. After just a few measures the tenor enters, producing a metrical tug-of-war that pits the ternary rhythms of the L'homme armé melody against staunchly duple-meter music in the other voices (see Example 1).1 Moving far beyond the brief triplet passages sometimes found in music of this period, Busnoys spins out extended phrases that combine duple and triple, at times leaving listeners metrically adrift. Ultimately triple wins out: at the end of the movement the free voices move into pervasive triplets, joining the tenor for a dazzling final flourish.

Example 1
Example 1

Example 1

Johannes Tinctoris doubtless heard, sang, and studied this music, for in the analogous section of his own Missa L'homme armé one finds the same sort of metrical conflict (see Example 2).2 Like Busnoys, Tinctoris sets the triple-meter L'homme armé melody (here first in the altus and then in the tenor) against unambiguously duple music, producing a strikingly similar effect. Although these Confiteor sections share little explicit melodic material, there is an undeniable aural connection between them. Tinctoris begins with the same dactylic rhythm in the superius; the first several pitches are almost identical (g′, g′, g′, c′′, b♭′, as compared to Busnoys's g′, a′, g′, c′′, b♭′); and the freely composed voices quickly establish duple meter before the L'homme armé tenor enters, grating against them with its ternary rhythms.3 Throughout his Confiteor, Tinctoris cultivates the same metrical struggle, with the freely composed voices flitting in and out of triple meter. Finally, the movement concludes with a similarly brilliant burst of triple meter.

Example 2
Example 2

Example 2

These passages sound like little else in the repertory of the fifteenth century. In a culture of borrowing and compositional one-upmanship—particularly within the broader L'homme armé tradition—they invite further analysis. And yet for all that they sound similar, they look quite different. Both composers use mensuration and proportion signs that, like the musical effects they record, are unusual. But Busnoys and Tinctoris do not use the same unusual notation; the relationship between these sections exists only at the level of sound. In this respect it stands apart from most other fifteenth-century instances of musical borrowing.

The reason for the notational differences is not hard to discern: we know from Tinctoris's treatise on proportions, the Proportionale musices (ca. 1472–75), that he disapproved of the mensuration signs that Busnoys uses in his Confiteor ( and ).4 Tinctoris is famous for criticizing his contemporaries—Busnoys among them—for their notational choices; the passage from the Proportionale in which he rebukes Busnoys has been reproduced many times (as it is again below). Thus it may be tempting to interpret Tinctoris's Confiteor as another instance, this time in music rather than prose, of his schooling Busnoys on proper notational practice.

But there is more to it than this. Today we tend to think of Busnoys as a composer and of Tinctoris as a theorist. It is not uncommon for scholars to interpret examples such as Tinctoris's Confiteor (and perhaps also Busnoys's) as fundamentally pedagogical, in the belief that exceptionally complex notation was meant—could only have been meant—to teach some theoretical principle.5 But this distinction between “theorist” and “composer” is far too stark, not to mention ahistorical. To describe Tinctoris's Confiteor first and foremost as a theoretical statement, a “correction” of Busnoys's notation, would be to ignore the subtleties of Tinctoris's music. What if we were to view notation, even very complex notation, as just another compositional tool? Tinctoris's musical “borrowing,” if that is even the right word, lies less in his notational choices than in the musical problems he tackles and the effects he achieves. Although his motivations may never be known, we can be fairly certain that “correction” was not his only or even his primary goal.

When confronted with complex musical notation it is easy to forget to listen. Our problem-solving instinct kicks in (why is it there? what does it mean?), all too often overshadowing the sounds these symbols represent. More often a means to an end, notation can in these situations appear to become an end unto itself. This danger may be strongest when we examine music by composers whom we know to have been invested in both notation and complexity—composers whose notation may have something to reveal. In the fifteenth century hardly any figure is more susceptible to this tendency than Tinctoris. Today we think of Tinctoris as primarily a music theorist, but this was just one aspect of his varied career. In addition to being the most famous theorist of the era, he also studied law, served as procurator of the German nation at the University of Orléans, advised King Ferdinand of Naples, translated official court statutes, and privately tutored Ferdinand's daughter Beatrice of Aragon.6 His theoretical writings have quite reasonably garnered the lion's share of scholarly attention; but it is increasingly clear that this has come at the expense of understanding his music as music in its own right.7 There is much to gain by approaching his music on its own terms—yes, as an extension of his theoretical principles, but also as independent artistic creations that show engagement with other music of the time.

This article takes up these issues through a close study of one of Tinctoris's major compositions, the Missa L'homme armé. I consider what makes it work while also reading it as evidence of sweeping engagement with Busnoys's Missa L'homme armé, at the levels of both notation and sound. The connections one finds between the two works do not readily fit our established categories of musical borrowing; as such these examples provide a new way of understanding musical innovation while also offering fresh insight into how Tinctoris juggled his composer and theorist hats. Thus while the article will contribute to the discourse on “borrowing,” it will also open out to a broader framework, asking what it means for a late medieval musician to theorize. Busnoys's mass presents a similar set of issues from the other side of the coin, engaging in what we might consider theoretical activity, expressed through notes rather than words. Taken together, these works raise a range of historiographical issues that invite us to rethink our notion of the “theorist-composer.”8 

Tinctoris Responds

While it is rarely possible to prove that musical borrowing has taken place, we can be certain that Tinctoris knew Busnoys's Missa L'homme armé. In fact, he had quite a bit to say about it in the Proportionale musices, his treatise on mensuration and proportions. In the final book of this treatise Tinctoris uses extracts from contemporary music to illustrate common mistakes—that is, notational practices of which he disapproves. Busnoys's mass features prominently, mostly as an example of what not to do.9 

For all that Tinctoris objects to using major prolation to signal augmentation, this is just one of several complaints he levels against his contemporaries in the Proportionale. His objections may be summarized as follows:

  1. Using a mensuration sign alone to signify a proportion. Tinctoris focuses on two particularly common versions of this error:

    • Using signs of major prolation to indicate mensural augmentation, explained in more detail below.

    • Using the signs and to indicate sesquitertia (4:3) and sesquialtera (3:2) respectively. Tinctoris says that these relationships should be indicated with the signs and . In such cases he is upset not only by a sign doing the job of a pair of numbers, but also by the signs themselves—modifications of mensuration signs that are “so frivolous, so wrong, and so far from the slightest hint of reason” that he considers it unnecessary to explain what makes them objectionable.10 Tinctoris's implied criticism is that neither nor is a proper mensuration sign: in terms of mensuration, specifies the same note divisions as , namely duple at every level.

  2. Following a mensuration sign with one numeral instead of two (e.g., rather than ), because true proportions require two numbers. Tinctoris writes, “There are others … who show themselves to be completely ignorant of arithmetic, since they indicate all their proportions with just one numeral (i.e., the number that is to be compared with another). … And nothing is more foreign to arithmetic—from which we take our proportions—than to indicate a proportion (that is, a number placed in relationship to another) with a single number (that is, without any relationship to another number).”11 He goes on to say that the practice of using only one number is misleading because it is unclear to what quantity that number should be compared.

  3. Using the signs and to indicate modus rather than tempus. This complaint stems from modus cum tempore signs such as , in which or indicates modus (the division of the long) and the numeral indicates tempus (the division of the breve).12 In addition to the problem of indicating a proportion with a single number rather than two, Tinctoris argues that and must always refer to tempus. To use these signs to indicate any other relationship is wrong. For Tinctoris, modus should be indicated with double- or triple-long rests (i.e., rests that fill two or three spaces on the staff) at the beginning of a piece, before the mensuration sign.13 

  4. Signaling proportions at the wrong mensural level. Although Tinctoris allows for the comparison of notes other than the minim, he says they must be of the same type (i.e., perfect or imperfect); if they are not, their semibreves and minims will not be comparable.14 This criticism reinforces his view that proportions must be signaled at the level of the minim, unless one voice is in augmentation or diminution.

Every one of these indiscretions appears in Busnoys's Missa L'homme armé. Table 1 lays out the mensuration signs that Busnoys uses and their effect on the speed of the cantus firmus. His alleged misuse of major prolation occurs throughout the mass. His predilection for is well attested, and indeed the sign appears in all five movements.15 His use of remains a subject of debate;16 regardless, Tinctoris would have objected. Last but certainly not least, Tinctoris could not have been happy with Busnoys's use—together or separately—of and in the Confiteor. Though Tinctoris does not mention explicitly, he would have had the same objection to it as to and , namely that it is a corrupted mensuration sign being used to indicate a proportion.17 

Table 1

Mensuration and cantus firmus treatment in Busnoys's Missa L'homme armé

Mass sectionPrevailing mensurationTenor mensurationRelationshipCantus firmus treatment
Kyrie I     
Christe  ( in VatC 234) – – tacet 
Kyrie II     
     
Et in terra     
Qui tollis     
Tu solus     
     
Patrem    Canon “Ne sonites cachefaton sume lychanosipaton” instructs the tenor to begin in d, thereby transposing down a fourth 
Et incarnatus    
Confiteor    
     
Sanctus     
Pleni sunt  – – tacet 
Osanna     
Benedictus  ( in VatC 234) – – tacet 
Osanna ut supra     
     
Agnus Dei I    Canon “Ubi thesis assint ceptra, ibi arsis et econtra” signals inversion; cantus firmus is effectively in the bassus; Agnus II tenor tacet 
Agnus Dei II  – – 
Agnus Dei III    
Mass sectionPrevailing mensurationTenor mensurationRelationshipCantus firmus treatment
Kyrie I     
Christe  ( in VatC 234) – – tacet 
Kyrie II     
     
Et in terra     
Qui tollis     
Tu solus     
     
Patrem    Canon “Ne sonites cachefaton sume lychanosipaton” instructs the tenor to begin in d, thereby transposing down a fourth 
Et incarnatus    
Confiteor    
     
Sanctus     
Pleni sunt  – – tacet 
Osanna     
Benedictus  ( in VatC 234) – – tacet 
Osanna ut supra     
     
Agnus Dei I    Canon “Ubi thesis assint ceptra, ibi arsis et econtra” signals inversion; cantus firmus is effectively in the bassus; Agnus II tenor tacet 
Agnus Dei II  – – 
Agnus Dei III    

Tinctoris's most biting critiques concern the way Busnoys notates mensural augmentation. In practice there were two types of augmentation: proportional augmentation and mensural substitution (though it is sometimes impossible to determine which is at work).18 Proportional augmentation causes a given note duration to increase by a specified factor—as in the instruction “sing each note five times as long [as you otherwise would].” In augmentation through mensural substitution, a given written note must be sung as if it were a different, larger note value. For example, at one level of mensural remove a minim () would be sung with the duration of a semibreve (), and a semibreve with the duration of a breve (). While this practice was common enough, there was no single, uncontroversial way of indicating it in writing. A common method—the one Busnoys uses—was to equate the minim under major prolation ( or ) with the semibreve under or (see Figure 1 for the relationship between signs); according to this notational convention, augmentation is signaled by the sign of major prolation—that is, the dot. In mass cycles this kind of augmentation is most often used to elongate the cantus firmus. It allows the quoted melody, often taken from a chanson, to retain its original notational appearance while sounding like a long-note tenor. Mensural augmentation allowed Busnoys to present L'homme armé at different speeds over the course of his mass while maintaining an unchanging notational appearance.

Figure 1

The “Relationship” column of Table 1 shows how the value of a minim under or changes depending on the sign in the other voices. The minim usually equates easily with a different note level under the prevailing mensuration. For example, in the sections in which the prevailing mensuration is , just one level of augmentation is active, and a minim under equals a semibreve under . This is possible because, in both cases, analogous note types divide into three: there are three minims to a semibreve in major prolation and three semibreves to a breve in perfect tempus. The same holds for the juxtaposition of and : the triple division of the long under parallels that of the semibreve under . (See Figure 1 again for the relationship between note durations under these signs.) This neatness, where under both signs there is at least one mensural “level” at which values divide into three, clearly appealed to composers of the period. Busnoys and others overwhelmingly restrict their use of as augmentation signs to those sections whose prevailing mensuration is ; they avoid pitting these signs against , under which all divisions are duple.19 That the preferred presentation of the L'homme armé melody was in major prolation may help to explain the widespread enthusiasm for augmenting it in this manner.20 

This type of augmentation assigns a minim under a sign of major prolation the same duration as a semibreve under . Using mensuration signs in this way is precisely what Tinctoris objects to, calling it the “error of the English” (“Anglorum error”).21 He vehemently defends the principle of minim equivalence, which for him means that a minim is a minim is a minim, whatever the governing mensuration sign. A minim cannot be equated with a semibreve because they are fundamentally different. Absent other kinds of instructions, a minim under is equal to a minim under . For Tinctoris, mensuration signs could only organize minims into larger hierarchical groups; they could not change the minim's temporal value. To do that a composer would have to introduce a proportion (essentially a fraction) or a verbal canon (a textual instruction) indicating the intended proportional change. While Tinctoris's system clearly went against the grain, it is logically consistent. In the name of clarity and correctness, he sought to uncouple mensuration (whether each type of note is duple or triple) from duration (the sounding length of a given note type). The error anglorum flouts the principle of minim equivalence.

The passage of the Proportionale musices in which Tinctoris criticizes his contemporaries for an improper use of major prolation signs has been quoted often, as much for its theoretical agenda as for its rhetorical flair. In decrying this practice Tinctoris unleashes some of his most scathing criticisms:

If de Domarto has been imitated in this error by Regis, Caron, Boubert, Faugues, Courbet, and many others, as I have seen in their works, it does not surprise me, since I have heard that they are barely literate. And who, without learning, can attain the truth not only of this but of any other liberal science?

But that Ockeghem and Busnoys, men known to have a sound Latin education, should stoop to this level in their masses De plus en plus and L'homme armé has struck my breast with no small amount of astonishment. Indeed, what is more astonishing than people with good vision entering the deserts of blindness? But because of their manner of composition, if it were marked as art requires, a difficulty of execution and even a destruction of the whole melody would result on account of the excessive speed. So it would be better that a canon [i.e., verbal instruction] be placed in the tenor, namely “Crescit in duplo” [it grows twofold] or its equivalent, as Du Fay has done so admirably in his Missa Se la face ay pale.22 

By the time Tinctoris wrote the Proportionale the use of and as integral signs—that is, as “primary” mensuration signs—had all but fallen out of use. In their songs from the 1420s Du Fay and Binchois had regularly used to indicate a fast triple meter akin to . (A textbook example, at least today, is Binchois's De plus en plus.) But by the time Ockeghem and Busnoys were composing in the 1460s–1470s and most commonly signaled augmentation in the context of a mass tenor. To indicate a quick triple meter these composers used the less codified (and thus controversial) signs , , , and .23 Not surprisingly, Tinctoris began to speak out against the “error of the English” just as this practice was becoming commonplace.

To understand Tinctoris's objection, consider the first few measures of Busnoys's Missa L'homme armé (see Example 3). Here a minim in the tenor, notated under (rendered as a half note), occupies the same amount of time as a semibreve (whole note) in the other voices, notated under . Augmentation causes the tenor to move through his line more slowly than the other voices. In those voices the mensura (beat) is on the semibreve; in the tenor it is on the minim.24 Augmentation also has the effect of visually singling out the borrowed voice, since lines that must be augmented usually include far fewer notes than non-augmented lines. These differences are easy to see in the original sources.

Example 3
Example 3

Example 3

What of Tinctoris's own Missa L'homme armé? Table 2 outlines the cantus firmus treatment and mensural usage in this mass, just as Table 1 outlines that in Busnoys's mass. These tables permit comparison of both musical ends and notational means. Both composers change the heard length of the L'homme armé tune over the course of their mass, though they do so by markedly different methods. Focusing on performed (or “resolved”) values allows us to compare the sounding results of these manipulations.25 

Table 2

Mensuration and cantus firmus treatment in Tinctoris's Missa L'homme armé

Mass sectionCantus firmus voiceCantus firmus manipulations and other remarksPrevailing mensurationCantus firmus mensurationWritten cantus firmus note valuesResolved cantus firmus note values
Kyrie I altus Canon “Crescit in duplum”; undoes canon     
Christe shared in all voices Begins with lower-voice duet; double-long rests in upper voices indicate minor modus     
Kyrie II tenor, altus, tenor All voices have some cantus firmus material; results in accelerated cantus firmus statement closer to integral     accelerated
 
       
Et in terra tenor      
Qui tollis superius/altus, tenor In the final measures, all voices have B material, but less systematic than most cantus firmus statements     
Cum sancto altus  causes accelerated speed with an effect similar to Busnoys's ; shift to at Amen     
       
Patrem [tenor] Cantus firmus very elaborated; long sections of freely composed material     
Et incarnatus altus, superius Superius-altus fuga at the fourth signaled by the canon “Absque mora primum ruit in dyatessaron ymum”     
Et resurrexit bassus, superius/altus, tenor Cantus firmus material is sung at some point by each voice, migrating from D to C to G to D     
Confiteor altus, tenor  gives three semibreves in the space of two in the other voices; against this sounds like integral
B: All voices have coloration, including cantus-firmus-bearing altus
A′ : Tenor has
Amen: superius, altus, and bassus in coloration 
    
       
Sanctus tenor, superius/altus, bassus Minim equivalence; top voices briefly move to when they quote portions of the cantus firmus , moments of     
Pleni sunt –   – – – 
Osanna altus Canon “Crescit in duplum”; triple-long rests indicate major modus     
Benedictus –   – – – 
Osanna ut supra altus Canon “Crescit in duplum”; triple-long rests indicate major modus     
       
Agnus Dei I altus Canon “Crescit in duplum”     
Agnus Dei II –   – – – 
Agnus Dei III altus      
Mass sectionCantus firmus voiceCantus firmus manipulations and other remarksPrevailing mensurationCantus firmus mensurationWritten cantus firmus note valuesResolved cantus firmus note values
Kyrie I altus Canon “Crescit in duplum”; undoes canon     
Christe shared in all voices Begins with lower-voice duet; double-long rests in upper voices indicate minor modus     
Kyrie II tenor, altus, tenor All voices have some cantus firmus material; results in accelerated cantus firmus statement closer to integral     accelerated
 
       
Et in terra tenor      
Qui tollis superius/altus, tenor In the final measures, all voices have B material, but less systematic than most cantus firmus statements     
Cum sancto altus  causes accelerated speed with an effect similar to Busnoys's ; shift to at Amen     
       
Patrem [tenor] Cantus firmus very elaborated; long sections of freely composed material     
Et incarnatus altus, superius Superius-altus fuga at the fourth signaled by the canon “Absque mora primum ruit in dyatessaron ymum”     
Et resurrexit bassus, superius/altus, tenor Cantus firmus material is sung at some point by each voice, migrating from D to C to G to D     
Confiteor altus, tenor  gives three semibreves in the space of two in the other voices; against this sounds like integral
B: All voices have coloration, including cantus-firmus-bearing altus
A′ : Tenor has
Amen: superius, altus, and bassus in coloration 
    
       
Sanctus tenor, superius/altus, bassus Minim equivalence; top voices briefly move to when they quote portions of the cantus firmus , moments of     
Pleni sunt –   – – – 
Osanna altus Canon “Crescit in duplum”; triple-long rests indicate major modus     
Benedictus –   – – – 
Osanna ut supra altus Canon “Crescit in duplum”; triple-long rests indicate major modus     
       
Agnus Dei I altus Canon “Crescit in duplum”     
Agnus Dei II –   – – – 
Agnus Dei III altus      

If we consider only the augmentation that the singer must effect, which takes place, as it were, “off the page,” then Tinctoris's mensural usage is seen to diverge significantly from Busnoys's. In terms of the performed speed of the cantus firmus, however, he follows Busnoys almost exactly. Whereas Busnoys achieves all of his alterations through mensural manipulation, Tinctoris makes his through a combination of mensuration signs, proportions, verbal instructions, and written note values. It was important to Busnoys to present the L'homme armé melody with a consistent visual appearance (necessitating strict cantus firmus treatment). Tinctoris, by contrast, was content to change written note values and embellish the tune; his priority was a clear, correct recording of musical sound, free from any potential ambiguity. Because he took issue with Busnoys's notational presentation, we would not expect him to imitate Busnoys in this respect, though others did.26 Busnoys and Tinctoris viewed the relationship between notation and sound differently. Nonetheless, the relative sounding durations of their respective cantus firmi are all but identical.

Tinctoris's mass is described here with reference to its only surviving source (VatS 35). When dealing with music of this period we must of course consider to what extent the sources accurately reflect the composer's conception. In the case of Tinctoris's Missa L'homme armé there is good reason to question the form of the piece as it has come down to us. Jeffrey Dean has observed that in the first sections of the Gloria and Credo the tenor is written in a different hand from that of the rest of the mass. On the basis of an analysis of Tinctoris's cantus firmus usage, Dean has argued that the Patrem tenor, in particular, represents a later compositional intervention (in other words, that Tinctoris's tenor has not survived), since every other mass section scored for four voices incorporates a significant amount of cantus firmus material.27 And it is not unreasonable to assume that Tinctoris would adopt similar cantus firmus treatment across his mass: although he freely embellishes the tune later in each movement, he otherwise always begins by presenting the L'homme armé melody once, complete and relatively unembellished. For all these reasons I am sympathetic to Dean's suggestion that in Tinctoris's original Patrem the tenor began by singing the cantus firmus in long note values; indeed, if this were true it would strengthen the connection between Tinctoris's mass and Busnoys's.28 Unfortunately, Dean's proposed reconstruction cannot be made to fit with the other voices. The counterpoint simply moves too quickly from one sonority to the next to accommodate a slow-moving, unembellished cantus firmus.

It can be difficult to describe Tinctoris's music, since he self-consciously cultivated an eclectic compositional style, one quite different from Busnoys's, as I discuss below. This challenge highlights a broader methodological issue that crops up again and again in considering relationships between specific pieces. Accounts of “musical borrowing” in this period often involve the identification of similar melodic lines, notational devices, cantus firmus treatment, or other structural elements. In looking for shared material we place a premium on close—and therefore irrefutable—correspondence.29 What Tinctoris takes from Busnoys's mass, though no less pervasive, is harder to pin down. He undeniably adapts the striking sound of Busnoys's Confiteor, but that is not the only point of correspondence. Even as he adapts Busnoys's mensural scheme, Tinctoris leaves on the table many distinctive features of Busnoys's mass. His composition is much more frenetic than Busnoys's, the measured quality of which causes moments of intense activity such as the Confiteor to stand out all the more noticeably. Yet while I focus on Tinctoris's engagement with Busnoys in this article, I do not mean to devalue his indebtedness to other models. Jennifer Bernard Merkowitz, who was the first to note the extraordinary correspondence between Tinctoris's and Busnoys's masses, suggests that Tinctoris also drew inspiration from L'homme armé masses by Guillaume Du Fay (“lively duets” and handling of texture), Johannes Regis (Sanctus trope), and the anonymous Naples masses (Kyrie tropes).30 Sean Gallagher has tightened the link with Regis, while Dean has unearthed further evidence of Tinctoris's referencing both Guillaume Faugues's and Regis's masses.31 Even Tinctoris acknowledged his own indebtedness to those he judged to be his finest contemporaries.32 

However pervasive, the correspondence between Tinctoris's mass and Busnoys's is not as obvious as other examples of borrowing in this period. It is fortunate that their Confiteor sections are so similar, because it allows detection of the more extensive relationship between the two works. Busnoys was hardly the first composer to begin a mass movement with the cantus firmus at one level of augmentation, change it at times to two levels of remove, and introduce moments when the tenor moves at the same speed as the other voices. But there is nothing else in the repertory quite like Busnoys's Confiteor.33 

Busnoys augments the L'homme armé melody according to a fairly regular scheme, beginning each movement of the mass with the tenor at one level of augmentation. Tinctoris also augments his cantus firmus at the beginning of each movement, but the augmentation may be either performed or written out. He begins his Kyrie as Busnoys does, with the L'homme armé cantus firmus in augmentation—only accompanied, true to form, by the canon “Crescit in duplum,” written just above the music. Indeed, this is the very canon that Tinctoris scolded Busnoys for not using. It is not so surprising that Tinctoris's notation follows the prescriptions he outlined in his treatise. But it is noteworthy that he used the same musical and notational technique as Busnoys (major prolation for the unadorned L'homme armé melody coupled with twofold augmentation) in a mass based on the same cantus firmus. Tinctoris has recognized a central feature of the L'homme armé tradition and adapted it to his own notational theory. In this Kyrie Tinctoris does exactly what he says Busnoys should have done in his mass.

In addition to the verbal canon, Tinctoris includes the fraction after the A phrase of the cantus firmus. These superimposed numerals instruct the singer to perform what follows in a 2:1 proportion with (that is, twice as fast as) what has gone before, effectively canceling out the augmentation signaled by the verbal canon. These two sets of instructions—“Crescit in duplum” and —bring this section conspicuously close to the passage in the Proportionale quoted above. Indeed, the conclusion that Tinctoris had both his treatise and Busnoys's Missa L'homme armé in mind when composing the Kyrie is almost irresistible.

The one section in which Tinctoris conspicuously deviates from Busnoys's mass is the Sanctus. Here he presents L'homme armé in against the prevailing , just as he does in the Kyrie and Agnus Dei, but without a verbal canon.34 While this is the same notational situation as we find in the analogous section of Busnoys's mass, Tinctoris's tenor relates to the other voices by minim equivalence, without augmentation. It is as if Tinctoris is saying, “See, Busnoys? Without a verbal canon or a proportion, there is no augmentation.”

While there is nothing remarkable in Tinctoris's relying upon notation that he himself says is correct, it should give us pause that he does so in precisely the contexts in which he had criticized Busnoys. It might therefore be tempting to read Tinctoris's mass as a corrective crusade that retains the heart of Busnoys's music but presents it in acceptable notation. Or perhaps as a practical treatise that addresses, in notes rather than words, the errors he sees in contemporary music. Both of these interpretations are reasonable, especially given the extent to which Tinctoris was clearly invested in theoretical correctness. Rob Wegman has described how Tinctoris “seized upon errors in compositions (rather than on viewpoints maintained in other treatises), and proceeded to rebut them as if they were propositions defended in an academic disputation.”35 He was the kind of individual who would go well out of his way to prove a point.

Still, following this path narrows our interpretive lens unnecessarily, depriving us of a richer, more musically sensitive understanding and a more historiographically significant conclusion. While there can be little doubt that the tenets of “proper” notation were present in Tinctoris's mind as he composed, it is difficult to believe that they thoroughly overshadowed all the other elements that go into creating an effective piece of music. Whatever its relationship to Busnoys's output, Tinctoris's music is extremely compelling in its own right. Hardly a piece of theoretical arcana, his Missa L'homme armé lays bare the pitfalls associated with appraising the figure of the composer-theorist.

Busnoys the Theorist

Busnoys, too, benefits from a rethinking of the composer-theorist divide. Despite his not having written a word of music theory (that we know of), the adventurous use of mensuration signs in his music evinces deep engagement with the theoretical literature. While his mensural usage is often peculiar, this is only because he paints himself into notational corners that do not have obvious solutions; in such situations he devises signs that suit his unique musical needs. There is a tendency to read his music as Tinctoris did, using the latter's encyclopedic treatises as our default interpretive lens. But while Busnoys's usage may seem incorrect from Tinctoris's perspective, I would argue that his “errors” are actually attempts to avoid the confusion that would arise in performance. As such, his notation is both internally consistent and highly revealing with regard to contemporary conventions of mensural practice. Busnoys does, in the end, make theoretical points, but through music rather than treatises, and never simply for the sake of it. In this period theoretical and aesthetic achievements are not mutually exclusive but may go hand in hand. In order to understand Tinctoris's response to Busnoys, it will be helpful to delve further into this aspect of Busnoys's career.

Let us return to the practice that Tinctoris so criticized: using major prolation to indicate augmentation. Depending on one's perspective, Busnoys is either a chief proponent of this useful technique or a serious transgressor of notational propriety. To modern musicians, substitution augmentation may seem a strange practice. Why would a composer choose to write one note value when the singer will only have to mentally swap it for another? Why not write the intended value from the start? In a period that predates the use of ties to link endless strings of notes, augmentation sometimes allowed composers to use durations longer than the longest note value (or shorter than the shortest, in the case of diminution), but this is rarely the motivation behind augmentation in Busnoys's day. Rather, augmentation allowed composers to maintain the visual appearance of a cantus firmus, either from its original source or, for example, across the five movements of a mass. Many masses that involve cantus firmus manipulation—particularly L'homme armé masses—consistently present borrowed material with unchanging notation in order to emphasize the cantus firmus's identity in the face of the extensive transformations it undergoes.36 

Major prolation and the presentation of the L'homme armé melody in minims and semibreves were important to the tradition from its earliest generation.37 Like several other composers—Ockeghem, the composer of the Naples masses, Faugues, and later Marbrianus de Orto, Obrecht, Josquin, and Bertrandus Vaqueras—Busnoys goes out of his way to notate L'homme armé in minims and semibreves throughout his mass. The other composers mentioned here preserve a constant visual appearance of the cantus firmus even as they subject it to ever more fanciful manipulations. Table 3 identifies masses that state the L'homme armé tune in minims and semibreves. This practice occurs consistently alongside strict cantus firmus treatment. Composers who do not use minims and semibreves (for example, Du Fay and Regis) or who use them in only a section or two (for example, Firminus Caron, Philippe Basiron, and Loyset Compère) tend to treat the tune with the greatest freedom. Figure 2 shows the appearance of the tenor in Busnoys's Kyrie. The tenor looks the same every time it is written. The only liberty Busnoys takes is in the number of rests between phrases. The paradox of visually consistent notation producing musical variety became a defining feature of the L'homme armé tradition, mensural augmentation emerging as a favored means of achieving it.38 

Table 3

Masses in which L'homme armé is notated in minims and semibreves

MassKyrieGloriaCredoSanctusAgnus Dei
Ockeghem ✓ ✓ ✓ ✓ ✓ 
Busnoys ✓ ✓ ✓ ✓ ✓ 
Naples I–VI ✓ ✓ ✓ ✓ ✓ 
Fauguesa ✓ ✓ ✓ ✓  
Obrecht ✓ ✓ ✓ ✓ ✓ 
Basiron   b   
Tinctoris c  d ✓ ✓ 
Caron e    f 
Compère    g  
Vaqueras ✓ ✓ ✓ ✓ ✓ 
Josquin s.v.m. ✓ ✓ ✓ ✓ ✓ 
MassKyrieGloriaCredoSanctusAgnus Dei
Ockeghem ✓ ✓ ✓ ✓ ✓ 
Busnoys ✓ ✓ ✓ ✓ ✓ 
Naples I–VI ✓ ✓ ✓ ✓ ✓ 
Fauguesa ✓ ✓ ✓ ✓  
Obrecht ✓ ✓ ✓ ✓ ✓ 
Basiron   b   
Tinctoris c  d ✓ ✓ 
Caron e    f 
Compère    g  
Vaqueras ✓ ✓ ✓ ✓ ✓ 
Josquin s.v.m. ✓ ✓ ✓ ✓ ✓ 
a

Kyrie II, Cum sancto, Confiteor, and Osanna

b

Et unam sanctam

c

Kyrie I

d

Et incarnatus est

e

Kyrie I

f

Dona nobis pacem

g

Pleni and Benedictus

Figure 2

One figure has been lurking behind the discussion thus far: Johannes Ockeghem. In the passage from his Proportionale quoted above, Tinctoris pairs Ockeghem with Busnoys because both committed the error anglorum and, as he says, they of all people should have known better. He criticizes Ockeghem's Missa De plus en plus, but he could as easily have pointed to Ockeghem's own Missa L'homme armé. There is good reason to believe that Busnoys took the idea for using augmentation in his L'homme armé mass from Ockeghem.39 Busnoys's mass is indebted to Ockeghem's in several respects. Like Busnoys, Ockeghem preserves consistent note values under major prolation throughout his mass.40 The two pieces share the G final—not to mention the same tenor, at a stage before there was any clear “tradition” of using the L'homme armé tune as a cantus firmus.41 Beyond this, as Leeman Perkins has demonstrated, they are related through contrapuntal procedure: both juxtapose major prolation ( or ) against to indicate twofold augmentation as their primary mensural combination, and both transpose the cantus firmus in the same mass sections, always via verbal instructions.42 The mensural and cantus firmus treatment of Ockeghem's mass are presented in Table 4. (Compare with that of Busnoys's mass in Table 1.)

Table 4

Mensuration and cantus firmus treatment in Ockeghem's Missa L'homme armé

Mass sectionPrevailing mensurationTenor mensurationRelationshipCantus firmus treatment
Kyrie I     
Christe     
Kyrie II     
     
Et in terra     
Qui tollis     
Tu solus 3 3  Not a formal section break 
     
Patrem    Canon “Descendendo in dyapenthe” (VatC 234) or “In subdyapente” (VatS 35) instructs tenor to transpose down a fifth 
Et resurrexit    
Et unam sanctam    
     
Sanctus     
Pleni sunt  – – tacet 
Osanna     
Benedictus  – – tacet 
Osanna ut supra     
     
Agnus Dei I    Canon “Descendendo in dyapason” instructs tenor to transpose down an octave; cantus firmus is effectively in the bassus; Agnus II tenor tacet 
Agnus Dei II  – – 
Agnus Dei III    
Mass sectionPrevailing mensurationTenor mensurationRelationshipCantus firmus treatment
Kyrie I     
Christe     
Kyrie II     
     
Et in terra     
Qui tollis     
Tu solus 3 3  Not a formal section break 
     
Patrem    Canon “Descendendo in dyapenthe” (VatC 234) or “In subdyapente” (VatS 35) instructs tenor to transpose down a fifth 
Et resurrexit    
Et unam sanctam    
     
Sanctus     
Pleni sunt  – – tacet 
Osanna     
Benedictus  – – tacet 
Osanna ut supra     
     
Agnus Dei I    Canon “Descendendo in dyapason” instructs tenor to transpose down an octave; cantus firmus is effectively in the bassus; Agnus II tenor tacet 
Agnus Dei II  – – 
Agnus Dei III    

Ockeghem presents his cantus firmus at similar speeds, beginning with one level of augmentation in the Kyrie, moving to integral values in the Credo, and shifting to two levels of remove in the Osanna and Agnus Dei III—namely the combination of diminution on the one hand and augmentation on the other. I address the use of specific mensuration signs below, but the greatest similarity occurs between the composers’ cantus firmus manipulations. Where in the Credo Ockeghem transposes by a fifth, Busnoys does so by a fourth and, like Ockeghem, by using a verbal canon. In the Agnus Dei, where Ockeghem had transposed his tune down an octave into an exceptionally low register (especially for a tenor), Busnoys inverts it. This inversion flips the tenor into the same low range as Ockeghem's transposed tenor, but the tune's range renders its lowest note yet one step lower—F as opposed to G.43 

While Ockeghem exclusively uses and for his tenor, there are two mass sections in which Busnoys presents the L'homme armé melody under a different sign: the Tu solus, where he uses , and the Confiteor under . Both are sections in which the L'homme armé tune sounds at the speed that would normally be implied by notation in minims and semibreves—that is, not in augmentation. The association of and with augmentation had grown so strong by this point that Busnoys must have felt he could not expect singers to interpret them according to their original, non-augmented meaning without clarification (though remember that this is the only way Tinctoris thought they should be used). Busnoys's choice of signs is a compromise between preserving visual integrity and avoiding the ambiguity that would be implied by a sign of major prolation. In fact, he may have taken two ambiguous spots in Ockeghem's mass as a warning.

Although Ockeghem usually confines major prolation to the tenor, in his Christe and Et resurrexit all voices receive the sign (see Table 4). There remains disagreement to this day as to what tempo Ockeghem intended, but I am convinced by Sean Gallagher's argument that these sections of his mass should be read with an integral (that is, fast) understanding of .44 Read in this way, Ockeghem's Christe and Et resurrexit move in the lively compound meter that had unambiguously implied earlier in the fifteenth century, as seen in pieces such as Binchois's De plus en plus and Du Fay's J'ay mis mon cueur. Indeed, they would move as Busnoys's Tu solus does, except that in that case Busnoys notates all voices under —the equivalent of in its non-augmented meaning. Perhaps he made this substitution in order to forestall any confusion about his desired tempo, as Richard Taruskin has argued, even though it involved departing from his pattern of using major prolation for the L'homme armé melody.45 

A similar desire to avoid confusion probably motivated the unusual mensural choices of Busnoys's Confiteor. As we have seen, this is one of the strangest and most stunning sections of his L'homme armé mass. It is also one of the most peculiar notationally. Notating this section must have posed particular problems. At first glance the solution Busnoys came up with might baffle even the savviest readers of mensural notation. He moves the L'homme armé–bearing tenor into while the other voices read under the extremely unusual . In order to understand how Busnoys came to this solution, we have to consider his musical motivations. His starting point was almost certainly the cantus firmus itself, whose constant visual appearance in major prolation he was invested in preserving. As for how he might handle the L'homme armé melody in this section, his Gloria may provide a clue. As described above, the pace of the cantus firmus accelerates in the Tu solus, with all voices notated in . So he may have been aiming for a similar accelerating effect at the end of the Credo. Such acceleration is common at the ends of long movements, as composers bring the section to a stirring climax with increased rhythmic activity.

Once Busnoys accepts these parameters, what are his options? He selects because he wants to achieve a sesquitertial relationship relative to (that is, ). He might have considered a more straightforward duple sign such as , but it would have caused additional confusion, since the combination of and means something different in other mass sections. What of Busnoys's decision to use the cut versions of these signs? As we have seen, in Busnoys's music without a stroke consistently implies augmentation, so in order to move the cantus firmus out of augmentation he had to use a different sign. His decision to use rather than solves the problem: the stroke essentially “undoes” the implied augmentation. With this much in place his decision to notate the other voices under is all but inevitable. The stroke in the tenor more or less forces one in the other voices in order to keep the vertical relationship clear. Put differently, once Busnoys had used a stroke in the tenor to avoid augmentation, he also had to use it in the other voices to preserve the vertical proportion.46 

Busnoys eschews in these sections, then, to avoid possible confusion. But why does he use two different signs to achieve the same effect? The reason is purely contextual. In the Confiteor the tenor is the only voice in imperfect tempus and major prolation. Since it follows a section in which carries its more common meaning of augmentation, the stroke simply cancels out this augmentation. In the Tu solus, however, all voices move to together. Since the tenor has the same function as the other voices, it would be misleading to align against vertically. Busnoys's sensitivity to local context led him to answer similar problems in different ways.

However abstruse the result, Busnoys's starting point in the Confiteor is sensible and familiar. More unusual is the musical impulse that underpins this section. Busnoys stages a metrical struggle between duple and triple: as we have seen, the section begins squarely in duple, but the familiar lilting triple of the L'homme armé melody exerts its pull, causing this section to sit uneasily between duple and triple before finally giving way to a triple ending. For later readers, whether of Tinctoris's day or our own, the notation commands attention. After all, this is the only time a composer introduces—and juxtaposes—the signs and .47 Whenever a composer of this period does something unusual and complex, it is tempting to conclude that it was motivated by a desire for complexity. But rather than willfully employing complex notation Busnoys may simply have needed a way of notating the sound he wanted while maintaining major prolation. Still, in exploring new musical ground requiring notational innovation, he perhaps inadvertently made a theoretical point about the so-called error anglorum and the rules governing the mensural system.

The use of major prolation to signal augmentation might have seemed relatively uncontroversial had it not been criticized so severely in Tinctoris's Proportionale. Tinctoris commands authority by virtue of his academic achievements, the comprehensiveness of his writings, and the way he grounds his work in writings by both classical authors and contemporary music theorists.48 Moreover, he presents his ideas as if they are universal and self-evident. He undoubtedly thought of them that way—after all, they are rooted in mathematical principles and derived by Aristotelian logic. His system of rhythmic notation prizes clarity above all else, and its reliance on mathematics makes it remarkably flexible. But his rhetorical strategies undersell the novelty of his ideas. His principles concerning rhythm and notation are far from obvious: they constitute an all-encompassing system for both conceiving and recording a seemingly infinite variety of rhythmic relationships, one that was emphatically not available before the 1470s.49 Tempting as it may be to see Tinctoris as the primary authority on fifteenth-century theory, we must recognize that his authority is in part a modern historiographical construction.

Caution is in order especially when considering music written before Tinctoris's treatises were in circulation, as Busnoys's mass certainly was.50 Even once his writings were widely disseminated, we must determine which tenets were broadly accepted and which, however intellectually defensible, were viewed by contemporary musicians as idiosyncratic or even impractical. It would therefore be unwise to characterize Busnoys's notational idiosyncrasies as intentional transgressions born of loyalty to his early mentors and training.51 While Busnoys's practice is, as Wegman rightly observes, often “patently erroneous by the standards of Tinctoris,” if we consider these matters from the perspective of Busnoys himself, composing shortly before Tinctoris had begun to theorize, things look very different.52 Busnoys's unusual mensural choices probably do stem from his own training, as Wegman suggests. And indeed this probably had nothing to do with Tinctoris: Busnoys was working with a system he had learned in his youth, expanding it where necessary to suit his purposes. I would contend that the ways he applied and expanded that system evince a kind of intellectual engagement that can properly be called theory in its own right.

Among the objects of Tinctoris's criticism are situations in which Busnoys uses a dot of division to divide things that do not need to be divided, as in the extract from Victime paschali laudes shown in Figure 3 and Example 4. Tinctoris would call the dot in question erroneous because imperfection alone is enough to ensure that the breve rest reduces the D long to two breves’ duration. This dot may not be necessary, but thinking of it as “cautionary” rather than “wrong” may bring us closer to Busnoys's reason for using it.53 This particular long is followed by a long string of breves. If the number of breves were a multiple of three, imperfection would not apply and the long would remain perfect. Busnoys's dot relieves the singers of having to count these breves on the fly, confirming that they should apply imperfection. Or perhaps, given that this is not an isolated example, Busnoys simply favored clarifying the minor-modus divisions with (extra) dots of division.54 

Figure 3

Example 4

The same pragmatic motivation is at play in another example criticized by Tinctoris, in which the numeral “3” appears beneath sets of colored notes (see Figure 4).55 Tinctoris's criticism is threefold: first, Busnoys should not have used the numeral “3” in conjunction with coloration, since the “3” is redundant; second, any such numeral should rightly be placed before the music, not beneath it; and third, “3” alone is insufficient as a proportion sign—only a fraction is acceptable (in this case, ). In fact, Busnoys's use of the numeral “3” was probably intended to stave off any confusion that might be caused by the emerging practice of minor color. Minor color, as it has come to be known, is the practice of interpreting pairs of filled-in notes (most often ) as a dotted figure (), rather than as the sesquialtera () otherwise implied by coloration.56 While transcribing minor color as a dotted figure has become an almost universal editorial convention, Ronald Woodley has cautioned that in the mid-fifteenth century this interpretation was not yet so widespread.57 In one sense Busnoys's “3” is redundant, but this redundancy contributes to disambiguation by reinforcing what coloration has already expressed. Whereas Tinctoris embraced the principle we call “Ockham's razor” (in the formulation quoted by Tinctoris himself, “Quod brevius fit, melius fit”—“Whatever is made more concise is made better”), Busnoys saw the value in this kind of redundancy.58 Coloration that diminishes note values by a third (that is to say, that results in triplets) would have rendered the example cited by Tinctoris as:

When read instead as minor color the same example becomes:

Aware that singers might opt for the latter interpretation, Busnoys included a “3” in order to clarify his intentions.59 Notating the figure with the seemingly superfluous “3” reflects the composer's sensitivity toward the changing meaning of notational symbols.

Figure 4

Busnoys's theoretical inventiveness extends beyond his Missa L'homme armé: his is one of the most daring mensural profiles of the fifteenth century. In his sacred music he rarely uses the simplest signs and alone, but always chooses signs that he believes will most clearly convey his intended musical effect.60 In other words, his primary motivations were musical, not, as it may sometimes seem, a desire to cultivate complex notation for its own sake. Busnoys writes complex music, and in the fifteenth century complex music all but required complex notation.

Around 1500 composers began to shy away from such elaborate constructions in favor of a more streamlined, immediately understandable set of norms centered on the pervasive use of . As mensural practice became more and more simplified, much of its inherent ambiguity fell away. The wider scope of mensural practice in the mid-fifteenth century, ungainly though it may sometimes appear, offers an opportunity to observe the system's rapidly changing conventions. In this respect Busnoys's mensural usage is of tremendous importance. By inventing signs to suit his needs Busnoys provides us with a glimpse of the extent to which notational and musical innovation progressed hand in hand. Only by studying the repertory in action, granting it an authority on par with contemporary theoretical writings, can we begin to appreciate the dynamic nature of this powerful notational system.

Theoretical Innovations

Tinctoris was not the only composer to draw inspiration from Busnoys's Missa L'homme armé. At least two other settings mirror Busnoys's cantus firmus structure and mensural profile: Obrecht's Missa L'homme armé and the unattributed Missa de Sancto Johanne Baptista, which Wegman has suggested is also by Obrecht.61 Such strict adaptation of Busnoys's framework necessarily involved dealing with his often complex metrical effects. Most challenging, not surprisingly, is the Confiteor. These masses take different approaches in responding to Busnoys's Confiteor. As such they inform our understanding both of these two masses and of Tinctoris's.

Oliver Strunk was the first to notice that “Obrecht's tenor and Busnoys's are identical [and that] Obrecht's formal structure is accordingly dependent to the last detail on Busnoys's. … Even the free (tenorless) sections have been made to correspond.”62 This kind of adaptation is unusual but not unprecedented: the way Obrecht uses the structure of Busnoys's mass as a starting point mirrors the way both he and Ockeghem adopt the framework of the anonymous Missa Caput.63 Yet even by comparison with these other examples Obrecht remains remarkably faithful to Busnoys's tenor and mensural framework.

This fidelity is what makes the Confiteor of Obrecht's mass so surprising: he changes the prevailing mensuration sign to avoid metrical conflict altogether (see Example 5). Obrecht presents the tenor under , as Busnoys does, but instead of pitting it against music in he writes the other voices in —one of his favorite mensuration signs.64 By substituting for Obrecht forgoes the hemiola effect of Busnoys's mass in favor of a quick, uniform triple meter in all parts. He continues to use one level of augmentation, such that a semibreve of corresponds to a breve of , but now the other voices match the tenor's ternary feel. The metrical conflict that characterizes Busnoys's Confiteor is completely absent.

Example 5
Example 5

Example 5

Why would Obrecht so closely follow Busnoys's mass in every section but this one? One possibility is that the surviving version of Obrecht's Confiteor is in fact a substitute setting, and that Obrecht's original Confiteor more closely matched Busnoys's. This explanation seems unlikely, since all three surviving sources for Obrecht's mass agree.65 Even so, his decision not to follow Busnoys's mensural scheme in this section alone is odd. Perhaps the departure reflects the fact that by the time Obrecht was composing (the 1490s) that particular combination of signs would have seemed eccentric. This notion alone is not altogether satisfying, given the unusual examples of mensural usage found elsewhere in Obrecht's output. Furthermore, Obrecht retains enough of Busnoys's outmoded notational practices (major prolation as augmentation, the use of ) to suggest that he was not attempting to conform to the emerging trend toward mensural simplicity.

There may be some significance in the mensuration sign that Obrecht uses for the free voices, . Bonnie Blackburn notes that Busnoys and Obrecht are the only composers to use this sign with any frequency prior to 1500; Obrecht expressly follows Busnoys in adopting it as a personal favorite, suggesting that the imitation may even constitute another example of Wegman's “mensural intertextuality.”66 Thus, while Obrecht departs from his mensural model, he still opts for a sign associated exclusively with Busnoys's works.

The unattributed Missa de Sancto Johanne Baptista, possibly also by Obrecht, uses the unique strategy of separating the cantus firmus from its treatment. Like Obrecht's Missa L'homme armé, the Sancto Johanne mass follows Busnoys's formal structure exactly, but instead of the familiar L'homme armé melody its tenor quotes chants from the Office for the Nativity of Saint John the Baptist. Rob Wegman recognized the extraordinary relationship between the Missa de Sancto Johanne Baptista and Busnoys's Missa L'homme armé, noting that the composer casts his cantus firmus in identical rhythms to Busnoys's and carries over the mensuration signs in all four voices, though without quoting the melody itself.67 This remarkable situation suggests that Busnoys's mass had assumed extramusical meaning beyond the L'homme armé melody alone. Wegman raises the possibility that the Missa de Sancto Johanne Baptista was composed for a specific donor who had a special connection with both Saint John and Busnoys—or at least with the latter's Missa L'homme armé.68 

The Missa de Sancto Johanne Baptista is more faithful to Busnoys's Missa L'homme armé than is Obrecht's L'homme armé mass, but even the Sancto Johanne mass does not use exactly the same mensurations as Busnoys. In its Confiteor it has in the tenor against in the other voices. Nonetheless, this section includes passages in coloration that bring the free voices in and out of phase with the tenor's triple meter (see Example 6). Thus the musical effect of the Sancto Johanne Confiteor is in fact in line with that of Busnoys's.69 The section begins like Busnoys's Confiteor, with the same dactylic rhythm in all voices. As the other voices reach their first cadence the tenor enters, introducing the conflicting triple meter (notated under ) for the first time. The section continues as Busnoys's does, alternating episodes in which duple and triple meter are set against each other with moments of straightforward duple (mm. 166–67), including a prominent passage (mm. 175–78) immediately before the concluding sesquialtera. Busnoys had prepared for the triple-meter finale with the longest and most straightforward duple episode since the very first measures of the Confiteor (see Example 1, mm. 180–82). The contrast is especially marked, as the four voices snap into triple meter almost at once (m. 183), without a break in either texture or forward momentum. Whereas Busnoys spins out successively longer phrases over the course of his Confiteor, the Sancto Johanne composer elides his first two phrases, but follows them with a series of progressively shorter phrases in the superius and bassus (mm. 160–75). Rather than Busnoys's steady accumulation of energy, the Sancto Johanne Confiteor gives the impression of pulling back in this series of short phrases before launching into the climactic shift from duple to triple.

Example 6

The biggest difference between the Sancto Johanne mass and Busnoys's Missa L'homme armé is the range of the cantus firmus, which affects perception of metrical change. In its Confiteor the Missa de Sancto Johanne uses the chant “Innuebant patri,” which cannot compete with the L'homme armé tune in terms of melodic vigor. Even though Busnoys instructs the singers to transpose the L'homme armé tune down a fourth from its usual starting point, from g to d, he crafts the other voices so that the tune pops out intermittently. At the melody's first entry (Example 1, m. 159) the texture thins so that the cantus firmus can be heard. Likewise, when the tenor rings out with the middle phrase of L'homme armé (mm. 167–70) the altus is brought low and the superius momentarily rests, allowing textural space for the tenor's fanfare. The Sancto Johanne tenor has a similar range in the Confiteor (c–c′, compared with Busnoys's d–e′), but it spends less time in the upper part of its register. The first tenor entries are buried within the texture, rendering the metrical conflict audible but not overwhelming. The superius gesture in measures 158–59 does more to introduce triple meter and owes a debt to the cadential flourish in Busnoys's measures 165–66.

While Busnoys's tenor seems to push the other voices toward triple meter, the Sancto Johanne tenor feels less like the driving force behind the metrical conflict. With its lower register and less insistent melody, “Innuebant patri” does not pack the same punch. The strength of L'homme armé as a cantus firmus derives not only from its rhythmic pattern but also from its repeated pitches and assertive fourth and fifth leaps. Busnoys's Confiteor tenor also has the benefit of syllabic texting, whereas in the Sancto Johanne Confiteor only about two-thirds of notes receive text.70 And whereas the text of the Confiteor is dominated by hard, plosive consonants, “Innuebant patri” features more vowels and fricative consonants. Texting plays a significant role in articulating rhythm and has the potential to reinforce rhythmic contrasts.

These echoes of Busnoys's mass in the Missa de Sancto Johanne Baptista provide a useful context for Tinctoris's setting. The Sancto Johanne composer picked up on many of the same elements as Tinctoris in reinterpreting the shifting metrical contexts. He could have retained Busnoys's mensuration signs while eschewing the metrical back-and-forth, but, like Tinctoris, he recognized that the metrical effect is the truly essential feature of this section. Reading the Sancto Johanne Confiteor against Busnoys's highlights those elements that give the latter its potency, offering insight into the way another composer responded to the same features in Busnoys's mass that inspired Tinctoris.

Busnoys may not have come up with the idea for his audacious Confiteor ex nihilo. Though the connection is less explicit than that between Busnoys's and Tinctoris's masses, we find what may have been the notional seed of Busnoys's duple-triple battle in the Missa Spiritus almus by Petrus de Domarto. Wegman has shown how de Domarto's mass served as a linchpin between (mostly English) developments of the early fifteenth century and continental practices from the 1460s and 1470s. Indeed, de Domarto's Missa Spiritus almus is among the earliest mass cycles—perhaps the earliest—to systematically subject its tenor to mensural reinterpretation. It was the archetype of the adaptation of major prolation to mean augmentation.71 Tinctoris even blames de Domarto for popularizing this practice on the continent, citing the beginning of the Et in terra from the Missa Spiritus almus as evidence that “de Domarto made several intolerable mistakes” by failing to use a proportion sign.72 Worse, he says, many other composers of the day have followed his example, perpetuating the error.73 Wegman argues that Busnoys not only knew de Domarto's mass but was one of these “imitators.”74 The final sections of both de Domarto's Gloria and his Credo feature triple-meter tenors set against prevailing duple music in a manner that is of interest for the present discussion.

The final sections of de Domarto's Gloria and Credo include little of the direct metrical conflict found in Busnoys's Confiteor, but they nevertheless engage in a push-and-pull between duple and triple meters. Example 7 shows the Et in spiritum from the Credo. Like the final section of the Gloria it begins in duple meter (), the tenor (signed ) entering several measures later. De Domarto equates a semibreve of with a breve of , as demonstrated in the example. exhibits triple division only at the level of the semibreve (implicit major prolation), and since the tenor of the Et in spiritum has no minims until measure 210, prior to that point it sounds as if this voice is in the same meter as the others.75 Besides, it is actually the superius that introduces triple meter by way of coloration (mm. 208–11), not the tenor. The duple-triple conflict is primarily located in the superius, which alternates between triple-meter duos with the tenor and duple-meter passages with the altus and bassus. Only in the full-textured finale do all voices break into triple meter, achieved by coloration in the voices.76 

Example 7
Example 7

Example 7

What we might call the “tripleness” of de Domarto's cantus firmus is deliberately weak. Being of plainchant origin, “Spiritus almus” has no intrinsic rhythm (as L'homme armé emphatically does). De Domarto has given his cantus firmus a series of note shapes that are intentionally ambiguous from a metrical standpoint so that it can be reinterpreted under different mensurations. Thus mensural reinterpretation is one of the mass's main conceits.77 What makes this section of de Domarto's mass compelling is less a sense of metrical ambiguity than the rapid alternation between duple and triple. As a result of its metrical superimposition and the unabashed tripleness of the L'homme armé tune, Busnoys's interpretation is tighter and more frenetic, and seems to have higher stakes. Whereas de Domarto introduces triple meter as a compositional intervention to build momentum toward a cadence, in Busnoys's mass the distinctive swing of the L'homme armé tune seems to slowly infect the other voices. It is easy to imagine Busnoys hearing the closing measures of de Domarto's Gloria and Credo and thinking, “That's a good idea; I could do something more with it.”

Notationally speaking, Busnoys is to de Domarto what Tinctoris is to Busnoys. That is to say, like Tinctoris, Busnoys found what seemed to him to be a more satisfying way of notating the duple-triple conflict. De Domarto notates his cantus firmus under in order to produce the feel of integral . This was a challenge, since he otherwise uses to signal augmentation, as Busnoys would later do.78 The other voices are signed , so that a breve of equals a semibreve of :

This is the same metrical relationship that Busnoys achieves between and . It is not at all obvious that and would relate in this way. These signs would appear to relate as 2:3 rather than 4:3. While we might be able to understand how de Domarto arrived at this combination of signs, the end result is not internally consistent. Unsurprisingly, this section too made Tinctoris's blood boil.79 

Such connections serve as a reminder that the network of relationships between pieces is inherently complex and more involved—and elusive—than mere melodic citation. De Domarto's mass may provide insight into Busnoys's musical choices and the process of moving from inspiration to execution. Busnoys's Confiteor offers a window onto the related realms of musical and notational innovation. His notation may even be read as a theoretical contribution, in that it clarifies de Domarto's mensural usage. Of course, we would say the same thing about Tinctoris. But our discussion of Tinctoris, as of Busnoys, should resist focusing myopically on notation at the expense of other musical considerations.

Tinctoris the Composer

We know how “Tinctoris the theorist” would have responded to Busnoys's Confiteor, but how might “Tinctoris the composer” have read it? To answer this question, let us review some of the musical choices Busnoys makes. He begins this section by establishing duple meter with a strong dactylic motive in all voices (refer back to Example 1). The other voices more or less stop when the tenor enters, such that we hear the tenor's triple-meter music but do not particularly hear metrical conflict. In measure 160 the superius draws attention away from the tenor through its entry on b♭′, a tenth above the tenor and an octave above the bassus. With the tenor now at the bottom of the texture, the bassus moves into the tenor's usual range, setting a series of duple semibreves against the tenor's triple cantus firmus statement in what is the first instance of duple-triple conflict.

Triple meter first creeps into one of the free voices in measures 165–66, in the superius's cadential flourish. At the cadence the tenor moves to the upper part of its range to begin the B section of the cantus firmus, reinforced rhythmically by the bassus. In measures 168–72 the superius and altus answer with a squarely duple passage before the tenor reenters, repeating the triumphal blast. The free voices now begin to adopt the tenor's triple meter, and the tenor's climax on its highest note, e′ (m. 177), is folded into a fauxbourdon-like—and equally climactic—gesture in all voices. This passage is emphasized by a shift, for the first time since the opening of the section, to a homorhythmic texture. Yet another shift back to duple follows, while the tenor rests between phrases (mm. 180–82). Small note values create a sense of propulsion that builds straight into the tenor's reentry (m. 183). The tenor ushers in a decisive return to triple meter, the L'homme armé melody now buried at the bottom of the texture beneath an active surface. Even after the tenor has reached its final note, the other voices continue in triple meter to conclude the movement with a bang.80 

Tinctoris picks up on many of these elements in his own Confiteor. He too establishes duple meter with the same strong dactylic statement in the superius, and he echoes Busnoys's initial melodic contour by leaping up to c″ in the third measure (refer back to Example 2). Unlike Busnoys's, Tinctoris's lower voices are extremely active from the very outset. Triple meter first breaks into a free voice in measure 182, when the lower voices align with the cantus-firmus-bearing altus as the superius cadences. In measure 184 the superius sweeps back in, decisively reestablishing duple meter. Tinctoris broadens the B section of the cantus firmus, staging it as dovetailed imitation at the unison between superius and altus at the top of the texture. He brings the other voices into triple meter to match the L'homme armé tune, but he goes further than Busnoys, remaining in triple meter through the end of the B section. He is also freer in quoting the L'homme armé material. He introduces semiminims in measure 199 to jerk us back into duple meter in an abrupt transition similar to Busnoys's in measure 180. He echoes Busnoys's final flourish with a similar upward trajectory in all voices, though Tinctoris's final phrase is more compact, the superius shooting up precipitously. In his final measures Tinctoris uses triple meter to broaden out and decelerate to a close, not unlike the end of his Gloria, whereas Busnoys builds continuously to a rather abrupt cadence. If Tinctoris's goal was to school Busnoys on matters of notation, he went to an awful lot of trouble to make his point.

It is all but irresistible to read Tinctoris's personality from his treatises. Few theorists of the time left such substantial bodies of writing; fewer still filled their works with rhetorical gems in the manner of Tinctoris. In addition to the previously quoted remarks from the Proportionale, we find references to threats by his critics to make him literally eat his words (in the form of a book) if he were to return to his homeland. Tinctoris cheekily replies that he has already returned several times, if only in his mind, without any harm befalling him.81 As Woodley has shown, Tinctoris took exceptional care with the tone of his treatises.82 And yet for all the progress we have made in coming to understand his intellectual disposition,83 we are on less familiar terrain when describing his compositional personality. Most studies of Tinctoris focus on the theoretical writings; what little has been written on his music has tended to relate his compositions to his theory.84 This all makes sense: Tinctoris's Missa L'homme armé can profitably be read as an extension of his theoretical writings. If we stop there, we have learned something. But if we stop there we also fail to take into account the relationship between his intellectual personality and his music. Much important groundwork having been laid, we are now well positioned to consider Tinctoris's music in its own right, as some recent work has already begun to do.85 

It does not take deep immersion in Tinctoris's music to recognize how eclectic it is. The idiosyncrasies of his Missa L'homme armé have made it difficult to situate within the L'homme armé tradition, since it does not fit the usual narrative of competition and one-upmanship. This difficulty arises in part because, as Edgar Sparks suggested, the mass suffers from a “lack of simple plan, of a dominant structural voice, or of any regular method of [cantus firmus] treatment.”86 But what Sparks singles out for criticism is something the theorist himself would have regarded as a virtue. In the Liber de arte contrapuncti Tinctoris praises the concept of varietas, borrowed from Ciceronian rhetoric:

Any really clever composer or improviser [upon a tenor] will bring about this diversity if he composes or improvises now by one mensuration, now by another, now by one kind of cadence, now by another, now by one proportion, now by another, now by one kind of melodic interval, now by another, now with syncopations, now without syncopations, now with fugae, now without fugae, now with rests, now without rests, now melodically embellished, now plain. … Therefore every composed work must be diverse in its quantity as well as its quality, as demonstrated by an infinite number of works, not only by me, but also by innumerable composers who are flourishing in the present age.87 

In recent years several scholars have helped to elucidate what Tinctoris means by this term.88 Even so, using varietas as the basis for analysis proves challenging, since it is so foreign to modern analytical paradigms, which privilege correspondence between things that are similar.89 

As a reflection of his aesthetic principles Tinctoris's heterogeneous cantus firmus treatment is no surprise. Though most often found in the altus, the cantus firmus moves freely among the voices and is often embellished, at times almost beyond recognition.90 In this respect his mass corresponds less closely to the strict forms of Ockeghem and Busnoys than to the freer treatments of Du Fay and Regis. Indeed, just after the passage from the Liber de arte contrapuncti quoted above, Tinctoris mentions Du Fay's Missa L'homme armé as an excellent example of varietas.91 Yet Tinctoris goes even further. Sometimes he decorates the cantus firmus, sometimes he leaves it unembellished; sometimes L'homme armé serves as a scaffold, sometimes it is integrated into the polyphonic fabric. He shifts mensurations often, subjects the tune to imitation canon, and presents it in a variety of note values, from semibreves and minims to longs and breves. Moreover, his music is distinctive for its surface complexity and—a related but ultimately separate characteristic—textural density. He arguably succeeds in creating a paradigm of varietas, broadly understood.

Tinctoris's very success may have doomed the mass in the eyes of earlier musicologists. Sparks dismissed it as a jumbled “wilderness of effects,” while Judith Cohen lamented that “the abundance of varying techniques creates no sense of intensification or an impression of the composer's brilliant command of his means.”92 Manfred Bukofzer noted this feature, calling the mass a “bewildering work” and contending that “the flow of the lines is often obscured by very intricate and crotchety rhythms.”93 Starting out from a more sympathetic view of varietas, Jesse Rodin has recently described this eclecticism in positive terms, characterizing the mass as “stylish, rigorous, [and] intense” and pointing to its control of rhythm and meter as its most impressive feature.94 Rodin's discussion is an outlier, however: much remains to be done before varietas is understood and appreciated as an aesthetic category largely opposed to the unity long prized in musicology.

The Gloria gives a good sense of what all the fuss is about (see Example 8). Although the metrical ambiguity of the Confiteor is unmatched, Tinctoris indulges in other instances of metrical instability. Rather than beginning with long note values and speeding up from there, Tinctoris jumps right in with an intricate altus-superius duo prominently featuring pairs of fusae. He obscures the mensuration beneath this active surface by bringing in the superius after only three minims, rather than waiting for the beginning of a tempus. With the voices in imitation, this “offbeat” entry causes the superius's accents to fall contrary to those of the altus, heightening the metrical uncertainty. We might expect this level of activity and rhythmic complexity later in the section, but to begin a movement in this way is unusual and unexpected. Indeed, the superius entry projects, albeit momentarily, a quick triple meter such as . The imitation continues into the next phrase, though the musical style changes dramatically. Here Tinctoris brings in the fanfare from the L'homme armé tune, first in the superius, then in the altus, presenting it in minims rather than semibreves. The groupings of three minims further imply a -like meter, although imitation at two semibreves’ distance does not. Even when the lower voices enter Tinctoris continues to write music whose underlying mensuration is ambiguous—or at least not unambiguously .

Example 8
Example 8

Example 8

In his Cum sancto Tinctoris again places the L'homme armé fanfare motive in imitation, this time in all four voices (see Example 9). The bassus initiates this string of falling fifths by dropping from a to d, and the superius, altus, and tenor echo in turn, all singing d′–d′–d′–g. Matching the altus and tenor in pitch, the superius reaches the bottom of its range, but it does not stay there long, rushing up again in staggered dotted figures to herald a cadence at which all voices shift to . Tinctoris probably took the idea from Busnoys, who also presents the L'homme armé fanfare motive in close imitation in the final section of his Gloria, the Tu solus (see Example 10).95 Busnoys first fires off this motive in stretto imitation (m. 134), then, in a separate statement, loosens the interval of imitation so that each new voice enters as the previous voice reaches its final note (mm. 136–38). In the first instance the entries pile up so rapidly that the imitation is over almost as soon as it has begun. In the second, the minims—three this time—form a grouping that emphasizes the moderate triple meter of . Tinctoris seems to have found something in this passage worth reusing.96 

Example 9
Example 9

Example 9

Example 10

Tinctoris's borrowing of this device from Busnoys has nothing to do with theory or notation: it is all about sound. He acts here like a “regular” composer, homing in on a memorable use of borrowed material, reusing it himself. If we are ever to understand his compositional style we have to start thinking of him as “just” a composer—and indeed this mass features a wealth of moments in which his composerly personality shines through. For another such moment we may turn to the beginning of the Agnus Dei, where he establishes two simultaneous metrical levels (see Example 11). The bassus and tenor sing a duet of rhythmically active lines, complete with fusae and syncopation, while the superius traces a broader, cantus-firmus-based arc in larger note values.97 The three come to a cadence on G in measure 5, from which they quickly move on. Like many fifteenth-century composers, Tinctoris does not dwell on his cadences, preferring to reestablish momentum right away. But just a measure later, as the altus enters with the cantus firmus, all four voices come to a stop on a G sonority with an explicit b′-mi in the superius. They all hold this arresting sonority for a perfect breve before moving forward, immediately reverting to B♭s. In a mass that has so far used B♭ exclusively, this b′-mi comes out of nowhere; coupled with a dramatic break from the otherwise relentless rhythmic activity, it marks a moment that recalibrates any sense of expectation.

Example 11
Example 11

Example 11

This abrupt pause on a sonority with an explicitly raised third recalls the way Regis opens each movement of his L'homme armé mass.98 Regis approaches the pause homorhythmically and sets it off from what follows with rests, but the impression produced by a pause and raised-third sonority is still similar. Rodin points to another instance of unexpected rhythmic inactivity in Tinctoris's Agnus Dei III (mm. 73–74), where he comes to rest for a full three semibreves;99 this is probably an imitation of another striking passage in Busnoys's mass.100 These are not the compositional decisions of someone interested only in making a theoretical point.

The system Tinctoris advocates in the Proportionale never quite caught on. He described practice as he thought it ought to be, not as it was. It is this rift between his theoretical ideas and contemporary practice that makes his own compositions so distinctive.101 In this regard two considerations seem particularly noteworthy. First, Tinctoris was concerned with clarity above all. This is not to be confused with simplicity, as the amplification of Busnoys's notational complexity in Tinctoris's own Confiteor amply demonstrates. Second, in order to uphold logical consistency Tinctoris was willing to forgo the visual consistency of the cantus firmus, in marked contrast to Busnoys and several other contemporary composers. Tinctoris's mass is therefore neither a simple reworking nor the product of a curmudgeonly theorist agitated about what he took to be misguided notational practice. On the contrary, it reflects a thoughtful, measured reading that blends revision with respect, innovation with influence.

The Fifteenth-Century Avant-Garde

If we are willing to suspend our view of Tinctoris as a theorist who wrote some music on the side, the boundary between theory and practice begins to collapse. Tinctoris's music has long provided a window onto the way his theory works in practice—like an appendix of extra musical examples. But of course it works in the other direction, too. Tinctoris's L'homme armé mass helps us to bridge theory and practice in ways that are not always obvious, by encouraging us to consider how composition and explicitly theoretical activities might have informed one another. To do this we must resist the impulse to map current views of the relationship between notation and composition onto earlier times.

Our tendency, born of roughly five centuries of musical practice, to understand notation as a relatively straightforward means to an end makes it difficult to tease apart Tinctoris's musical and theoretical motivations. In fact it may be wrong even to ask whether his goals in responding to Busnoys's mass were primarily notational or musical. The combination of historical distance and the flexibility of modern notation can make us forget that fifteenth-century composers were working within a less firmly established system. Several composers extended the rules to allow for new possibilities; the difference with respect to Tinctoris is that he codified his ideas in prose. I do not mean to undersell his achievements: his treatises present a comprehensive rethinking of the entire system of musical composition and notation. But rather than setting the bar for theoretical activity they are the high-water mark.

It is not surprising, then, that when he composed Tinctoris put his own ideas into practice. His Missa L'homme armé includes signs of mensuration and proportion such as , , and even that are perfectly in keeping with his precepts, even if we would be hard-pressed to find these signs in the music of his contemporaries. He cared that music be notated properly; the unusual signs one finds in his works reflect his notational theories. This is just Tinctoris being Tinctoris, we might say. But while that may well be true, it is not the whole story. Tinctoris is one of a handful of theorists of the early Renaissance who produced a substantial body of music that warrants comparison with that of the major composers of the period.102 And Tinctoris is unusual in the extent of his engagement with the contemporary repertory—in both his theoretical writings and his music. Compositionally he takes part in the same practices of borrowing as his peers; and his treatises are the first to critically evaluate music of his own time.

Having used Busnoys's and Tinctoris's L'homme armé masses to think harder about the cross-pollination between composers and theorists, we are now in a position to step back and consider the role of notation in fifteenth-century music more generally. To return to Busnoys's Confiteor, the fact that an anomalous notational usage is intriguing does not mean that it was the driving force behind a given composition. It is dangerous to assume that what catches our interest was also the composer's motivating concern. Within the subclass of fifteenth-century works engaged in both musical and notational innovation, the L'homme armé masses are shining examples. Here composers do not simply work within the constraints of the system, pushing gently against them: they invent new ways of writing because doing so facilitates new sounds. In the process, even mere “composers” achieve significance as “theorists.” We have observed Busnoys's struggle to notate certain musical effects; while he may have come to solutions that Tinctoris did not approve of, they are soundly reasoned and theoretically grounded.

During this period, notation and composition were intertwined to a degree not matched until the mid-twentieth century. Although some composers in the West continue to develop new methods of notation, musical innovations largely take place within or as further refinements to a common system. Or they may take place outside the notational system entirely, thanks to the advent of audio recording technology. In the later Middle Ages notation was the major musical technology, and composers productively used it to generate a flood of new musical ideas. In turn, they sometimes had musical ideas that demanded new notation. It is difficult to imagine what it was like to compose at a time when the most basic tenets of rhythmic notation changed generation by generation, when note shapes did not contain a stable number of beats, and when the very practice of using note shapes to indicate duration was less than two centuries old. Shifting our view of notational complexity from willfully abstruse to functional and generative has the potential to make us more empathetic listeners—and readers.

All of this can help to break down the unhelpful disciplinary binary we sometimes impose on the activities of theorists and composers. In ways that have not yet been adequately recognized, these activities often existed in the same orbit. Pieces of music could function as theoretical texts, and theoretical texts could inform pieces. By viewing Busnoys's “theory” next to Tinctoris's, we stand to develop a more nuanced view of the way composers did or did not represent their musical ideas “correctly.” By avoiding the tendency to use Tinctoris's writings as a key to every notational question of the period, we can adopt a broader perspective that allows for a fuller—if messier—view of fifteenth-century music and music theory. Softening the division between composition and theory parallels the fluid positions from which we may approach this music: as historians, theorists, analysts, and music lovers.

 

Notes

Notes
The section of this article entitled “Busnoys the Theorist” was conceived under the guidance of Sean Gallagher, whom I thank for introducing me to Busnoys's music and first helping me to make sense of it. Earlier versions of the article were presented at the Medieval and Renaissance Music Conference, Barcelona, 2011, and the annual meeting of the American Musicological Society, San Francisco, 2011, where it benefitted from suggestions by Anna Maria Busse Berger, Bonnie Blackburn, Jeffrey Dean, Roger Grant, Leofranc Holford-Strevens, and Ronald Woodley. I owe special thanks to Lawrence Bernstein, Emma Dillon, Darien Lamen, Evan MacCarthy, Jesse Rodin, Anna Zayaruznaya, and the Journal's anonymous reviewers for generously reading various drafts. I additionally thank Jeffrey Dean for allowing me to use his mensuration font for the representation of notational symbols throughout the article.
1.
In all music examples I have left note values unreduced, including those in voices that must be augmented in performance. I have otherwise followed modern conventions for representing durations, explicitly dotting perfect notes and replacing altered notes with the next largest value. Examples are barred at the level of the breve, though in some cases I distinguish metrical levels by using both dashed and solid bar lines.
2.
Tinctoris's mass is edited in Tinctoris, Opera omnia, and Tinctoris, Missa super L'homme armé, the latter edited by Lawrence Feininger. Although I will refer to Tinctoris's mass as his Missa L'homme armé, the words “L'homme armé” do not actually appear in its only surviving source (VatS 35). Because the mass has troped Kyries it might reasonably be referred to as the Missa Cunctorum plasmator summus, after the Kyrie trope. I retain the title Missa L'homme armé for the sake of simplicity and because the mass clearly participates in the L'homme armé tradition.
3.
I refer to pitch octave in this article using the Helmholtz system.
4.
On the dating of Tinctoris's Proportionale, see Woodley, “Proportionale musices,” 69–70. Dating the masses proves much trickier. The most we can say with any certainty is that Busnoys's Missa L'homme armé must date from before 1472, given that it is cited in the Proportionale, and that Tinctoris's must date from before 1488, when the copying of VatS 35 was begun. They may, however, date from significantly earlier.
5.
Many examples of complex notation in late medieval music have been ascribed a “pedagogical” intent, particularly when complexity is combined with a comprehensive exploration of a given theoretical topic (for example, systematically employing all the major mensuration signs). While some pieces were surely composed at least in part to demonstrate a theoretical principle, we should be cautious about applying the ready-made interpretation of pedagogy in order to explain away complexity. A clear example of a theoretically instructive motet is Tinctoris's own Difficiles alios delectat, once thought to be lost but since identified by Bonnie Blackburn. The title alone, “He delights in composing other difficult songs,” warns singers explicitly about the challenges it contains. In addition to its difficult mensural usage, imperfection, alteration, coloration, and proportions, it is preserved not in a choirbook but in a collection of didactic musical examples. Blackburn mentions two such collections from the early sixteenth century, PerBC 1013 (in which she identified the motet in question) and BolC A 71: Blackburn, “Lost Guide.”
6.
For the most up-to-date biographical information, see “Johannes Tinctoris: Biographical Outline,” in “Johannes Tinctoris: Complete Theoretical Works,” Early Music Theory website, accessed September 9, 2017, www.earlymusictheory.org/Tinctoris/Tinctoris/BiographicalOutline/#. See also Woodley, “Iohannes Tinctoris: A Review”; Woodley, “Tinctoris and Nivelles”; Woodley, “Tinctoris's Italian Translation”; Atlas, Music at the Aragonese Court, 71–77; Sherr, “Biographical Miscellany”; D'Agostino, “Note sulla carriera”; Blackburn, “Music Theory and Musical Thinking,” 302–3, 325–33; Palenik, “Early Career of Johannes Tinctoris,” 7–50, 129–214; and MacCarthy, “Tinctoris and the Neapolitan eruditi.”
7.
This is not to say that Tinctoris's music has received no attention. As I discuss in greater detail below, major studies that consider his compositional activity include Melin, “Music of Johannes Tinctoris”; Gronemann, Varietas delectat; Rodin, Josquin's Rome, 179–88; and Dean, “Towards a Restoration,” 18–25, 35–40. Gronemann's is the only extended study to focus on Tinctoris's music, though I find its conclusions about hidden symbolic meanings unconvincing.
8.
Bonnie Blackburn discusses the category of the theorist-composer, noting that “Behind every word of his theoretical treatises stands Tinctoris the singer and composer. … It would be equally just to call Tinctoris a composer-theorist”: Blackburn, “Lost Guide,” 102–3. Tinctoris is not alone among fifteenth-century theorists in having left a substantial body of compositions, but his appear to have been the most influential. John Hothby left a handful of pieces, as did Ugolino of Orvieto, Bartolomé Ramos de Pareja (now mostly lost), Giovanni Spataro, Adam von Fulda, and Pietro Aaron. Franchinus Gaffurius composed a large number of pieces, mostly for the Milanese liturgy. Greatly influenced by Tinctoris, he should certainly be considered beside him as a theorist-composer. See Hothby, Musical Works, and Gaffurius, Messe. Johannes Ciconia and Guillaume Du Fay are also known to have written theoretical treatises. Ciconia's Nova musica and De proportionibus have survived, but they are entirely speculative and do not deal with contemporary musical practice. The title of Du Fay's treatise Musica, which we know of only from citations in another theory treatise, gives little indication of its contents; see Gallo, “Citazioni da un trattato.” François-Joseph Fétis reports that a sixteenth-century copy of another treatise by Du Fay—Tractatus de musica mensurata et de proportionibus—was sold in 1824, but there has been no trace of this work since; see Planchart, “Du Fay [Dufay; Du Fayt], Guillaume.” There is even the possibility, again mentioned by Fétis, that Josquin des Prez wrote a theoretical treatise, though the evidence for this is very thin; see Fétis, untitled postscript to “Quelques notions,” and Dean, “Josquin's Teaching,” 741–42.
9.
On the ways in which theory could influence composition, see Blackburn, “Did Ockeghem Listen to Tinctoris?”
10.
Tinctoris, Proportionale musices, 82 (III.ii.28): “hec signa adeo frivola, adeo erronea, adeoque ab omni rationis apparentia sunt remota ut nec exemplo digna crediderim.” (Translations are mine unless otherwise indicated.) While I have drawn the Latin text and its numbering from the edition by D'Agostino, I look forward to the digital edition by the team of Ronald Woodley, Jeffrey Dean, and David Lewis, who are preparing editions, translations, and online facsimiles of Tinctoris's complete writings. At the time of publication they had not yet tackled the Proportionale musices, but many of Tinctoris's other texts, including several of the less well known treatises, are available online at www.earlymusictheory.org/Tinctoris (accessed August 12, 2016).
11.
Tinctoris, Proportionale musices, 76 (III.ii.13–14): “Sunt et alii … se penitus expertes aritmetice manifestantes, una tantum cyphra, videlicet eius numeri qui ad alium refertur, omnes quas practicant proportiones signant. … Et hoc nihil magis est ab aritmeticis—a quibus proportiones accepimus—alienum, signo pertinenti numero per se, id est sine relatione aliqua constituto, numerum ad aliquid, id est qui relative ad alium comparatur, tantummodo signare.”
12.
I follow Anna Maria Busse Berger in adopting the term “modus cum tempore” to refer to these signs, though it originates in the circle of John Hothby and is never actually used by either Tinctoris or Busnoys: Berger, Mensuration and Proportion Signs, 20–23.
13.
Modus cum tempore signs are admittedly rather unusual signs, since they shift the levels of mensuration up by one. In this case Tinctoris's complaints are easy to understand. See ibid., 148–63.
14.
This is presumably why Tinctoris accepts the use of for duple proportion, since the sign's pervasive duple division poses no problems, regardless of the level at which it is understood. He says, “This, as de Domarto and Faugues will be pleased to hear since they used the sign in their masses Spiritus almus and Vinus, I find tolerable because of a certain equivalence between proportion and prolation: for when something is sung ad medium [i.e., under ], two notes are commensurate with one, just as in duple proportion”: Tinctoris, Proportionale musices, 78 (III.ii.21) (“Quod, ut de Domarto et Faugues in missis Spiritus almus et Vinus ita signantibus placeam, tolerabile censo propter quandam equipollentiam illius proportionis ac istius prolationis: dum enim aliquid ad medium canitur, due note sicut per proportionem duplam uni commensurantur”).
15.
Richard Taruskin proposes that in the Christe and Benedictus the prevailing mensuration should be , as found in VatC 234 and BarcBC 454, rather than , as transmitted by the other sources (VatSM 26 has for the Christe and for the Benedictus): Taruskin, “Antoine Busnoys,” 269–70. But should surely be seen as the lectio difficilior. As Sean Gallagher has demonstrated, the renotation of music from to or was a common practice; indeed, “there are no clear examples of being replaced with ”: Gallagher, Johannes Regis, 104–7, here 104. See also Wegman and Taruskin, letters to the editor; Brothers, “Vestiges of the Isorhythmic Tradition,” 10–24; and DeFord, “Tactus,” Mensuration, and Rhythm, 279. When discussing issues of notation it is important to remember that we are dealing with texts that have passed through many hands between the composer's and our own. It is always possible that notational quirks were introduced by an enterprising scribe. Tinctoris's admonishment of Busnoys strongly suggests that such “errors” emanate from the composer himself. As Woodley has noted, Tinctoris writes as if he has access to reliable copies of the pieces he discusses: Woodley, “Did Tinctoris Listen to Okeghem?” Wegman and Gallagher have also documented cases in which the sole surviving copies of Regis's Missa Dum sacrum mysterium / L'homme armé (VatS 14) and Faugues's Missa Vinus vina (VatS 51) use different notation from the copies Tinctoris clearly knew: Wegman, “Guillaume Faugues,” 52–56; Gallagher, Johannes Regis, 98–114. Such cases provide evidence that imperfect correspondence between Tinctoris's descriptions and the surviving copies of Busnoys's works does not imply that Tinctoris was referring to pieces that do not survive.
16.
See Busnoys, Collected Works, 3:29–31; Berger, Mensuration and Proportion Signs, ch. 5; and Wegman, “Petrus de Domarto's Missa Spiritus almus,” 255–58.
17.
Perhaps Tinctoris even had Busnoys's mass in mind when he enumerated his complaints about current mensural practice in the Proportionale. The two track quite closely, and since he mentions Busnoys's mass we can be sure he knew it well. This possibility nevertheless remains within the realm of speculation.
18.
Note that my use of the terms here is slightly different from, though compatible with, that proposed by Ruth DeFord in her recent book. DeFord indicates whether or not the mensura (time unit) is of known duration, but not the notational mechanism for achieving augmentation or diminution, which is relevant to the present argument. DeFord, “Tactus,” Mensuration, and Rhythm, 114–43; see also DeFord, “On Diminution and Proportion,” 1–10. On related concerns regarding diminution in earlier music, see also Berger, “Myth of diminutio per tertiam partem,” and Bent, “Myth of tempus perfectum diminutum.”
19.
Although all levels are also duple under , there is no alignment problem between and , since the stroke of implies diminution, creating a second level of remove relative to the augmented sign of major prolation. This renders the relationship between notes all but identical to that created by the combination and . does not imply the triple division of the long that does, but if longs are not present (and they rarely are) there is no conflict. Examples of cantus firmi in that are not part of the L'homme armé tradition include Cornelius Heyns's Missa Pour quelque paine, the anonymous Missa Gross senen (TrentC 89), Johannes Martini's Missa La martinella, and sections of several masses by Jacob Obrecht, including Petrus apostolus and Graecorum.
20.
The use of major prolation in L'homme armé masses is discussed below.
21.
Tinctoris, Proportionale musices, 80 (III.ii.26). Writing in 1482 Bartolomé Ramos de Pareja was the first to give detailed instructions describing—and sanctioning—the so-called error anglorum. And in his Toscanello in musica of 1523 Pietro Aaron specifically defends it against those who advocate minim equivalence. See Berger, Mensuration and Proportion Signs, 91–99. The practice of equating a minim of with a semibreve of seems to have begun in English music at the beginning of the fifteenth century, which is presumably why Tinctoris refers to it as the “error of the English.” In these cases, however, probably does not imply augmentation but should rather be considered as the tactus-carrying sign.
22.
Tinctoris, Proportionale musices, 84 (III.iii.7–11): “Quemquidem de Domarto, si in hoc errore Regis, Caron, Boubert, Faugues, Courbet aliique plurimi, ut in eorum operibus vidi, sint imitati, non miror quom illos minime litteratos audiverim. Et quis sine litteris veritatem huius non solum sed cuiusvis scientie liberalis attingere valebit? Sed eis fuisse pares in missis De plus en plus et L'homme armé Okeghem et Busnois, quos competenter constat latinitate preditos, non mediocrem pectori nostro admirationem incutit. Quid enim admirabilius est, quam videntes avia cecitatis ingredi? Sed quoniam in tali eorum componendi modo, si ita signaretur: , prout ars requirit, difficultas pronuntiationis, immo totius melodie destructio propter nimiam velocitatem oriretur, melius tenori canon apponeretur, scilicet ‘Crescit in duplo,’ vel equivalens, sicut laudabiliter fecit Dufay in missa Se la face ay pale.” (In reproducing the Latin text here I depart from D'Agostino's edition in one respect: D'Agostino gives “quam videntes a via cecitatis ingredi.”)
23.
Ockeghem's L'autre d'antan and Prenez sur moy are prime examples, though the realization of Prenez sur moy, a 3-ex-1 canon, has proven troublesome. In the Proportionale Tinctoris also takes issue with composers who use any of these signs at the beginning of a piece of music, since in his view they imply reference to a previous sign. He does not allow, as some other composers seem to, that they might relate to a sort of “platonic” mensuration (for example, ) that is understood but not written.
24.
On the concept of mensura in Renaissance music, see DeFord, “Tactus,” Mensuration, and Rhythm, esp. ch. 3.
25.
A number of manuscripts from the fifteenth century include “resolutions” of canonically notated tenors that effectively write out the procedure that the singer is instructed by the canonic notation to perform. In the VatS 14 copy of Busnoys's Missa L'homme armé the tenor is written not once but twice, the second time immediately after the first. One statement is in minims and semibreves under either or , while in the other all manipulations (in this case augmentation, transposition, and inversion) are written out under the prevailing mensuration. To look at one movement in particular, the resolution of the Agnus Dei presents the tenor in longs and breves under the prevailing mensuration , and with the melody written in inversion, so that it can be sung exactly as it is written. On the practice of resolution in the Vatican manuscripts, see Rodin, “Unresolved.”
26.
Notably Obrecht in his own Missa L'homme armé and the anonymous composer of the Missa de Sancto Johanne Baptista, preserved uniquely in VatS 160; see Wegman, “Another ‘Imitation,’” 189–95. These pieces are discussed in greater detail below.
27.
Dean further proposes that the tenor's triple-long rests point to an original mensuration sign of , rather than the surviving : Dean, “Towards a Restoration,” 22.
28.
In that case my comparison of specifically heard note values would not be necessary, since the notation of Tinctoris's mass would match that of Busnoys's more closely than it does in the surviving versions.
29.
On melodic borrowing, see, for example, Brown, “Emulation, Competition, and Homage”; Burkholder, “Johannes Martini”; Meconi, “Does imitatio Exist?”; Meconi, Early Musical Borrowing; and Reynolds, “Counterpoint of Allusion.” On shared notation and compositional procedures, see Wegman, “Mensural Intertextuality,” 189–93, and Wegman, “Another ‘Imitation,’” 196–202. See also Milsom, “‘Imitatio,’ ‘Intertextuality,’ and Early Music”; Rodin, “‘When in Rome … ,’” 319–64; Rodin, “L'homme armé Tradition,” 77–81; and LaRue, “Significant and Coincidental Resemblance.”
30.
Bernard, “Tinctoris's Missa L'homme armé,” 7–11.
31.
Gallagher, Johannes Regis, 78–79; Dean, “Towards a Restoration,” 37–39.
32.
In Tinctoris's own words, “At the present time … countless composers flourish, such as Johannes Okeghem, Johannes Regis, Antoine Busnoys, Firminus Caron, Guillaume Faugues, who pride themselves on having as their teachers in this divine art the recently deceased John Dunstaple, Gilles Binchois, Guillaume Du Faÿ. … So just as Vergil in that divine work the Aeneid took Homer for his model, so, by jiminy, do I take these in my little works, especially in so far as, in arranging the concords, I have plainly imitated their admirable style of composing”: Tinctoris, Liber de arte contrapuncti, prologue (“Hac vero tempestate … infiniti florent compositores, ut Joannes Okeghem, Joannes Regis, Antonius Busnois, Firminus Caron, Guillermus Faugues, qui novissimis temporibus vita functos Joannem Dunstaple, Egidium Binchois, Guillermum Dufai, se preceptores habuisse in hac arte divina gloriantur. … Unde quemadmodum Virgilius in illo opere divino Eneidos Homero, ita iis hercule in meis opusculis utor archetypis, presertim autem in hoc in quo, concordantias ordinando, approbabilem eorum componendi stilum plane imitatus sum”). Translation also from Tinctoris, Liber de arte contrapuncti.
33.
For one possible precedent, see the discussion of Petrus de Domarto's Missa Spiritus almus below.
34.
Busnoys usually pairs with rather than , but because the theoretically important level is prolation, not tempus, the issue remains the same.
35.
Wegman, “Mensural Intertextuality,” 179.
36.
On the broader context of the fifteenth-century affinity for such visual consistency, see Zazulia, “Verbal Canons and Notational Complexity,” 133–203.
37.
In fact, most masses that present the melody in minims and semibreves also use signs of major prolation, though this may have as much to do with the signs’ association with augmentation as with any original version of the melody.
38.
Preserving the appearance of a cantus firmus took on great importance for some fifteenth-century composers. I explain the phenomenon, which I call “notational fixity,” and its consequences in Zazulia, “Transformative Impulse.”
39.
Ockeghem was probably not responsible for translating the “error of the English” to the continent, however. Rob Wegman has given this distinction to Petrus de Domarto: Wegman, “Petrus de Domarto's Missa Spiritus almus,” 252–57.
40.
Ockeghem, Masses and Mass Sections, vol. 2, fasc. 2.
41.
Wegman makes this point, writing, “It is far from obvious that the L'homme armé tradition was consciously initiated as a tradition. After all, how could the composer of the first mass have suspected that others might follow his example, and have selected the L'homme armé tune in this awareness?”: Wegman, “Mensural Intertextuality,” 193. In dealing with the earliest layer of L'homme armé masses we must take care not to retroactively ascribe to it elements from later stages of the tradition. Indeed, there are other smaller “families” of masses that did not grow to become “traditions” in the manner of L'homme armé, such as those based on Malheur me bat, Allez regretz, Fors seulement, La belle se siet, Le serviteur, and Fortuna desperata.
42.
Perkins, “L'homme armé Masses,” 380–81.
43.
While it is not my goal to posit a definitive order for the L'homme armé masses, chronology inevitably comes into play when discussing issues of borrowing. I agree with Richard Taruskin that Busnoys's mass was tremendously influential—perhaps the most influential early L'homme armé mass—but not that it was the first. These two points need not go hand in hand, as influence is not evidence for chronological primacy. Busnoys's mass must have followed Ockeghem's: the two are so closely related that one has to be a response to the other, and it is all but impossible to read Ockeghem's mass as the response, Busnoys's treatment exceeding Ockeghem's in terms of mensural use, verbal-canon wording, and use of inversion in place of transposition. This view is put forth in Planchart, “Origins and Early History,” 351–52; Rodin, “‘When in Rome … ,’” 325; and DeFord, “Tactus,” Mensuration, and Rhythm, 272–73. On the dating of these masses, see Perkins, “L'homme armé Masses,” 370–84; Taruskin, “Antoine Busnoys,” 257–68; Busnoys, Collected Works, 3:3–6; and Rodin, “L'homme armé Tradition,” 71–73. Taruskin's article sparked a firestorm of correspondence relevant to the question of chronology; see Haagh, Giller, Fallows, and Taruskin, letters to the editor; Strohm and Taruskin, letters to the editor; and Wegman and Taruskin, letters to the editor.
44.
Gallagher, “Ockeghem's Oronyms.” Pietro Aaron and Giovanni Spataro discuss this very example, and Anna Maria Busse Berger interprets their commentary as advocating minims equal under and —that is, not augmentation: Berger, Mensuration and Proportion Signs, 102–4. Margaret Bent has argued that the tenor in this section would have remained at its slower, augmented tempo for the Christe and Et resurrexit and the other voices would slow to match it: Bent, “Use of Cut Signatures,” 647. See also Blackburn, “Did Ockeghem Listen to Tinctoris?,” 617–20; DeFord, “Tactus,” Mensuration, and Rhythm, 269–71; Taruskin, “Antoine Busnoys,” 261n15; and Ockeghem, Masses and Mass Sections, vol. 2, fasc. 2, xi–xii.
45.
Taruskin, “Antoine Busnoys,” 287–88. For further remarks on Busnoys's use of , see Busnoys, Collected Works, 3:29–31, and Rodin, Josquin's Rome, 210.
46.
It might seem as if Busnoys had an alternative option: to notate the Confiteor as Tinctoris did. This is not the case, for two reasons. First, Busnoys was committed to presenting the L'homme armé melody in minims and semibreves, which would entail using the mensuration and proportion signs instead of the that Tinctoris uses. But in order to use this notation in the Confiteor he would also have to accept Tinctoris's view of minim equivalence throughout his mass; otherwise using as an integral sign would cause confusion for the reasons already described.
47.
Rob Wegman has suggested that Busnoys may have drawn inspiration from another of the most metrically disorienting passages in fifteenth-century music—Du Fay's setting of “Genitum non factum” in the Patrem of his Missa L'homme armé. Du Fay uses a similar series of mensuration signs— and , without slashes—combined with integral and with coloration. See Wegman and Taruskin, letters to the editor. Busnoys may have been influenced by the metrical disorientation, but the precise effect of Du Fay's passage is altogether different from that of Busnoys's, both in its theoretical underpinnings and in its musical impact. Du Fay does not use in its augmented meaning: breves of and are of the same duration, but their minims are grouped into twos and threes respectively. Du Fay's “Genitum non factum” comes between passages squarely in and does not constitute a discrete section as Busnoys's Confiteor does. The effect may be compared to a canoe temporarily rocked by the wake of a passing speedboat on otherwise calm (or at least predictable) seas. The climactic force of Busnoys's metrical conflict, bringing the movement to a close, is not the goal of Du Fay's example. Du Fay's temporary metrical instability is thus even harder to explain than Busnoys's. Though portions of Du Fay's mass survive in three manuscripts, the Credo appears only in VatS 49. On Du Fay's “Genitum non factum,” see also Hamm, Chronology of the Works of Guillaume Dufay, 145. The two passages also share little in terms of overall effect. Busnoys's primary metrical conflict is between the triple meter of the L'homme armé tune and the duple meter of the freely composed music. By the end of the section the free voices fall into line with the tenor by switching to coloration. Du Fay stages a continuous conflict between meters, the most apparent being the discantus's nine (colored) minims against the contra's eight. The 2 x 3 minim pairs of the bassus occasionally add to the disruption, but because the line consists mostly of semibreves it largely aligns with the altus. Du Fay's tenor, in contrast to Busnoys's, presents the L'homme armé tune in long note values—a steadying force that remains apart from the metrical conflict entirely.
48.
On Tinctoris's intellectual context, see Berger, Mensuration and Proportion Signs; Blackburn, “Lost Guide”; Gallagher, “Models of varietas,” 39–79, esp. 49–64; Holford-Strevens, “Humanism and the Language of Music Treatises,” 424–28; Luko, “Tinctoris on varietas”; MacCarthy, “Tinctoris and the Neapolitan eruditi”; Wegman, “Tinctoris's magnum opus”; Woodley, “Renaissance Music Theory as Literature”; and Woodley, “Did Tinctoris Listen to Okeghem?”
49.
There are precedents for using superimposed numerals (fractions) to represent proportions that go back as far as the early fifteenth century, but not in the context of a system that takes full advantage of arithmetic possibilities. Prosdocimus was the first theorist to describe the use of fractions in musical sources in his Expositiones tractatus practice cantus mensurabilis magistri Johannis de Muris (ca. 1404). As Jason Stoessel reports, however, fractions were the least commonly used method of representing proportions, and were used alongside single numerals, verbal canons, and other symbols (including mensuration signs) that took on proportional significance. Stoessel also shows that temporal proportions and the use of numerals to represent them did not enter practice at the same time. Tinctoris's explicit separating of mensuration from proportion was an innovation, as was understanding these proportions as arithmetic fractions that could be multiplied and therefore understood cumulatively. For a thorough overview of this early use of proportions and arabic numerals, see Stoessel, “Captive Scribe,” 273–316; see also Berger, Mensuration and Proportion Signs, 178–96, and Dean, “Towards a Restoration,” 26. Anna Maria Busse Berger notes that Tinctoris was the earliest theorist to stress that the mensurations of compared quantities must match. (This is Tinctoris's point that perfect and imperfect breves cannot be compared; see point 4 in the numbered list in the section “Tinctoris Responds” above.) Ugolino and Hothby, for example, allowed for the proportional comparison of perfect and imperfect breves. This context makes clear why Tinctoris was so wedded to minim equivalence, even after it had fallen out of favor. See Berger, Mensuration and Proportion Signs, 203–10.
50.
This is the rare case in which chronology poses no problem. We can be absolutely sure that Busnoys's mass was written before Tinctoris's Proportionale, since Tinctoris discusses the mass in his treatise.
51.
On Busnoys's intellectual biography, see Higgins, “In hydraulis Revisited.”
52.
Wegman, “Mensural Intertextuality,” 187.
53.
Concern over scribal intervention inevitably follows quickly upon discussions of notation, but in this case it looms less large than usual. The copies of Busnoys's works in BrusBR 5557 are of exceptional authority—so much so that Wegman has proposed that they may have been entered by Busnoys himself. At the very least, several notational elements must come from the composer, providing further defense for the dot in question. As Wegman also rightly notes, there is a theoretical consistency to Busnoys's idiosyncrasies, which further supports the case for them as authorial rather than scribal. See Wegman, “New Data” and “Mensural Intertextuality.”
54.
Of the examples of notational errors cited by Wegman many are of this sort—dots of division at the level of minor modus under . They confirm examples of imperfection that likely would have been understood even without the dot. See Wegman, “Mensural Intertextuality,” 182–83.
55.
Tinctoris cites this example in a passage in the Proportionale that has proven tricky to translate: “Ab his vero tribus pariter articulis Busnois unicus dissidet, qui suas emyolias etiam per impletionem notarum designatas suppositione istius cyphre 3, iterum et iterum signat, ut patet in isto moteto suo animadvertere”: Tinctoris, Proportionale musices, 88 (III.iv.11). Ronald Woodley translates the passage as follows: “The only composer, indeed, who disagrees equally with each of these three points [i.e. how, when, and where proportions should be indicated] is Busnoys, who, having already indicated his passage of emyolia by filling in the note heads, then proceeds to add the figure 3 repeatedly under them, as can be seen in this motet of his, Animaduertere”: Woodley, “Minor Coloration Revisited,” 46. Rob Wegman translates it thus: “Indeed, from all these three articles [concerning the indication of proportions], Busnoys alone dissents, for again and again he indicates his hemiolas, even though designated by the filling-in of notes, by [the] placing underneath of the figure 3, as can be observed in this motet of his”: Wegman, “Mensural Intertextuality,” 184. Wegman believes that the word “animadvertere” is not the motet title but part of Tinctoris's syntax. He recognized the example cited by Tinctoris as measures 71–72 of the motet Gaude caelestis Domina in VatS 15, though in that source it is without the offending “3” and has a slightly altered rhythm. By understanding “animadvertere” as syntax rather than motet title Wegman removes any impediment to identifying the example with Gaude caelestis Domina. Wegman, “Mensural Intertextuality,” 184–85. Woodley expresses some reservations about—though not rejection of—Wegman's interpretation because it implies peculiar syntax. But he admits that Tinctoris could have been working from incomplete notes or from memory, or the word could have been an annotation to prompt further consideration of the notational issue. Woodley, “Minor Coloration Revisited,” 46–47.
56.
Woodley notes that the term “minor color” originates in Willi Apel's ubiquitous notation manual and does not appear in earlier texts on notation. He discusses the consequences of this “received wisdom,” suggesting that the dotted reading did not take hold until later than Apel suggests: “The awkward question of how and when the changeover came about from true sesquialtera to dotted equivalence is distinctly glossed over—unsurprisingly, since it is clearly a subject not amenable to easy prescription. … [I]ts effective suppression in many editions today should rather be read as a symptom of the seductions of normalization for editors confronted with apparently random or inconsistent patterns of colour and dots in their sources, and their (understandable) desire to focus on a reductive Urtext policy rather than address the particular historical or musical nature of the variants.” Woodley, “Minor Coloration Revisited,” 40–41. Apel himself says that the figure's meaning changed in the late fifteenth century, and that by the sixteenth century and were used interchangeably: Apel, Notation of Polyphonic Music, 128–29. In modern editorial practice the figure has been understood as the notational synonym of , even in much earlier music. Alexander Blachley defends Busnoys's “3” from another perspective: while coloration usually creates hemiolas by imperfecting values that would otherwise be perfect (i.e., three colored breves taking up the space of two), Busnoys's coloration effects a 3:2 proportion of already imperfect semibreves and minims. Blachley surmises that Busnoys may have included the “3” to distinguish from straightforward imperfection coloration. Blachley, “Mensuration and Tempo,” 188–90. That said, Tinctoris is clear in saying that the “3”s are redundant, which suggests that he understood the coloration to be sufficient for indicating the proportion and not lacking in the way Blachley suggests.
57.
Woodley was also the first to suggest that Busnoys's use of the numeral “3” in the example criticized by Tinctoris may have been due to changing ways of interpreting brief passages of coloration: Woodley, “Minor Coloration Revisited,” 46–47.
58.
Tinctoris, Proportionale musices, 76 (III.ii.11). Jeffrey Dean also cautions against siding too quickly with Tinctoris against redundancies, since they may clarify otherwise ambiguous notation: Dean, “Verona 755,” 99.
59.
See Woodley, “Minor Coloration Revisited,” 46–47.
60.
One exception may be Busnoys's hymn Conditor alme siderum, whose four voices simultaneously present the signs , , , and . The bassus moves to and then , and all voices have passages in coloration, further affecting the mensural relationships of this short piece. This is genuinely complex music, and fitting these lines together in performance must have taken some practice. That said, the only source for this hymn is the theory manuscript PerBC 1013, so we may reasonably surmise that, unlike other examples of notational complexity, the hymn was intended to serve as an example of mensural extremes. See Seay, “Conditor alme siderum,” and Busnoys, Collected Works, 3:70–74, which includes a facsimile of the original.
61.
Wegman, “Another ‘Imitation,’” and Wegman, Born for the Muses, 213–18.
62.
Strunk, “Origins of the ‘L'homme armé’ Mass,” 25.
63.
See Wegman, “Another ‘Imitation.’” Ockeghem and Obrecht's curious decision to adopt the earlier mass's structure wholesale has been overshadowed by the eccentricity of the “Caput” tenor itself. That they would write masses based on a small fragment of Sarum chant is most unexpected, since the chant's origin would have been liturgically foreign to continental composers. Because of both this liturgical inaptness and the widespread influence of the English Missa Caput, Ockeghem and Obrecht are thought to have taken the tenor of the English mass, not the “Venit ad Petrum” melisma, as their starting point. Viewed in this light, their masses may be more closely aligned with chanson masses, which use a voice of a preexisting chanson as their cantus firmus, than with other plainchant masses. These examples provide a precedent for Obrecht's Missa L'homme armé.
64.
On the use of this sign, particularly in the works of Obrecht and Busnoys, see Blackburn, “Sign of Petrucci's Editor” and “Obrecht, Busnoys.”
65.
These sources are ModE M.1.2, UppsU 76e, and VienNB 11883. Jesse Rodin has identified an analogous substitute Benedictus in the FrankSU 2 copy of Josquin's Missa L'homme armé super voces musicales, noting that this is “a phenomenon so uncommon in the music of this period that we do not really have a name for it.” This substitution appears in a single source geographically removed from the mass's likely place of composition—a very different situation from Obrecht's Confiteor. See Rodin, “Josquin Substitution,” 255.
66.
Blackburn, “Sign of Petrucci's Editor,” 421; see also Wegman, “Mensural Intertextuality.”
67.
Wegman, “Another ‘Imitation,’” 192–94.
68.
Ibid., 200–201. Michael Anderson has also recently written about the appearance of the mass in VatS 160, a choirbook prepared expressly for Pope Leo X (born Giovanni de’ Medici) and copied in the Alamire workshop, likely between 1516 and 1519: Anderson, “‘His Name Will Be Called John.’” On VatS 160, see Warmington, “Vatican City.”
69.
Perhaps the added “3” in the tenor was intended to replace the implied sesquitertia of the reversed () used by Busnoys. Or perhaps the composer is conflating the canonic and resolved notation in the Vatican orbit copies of Busnoys's mass (VatS 14, VatS 63, and VerBC 759), which preserve for the canonic notation and in the resolutio.
70.
The VatS 160 copy of the Missa de Sancto Johanne is carefully underlaid with the “Innuebant patri” text, which I have followed in my transcription (Example 6).
71.
See Wegman, “Petrus de Domarto's Missa Spiritus almus,” 244–48.
72.
Tinctoris, Proportionale musices, 82 (III.iii.3): “In quo de Domarto pluries … intolerabiliter peccavit.” De Domarto writes the tenor in