From treatise to classroom: Teaching fifteenth century improvised counterpoint

From Treatise to Classroom: Teaching Fifteenth-Century Improvised Counterpoint* Ni e ls Beren tsen The primarily oral and aural understanding of counterpoint in the fifteenth century has become widely recognized by scholars and practitioners of early music in recent decades. In his Liber de arte contrapuncti (1477) Tinctoris informs us that ‘absolute’ counterpoint is sung together, using only one’s mental faculties. This is what he calls ‘cantare super librum’: singing counterpoint on plainchant from a chant book (hence ‘singing upon the book’).1 ‘Cantare super librum’ played a vital role in the singing of the liturgy, as well as in the training of musicians during the Renaissance. Adrianus Petit Coclico, for instance, constantly stresses the importance of ex tempore counterpoint as part of musical training in his Compendium musices.2 Vicente Lusitano’s Del arte del contrapunto (c. 1550), recently edited by Philippe Canguilhem as part of of the FABRICA project, gives us a very detailed account of how sung counterpoint would have been taught in the sixteenth century.3 When the Hungarian musicologist and pedagogue Ernst Ferand (1887-1972) published his Die Improvisation in der Musik—the first systematic modern discussion of historical improvisation—in 1938, his motivation was largely a pedagogical one. Ferand saw an ‘omnipresent misbalance between knowledge and ability, as well as theory and practice’ in his own time, which he sought to remedy by reintroducing elements of historical improvisational teaching.4 It is therefore not surprising that important contributions to our understanding of sung counterpoint in the last forty years have been made by pedagogues such as Jean-Yves Haymoz (Haute École de Musique de Genève), Peter Schubert (McGill University, Montreal), and Markus Jans (Schola Cantorum Basiliensis). The treatise De preceptis artis musicae, written by one Guillelmus Monachus around 1470, has played an essential role in this recent pedagogical revival of ‘cantare super librum’.5 Introductory texts on fifteenth-century improvised counterpoint, such * My thanks go to the Royal Conservatoire of The Hague and Stichting De Zaaier for funding this research, to my Ph.D. supervisor Gérard Geay for his insights into early polyphony and pedagogy, to my supervisor Frans de Ruiter, as well as to my students and friends who have been my co-improvisers over the years. Finally I would like to thank several colleagues for sharing their insights into the pedagogy of ex tempore counterpoint: Jean-Yves Haymoz (Haute École de Musique de Genève), Jacques Meegens (Centre d’Études Supérieures Musique et Danse, Poitou-Charentes), David Mesquita (Schola Cantorum Basiliensis), Peter Schubert (McGill University, Montreal), Gaël Liardon (Haute École de Musique de Genève), and Isaac Alonso de Molina (Royal Conservatoire, The Hague). 1 Johannes Tinctoris, Liber de Arte Contrapuncti, ed. Albert Seay, Musicological Studies and Documents 5 (s.l., 1961), 102-3 (Book 2, ch. 20). 2 Adrianus Petit Coclico, Compendium musices (Nuremberg, 1552). 3 Philippe Canguilhem, Chanter sur le livre à la Renaissance. Les traîtés de contrepoint de Vicente Lusitano (Turnhout, 2013), 137-341. 4 Ernst Ferand, Die Improvisation in der Musik (Zürich, 1938), vii-viii, translation by the author. 5 The treatise survives in a single manuscript: Venice, Biblioteca Nazionale di San Marco, Lat. 336 (Contarini), coll. 1581. Andrew Hughes dates the treatise around 1470; see Hughes, ‘Guillelmus Monachus’, in The New Grove Dictionary of 10.1484/ J . J A F.5.102766 jaf_6_2.indd 221 J O U R N A L O F T H E A L A M I R E F O U N D AT I O N 6 (2014) 221 6/10/14 13:36 as the articles by Klaus-Jürgen Sachs, Markus Jans, and Ross Duffin in the Basler Jahrbuch für historische Musikpraxis, and Barnabé Janin’s improvisation manual Chanter sur le livre, rely heavily on De preceptis for their information.6 What is the best way to use the information in De preceptis to teach counterpoint in our modern classrooms? This is the main question this essay hopes to answer. In doing so I will concentrate on two-voice and parallel types of three-voice counterpoint, known as fauxbourdon. This means leaving aside techniques with a contratenor bassus and the four-voice models that De preceptis gives in its sixth chapter, which have already been discussed extensively elsewhere.7 Due to the rather unsystematic nature of the treatise I will not discuss the contrapuntal models in the order in which they appear in the source, but instead in an order that appears most logical to me as a modern reader and pedagogue.8 I have thus opted for a progression from simple to complex two-voice counterpoint, with the three-voice models as a final step. A comparison of the different contrapuntal models of De preceptis with several late fourteenth- and fifteenth-century compositions will provide further insights into singing on the book. On the basis of this analysis and comparison I will propose a model for teaching improvised counterpoint. This pedagogic model is naturally based on my own experiences of singing and teaching counterpoint, as well as on a critical reading of the historical sources. Such an approach has its limitations; firstly, modern students do not share the learning process and capabilities of their medieval counterparts. They cannot, for example, be expected to memorize Monachus’s ‘palmae contrapunctorum’, a listing of all possible consonances within the gamut which, as Anna Maria Busse Berger has shown, was common practice at the time.9 Secondly, I am primarily using one theoretical source, which does not contain information about certain types of polyphony we know were commonly improvised in the fifteenth century, such as canons. A more general view of fifteenth century sung-counterpoint practices and pedagogy can be gained from other publications.10 I have found, however, that the models of two- and three-voice 6 7 8 9 10 Music and Musicians, ed. Stanley Sadie and John Tyrell (London, 22001). For a modern version, see Eulmee Park, ‘De preceptis artis musicae of Guillelmus Monachus: A New Edition, Translation, and Commentary’ (Ph.D. diss., Ohio State University, 1993), available online at <http://rave.ohiolink.edu/etdc/view?acc_num=osu1220457317>. This dissertation, the most recent and accessible edition of the treatise, will be used for references, including indicating the pages of the corresponding translation. Musical examples taken from De preceptis have been transcribed from a microfilm reproduction of the source, retaining the original note-values and proposing corrections where necessary. Other musical examples have been transcribed from facsimile editions or online photographic reproductions, retaining the original note-values unless otherwise indicated. Klaus-Jürgen Sachs, ‘Arten improvisierter Mehrstemmigkeit nach Lehrtexten des 14. bis 16. Jahrhunderts’, in Basler Jahrbuch für historische Musikpraxis 7 (1983), 166-83; Markus Jans ‘Alle gegen Eine. Satzmodelle in Note-gegen-Note Sätzen des 16. und 17. Jahrhunderts’, in Basler Jahrbuch für historische Musikpraxis 10 (1987), 101-20; Ross W. Duffin, ‘Contrapunctus simplex et diminutus: Polyphonic Improvisation for Voices in the Fifteenth Century’, in Basler Jahrbuch für historische Musikpraxis 31 (2007), 69-90; Barnabé Janin, Chanter sur le livre. Manuel pratique d’improvisation de la Renaissance (15me et 16me siècles) (Langres, 2012). See for instance Jans ‘Alle gegen Eine’, 104-5 and Duffin ‘Contrapunctus simplex et diminutus’, 80-81. Andrew Hughes has proposed that De preceptis might be a compilation, taking passages of earlier, now unknown, texts, because of the unsystematic, haphazard structure of the treatise. Counterpoint, for instance, is discussed in chapters IV and VI of the treatise, and briefly returned to in chapter VIII. The different types of counterpoint are not discussed in any apparent order and a lot of information from chapter IV is repeated in chapter VI. See Hughes, ‘Guillelmus Monachus’. Busse Berger clearly demonstrates that the practice of rote-learning consonances and consonance progressions played an important role in the medieval musicians’ training. See Anna Maria Busse Berger, Medieval Music and the Art of Memory (Berkeley etc., 2005), 111-58. Recommended are: Sarah Fuller, ‘Organum - discantus - contrapunctus in the Middle Ages’ and Peter Schubert ‘Counterpoint Pedagogy in the Renaissance’, in The Cambridge Companion to Western Music Theory, ed. Thomas 222 jaf_6_2.indd 222 NIELS BERENTSEN 6/10/14 13:36 counterpoint discussed in this article form an excellent practical introduction to singing on the book. Existing modern scholarship on De preceptis extensively treats its three- and fourvoice models, but little attention has been given to the useful insights the treatise can provide into two-voice counterpoint. In my discussion of Monachus’s parallel threevoice techniques, I will point to some hitherto unobserved relationships with composed polyphony and offer some suggestions as to how these can inform us about improvisation. Although this essay is written primarily with a practical aim, I hope that my analysis of Monachus’s text and examples, and the comparison with written music, may also be of interest to historical musicologists working on this repertoire. One obstacle in interpreting the teachings on counterpoint in De preceptis is that the treatise does not clearly distinguish between composed and extemporized music. There is no apparent reason, for instance, why the examples at the end of chapter VI are meant to illustrate a ‘way to compose’ (‘modus componendi’), while the gymel and fauxbourdon illustrated earlier in the chapter are referred to as ‘sung’.11 This incongruity can be explained by the fact that the fifteenth-century mindset attached no particular value to the ‘improvised’ character of singing on the book; most records and treatises refer to it simply as ‘contrapunctus’, a term that could be used for written polyphony as well.12 Margaret Bent has argued against equating singing on the book with ‘improvisation’ because this implies too much of a random and unpremeditated process. She offered the suggestion that singers may have memorized pieces put together in rehearsal, meaning that their singing on the book was as ‘fixed’ as a performance read from notation.13 While I agree with Bent that the term ‘improvisation’ is not fifteenth-century vocabulary, I do not see the advantage of abandoning it. Practising musicians understand that improvisation is not the completely spontaneous or unprepared process which the definitions cited by Bent make it out to be.14 Most types of musical performance we call improvised—for example, certain types of jazz or traditional music— use pre-learned musical material, involve coordination between the performers both beforehand and during the performance, and require years of musical training and practice.15 The most helpful way to envisage the relationship between composition (‘resfacta’) and singing on the book is as points on a continuum. On the one end we have ‘fixed’ performances, be they read from notation or memorized; on the other, we have more impromptu forms, where the musician has to actively engage their mental and vocal 11 12 13 14 15 Christensen (Cambridge, 2002), 477-502 and 503-33; and Peter Schubert, ‘Musical Commonplaces in the Renaissance’, in Music Education in the Middle Ages and the Renaissance, ed. Russell E. Murray, Susan Forscher Weiss, and Cynthia J. Cyrus (Bloomington, 2010), 161-92. De preceptis, ch. VI § 64-71 (Park, ‘De preceptis’, 71-73 [trans. 192-207]) and ch. VI § 27 (Park, ‘De preceptis’, 61 [trans. 176]). Chapter and paragraph numbering here and later according to Park’s edition. For the indifference of church records as to how polyphony was produced see Rob C. Wegman, ‘From Maker to Composer: Improvisation and Musical Authorship in the Low Countries: 1450-1500’, in Journal of the American Musicological Society 49 (1996), 409-79, esp. 413 n. 6. Margaret Bent, ‘Resfacta and Cantare Super Librum’, in Journal of the American Musicological Society 36 (1983), 371-91, esp. 378. Bent ‘Resfacta and Cantare Super Librum’, 374. I would argue that the dictionary definitions cited by Bent ultimately echo the mystification of the improvising ‘virtuoso’, a process that began in the nineteenth century, and do not correspond to the reality of non-written music-making. Bent slightly nuanced her position on this issue in Counterpoint, Composition and Musica Ficta (New York-London, 2002), 49. F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 223 223 6/10/14 13:36 skills to produce an immediate result. A musician would draw on virtually the same aural, vocal, and mental abilities in all of these forms. When reading a part from a choirbook one needs to control the counterpoint aurally, precisely as in singing on the book, in order to apply musica ficta or to correct mistakes.16 When singing on the book, memorized ornaments or passages—which may be taken from compositions or treatises—can be used. Moreover fifteenth-century composers worked their pieces out ‘in the mind’, without the aid of a vertically aligned score, relying instead upon their memory and knowledge of counterpoint.17 In this light, the ‘undifferentiated’ fifteenthcentury approach towards composition and improvisation becomes less of a problem and more of an opportunity; information on non-written musical practices may well be drawn from written music and composition rules because they arose from the same training and skill-set. For this reason, every description and example in De preceptis will be examined in order to glean what may be inferred regarding improvised counterpoint, without a priori assuming it, or the whole of it, to be an illustration of ex tempore singing. A second obstacle to a proper assessment of Monachus’s contrapuntal techniques is the somewhat surprising fact that no completely satisfactory edition or translation has been published of this important text. Albert Seay’s 1965 edition of the treatise is limited to a diplomatic transcription and does not offer score-transcriptions of the examples. Seay also does not consider how the examples should be placed in the text, a matter which is particularly important because of their haphazard layout in the source.18 Eulmee Park’s edition of 1993 is more useful in this respect, but has some problems of its own; firstly it is regrettable that Park’s transcriptions of the examples fail to indicate that the ‘cantus firmus’ part is not to be sung together with the other voices. In fact, this part appears to serve the purpose of illustrating how a florid superius can be derived from a chant in long notes. The musical examples in the single source of De preceptis contain some remarkable errors, for which a correction should be offered in a critical edition.19 Finally, some passages in Park’s translation seem to be at odds with the teaching of the treatise: for instance references to the visualization technique of ‘sighting’ are confused with doubling in parallel octaves.20 I will be pointing out a few of these problems in my discussion of Monachus’s contrapuntal models, but a comprehensive revision of Park’s work lies outside of the scope of this article. 1. Two-Voice Counterpoint In the first part of this essay I will present an itinerary for acquiring the skill of extemporizing two-voice counterpoint, based on De preceptis artis musicae, and a 16 17 18 19 20 Bent, ‘Resfacta and Cantare Super Librum’, 377. Bent, ‘Resfacta and Cantare Super Librum’, 376. Guillelmus Monachus, De Preceptis Artis Musicae, ed. Albert Seay, Corpus Scriptorum de Musica 11 (s.l., 1965). See also Park, ‘De preceptis’, 5-6, on the problems of this edition. See for instance the musical example on fol. 34r-v (Park, ‘De preceptis’, 72-73, Ex. 61 [transcr. 192-93]), where the scribe seems to have notated the contratenor a third too high, from b. 10 of the transcription. See Example 15 below. See my remarks below on Park’s translation of ‘reiterando ad octavam bassam’ in ch. IV § 6 of De preceptis. Another example of confusion is her translation of the chapter heading ‘Regula ad componendum cum tribus vocibus non mutatis’ (ch. IV § 7) as ‘Rule for composing with three independent voices’ (italics mine). This makes sense in relation neither to the text, nor the example given within the chapter, on fol. 19v, which shows a largely parallel and homophonic technique (Park, ‘De preceptis’, 44-45 [trans. 160-161]). 224 jaf_6_2.indd 224 NIELS BERENTSEN 6/10/14 13:36 comparison of its teaching with compositions and other theoretical sources. Starting from singing in parallels, more free types of extemporization can be learned through alternating between parallel intervals and the use of simple contrary motion. In this way, two-voice counterpoint can be taught using elementary techniques or ‘recipes’ which invite students to improvise, rather than giving them a strict set of rules and prohibitions. 1.1 Simple Gymel and ‘Sighting’ In his treatise, Guillelmus Monachus first refers to two-voice counterpoint in chapter IV, entitled ‘Ad habendum veram et perfectam cognitionem modi Anglicorum’ (‘To have a true and correct understanding of the ways [to sing counterpoint] of the English’).21 After discussing three-voice fauxbourdon, Monachus introduces another way of singing, in two voices, which is called gymel.22 The consonances used in this technique are the lower and higher third and the unison, which can be ‘repeated at the lower octave’ (‘reiterando ad octavam bassam’) as the octave, sixth, and tenth.23 The example Monachus gives for this technique shows the improvised voice in dots, as opposed to the white mensural notation of the ‘cantus prius factus’ (see Example 1).24 Example 1. Gymel (De preceptis, fol. 20r)
    
                     
  Eulmee Park confusingly translates ‘reiterando ad octavam bassam’ as ‘doubling at the lower octave’, implying that gymel could be performed in three or four voices singing in parallel octaves.25 My interpretation would be that, instead of digressing into three-voice music, Guillelmus is referring to a kind of visualization technique related to the English ‘sighting’ procedure. This system entailed the imaginary transposition of the plainchant an octave up in the ‘treble sight’, a twelfth up the ‘quadruple sight’ and a fifth down in the case of the ‘countir sight’.26 In this way contrapuntal intervals could be visualized conveniently within the range of a four- or five-line staff. Of these imaginary transpositions Monachus only retains the ‘treble sight’: a visualized third below ‘in sight’ will produce a sixth above the cantus firmus, whereas visualized upper thirds will 21 22 23 24 25 26 Park, ‘De preceptis’, 43-44 (trans. 159-61). The name for this technique was clearly derived from the word gemellus, the Latin for ‘twin’. This is corroborated by a sixteenth-century English-French vocabulary giving the translation ‘iumeau’ for ‘Gymmell song’; see Ernest H. Sanders, ‘Gymel’ in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie and John Tyrell (London, 22001). Monachus corrects his omission of the tenth as an interval for gymel in ch. VI § 43 (Park, ‘De preceptis’, 64 [transcr. 180]). See also Park, ‘ De preceptis ‘, 44, Ex. 46 (transcr. 160). De preceptis ch. IV § 6. (Park, ‘De preceptis’, 44 [trans. 160]). This idea is also advanced by Markus Jans, who ascribes to Monachus several three-voice techniques involving parallel octaves, presumably based on this passage. See Jans ‘Alle gegen Eine’, 106, Ex. 7-8. A more plausible sense of reiteratio or reduplicatio, as the repetition of consonances over the octave may be found, for instance, in Pseudo-Johannes de Muris, Ars Contrapuncti. See <http://www.chmtl.indiana.edu/tml/14th/MURARSC_TEXT.html> (accessed 14 July 2014). Fuller, ‘Organum – discantus – contrapunctus’, 496-97. Brian Trowell, ‘Sight, sighting’ in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie and John Tyrell (London, 22001). F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 225 225 6/10/14 13:36 produce tenths above.27 In several of his examples, Guillelmus shows a way to visualise counterpoint when the superius is paraphrasing a chant at the higher octave (‘at treble sight’). The lower voice visualizes upper or lower thirds with the written chant, which could be called a ‘phantom tenor’, producing sixths or tenths below the superius.28 Besides gymel, this visualization technique is very useful for singing the kinds of three-voice fauxbourdon which will be examined later in this essay. I have found Monachus’s version of the ‘sights’ to be very easy to use in the classroom. Asking a student to sing her counterpoint or the chant ‘in her own octave’ suffices to let her use the ‘treble sight’. Practice of parallel organum in fourths, fifths, and octaves will quickly introduce students to the idea of reading a chant on different pitches as well. I have found that this visualization technique works best on cantus firmus melodies in original clefs, as these tend to fit neatly within the musical staff without using ledger lines, making it easy to visualize thirds above and below every chant note. After considering these issues, the description and example of gymel in De preceptis paint quite a straightforward picture: 1. The improvised gymel begins in unison with the cantus firmus. 2. Then it follows it in thirds below or above. 3. At the cadences the gymel returns to the unison.29 4. These intervals can be ‘reiterated at the lower octave’ as sixths, tenths, and octaves when the cantus firmus is paraphrased in the upper voice, or above the cantus firmus if it is sung on the written pitch. Looking at the English repertoire before c. 1470 we can find a few compositions employing this kind of counterpoint. The clearest example is Virgo salvavit hominem, dating from the end of the fourteenth century, which departs from its parallel sixth only for cadences and the occasional ornament (see Example 2).30 Example 2. Virgo salvavit hominem, excerpt (London, British Library, Ms. Sloane 1210, fol. 139v-140r)


       



  
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   See also Fuller, ‘Organum – discantus – contrapunctus’, 498. See the present article, Examples 3 and 11. If the cantus firmus presents an upward soprano-clausula, the gymel must sing a few (sighted) thirds above and make a downward tenor-clausula, as the last three notes of Ex. 1 illustrate. Another option is to arrive at the final note of the chant and add a cadence with a tenor-clausula in the gymel and a soprano-clausula in the cantus firmus. Manuscript breves are transcribed as crotchets, and semibreves as quavers or semiquavers; see Frank Ll. Harrison, Ernest H. Sanders, and Peter M. Lefferts (eds.), English Music for Mass and and Offices (II), Polyphonic Music of the Fourteenth Century 17 (Monaco, 1986), No. 30. 226 jaf_6_2.indd 226
 
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 NIELS BERENTSEN 6/10/14 13:36 1.2 Mixed Gymel Monachus continues his discussion of the ‘contrapunctus Anglicorum’ in chapter VI. Some of the ‘exempla notata’ at the end of this chapter can shed further light on the practice of gymel. The first of these examples is a straight-up gymel at the lower sixth, in which the superius is derived from the cantus firmus.31 The two following examples also show twovoice gymels, but now alternating between sixths, tenths, and thirds (see Example 3).32 Example 3. ‘Mixed gymel’ (De preceptis, fol. 30r-v)
   


        
            
        
        
       
                  
 
   
                      This horizontal combination of different gymels—analogous to the vertical combination of them in fauxbourdon—I have dubbed ‘mixed gymel’, and this is actually the technique we encounter most in Monachus’s examples, as well as in written music. Presumably there would have been little use for the simple gymel illustrated by Monachus in chapter IV to be written down, since every choirboy could produce it ex tempore. The pedagogic benefit of mixed gymel is that it offers students a somewhat restricted choice, preparing them for more advanced types of two-voice counterpoint. 1.3 Discantus The next step is to learn to improvise a counterpoint mainly in contrary motion. This may sound intimidating to beginners, but is in fact not much harder than singing gymel, 31 32 Park, ‘De preceptis’, 66, Ex. 56-1 (transcr. 182). See my remarks above on this ‘phantom tenor’. See also Park, ‘De preceptis’, 67, Ex. 56-2 (transcr. 184). F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 227 227 6/10/14 13:36 if the right rules of thumb are provided. In chapter VI of his treatise, Monachus cites a principle of counterpoint by ‘neighbouring consonances’, which is found in other fourteenth-century treatises. According to this principle, a cantus firmus that ascends and descends by step is complemented by an expanding and contracting succession of intervals: in contrary motion, unison is followed by third, third by fifth, and sixth by octave. In addition, fifth can be followed by sixth in oblique motion. Example 4. Counterpoint by neighbouring consonances




               

                            
After mastering the principle of counterpoint by neighbouring consonances, and learning to alternate between consonances above and below a repeated tenor-note (oblique motion), students can learn to extemporize a simple discantus piece. As examples, ‘archaic’ note-against-note settings may be used, which can be found in sources up to the end of the fifteenth century (see Example 5).33 Example 5. Dies est leticie, excerpt (Brussels, Koninklijke Bibliotheek, Ms. II 270, fol. 137v)

                    



 
  
     




      
    

 

  
         

   

             
                    

      

   The teaching of discantus, although almost absent from De preceptis is, in my opinion, vital to understanding fifteenth-century music. In other words, while it is clear that singing long chains of parallel imperfect consonances was acceptable, a style of singing—and certainly of writing—that included contrary motion would have been considered more artful. Finally, this procedure of singing by neighbouring consonances permits improvising in the style of some early fifteenth- and fourteenth-century genres, such as two-voice conductus or cantus planus binatim, that, although they are rather simple, are now not generally considered in courses on improvised counterpoint.34 33 34 Puncta transcribed as semibreves, and double puncta as breves. See Bruno Bouckaert et al. (eds.), Brussel, Koninklijke Bibliotheek MS II 270. Collection of Middle Dutch and Latin Sacred Songs, Monumenta Flandriae Musica 7 (LeuvenNeerpelt, 2005), No. 19. On cantus planus binatim (‘doubled plainchant’) see F. Alberto Gallo, ‘“Cantus Planus Binatim”: Polifonia Primitiva in Fonti Tardive: Firenze, BN, II XI 18; Washington, LC, ML 171 J 6; Firenze, BN, Pai. 472’, in Quadrivium 7 (1966), 79-89. 228 jaf_6_2.indd 228 NIELS BERENTSEN 6/10/14 13:36 1.4 Syncopation and Species-Counterpoint In chapter VIII (‘Regula circa cognitionem syncoparum’) Monachus provides two more important pieces of information for the pedagogy of singing on the book.35 The first is, as the title of the chapter suggests, the rule of syncopation: when the cantus firmus ascends stepwise we can make syncopations with a sixth changing into a fifth on the next note of the tenor, and when it descends, with a sixth changing into a seventh. He explains, as is also shown in the example, that the fifths and sixths—in ascent—can be visualized as fourths and thirds below, the sixths and sevenths—in descent—as seconds and thirds below (see Example 6).36 Example 6. Syncopations (De preceptis, fol. 42v)
      
            
   
         
         
 
     The other example given in this chapter is not accompanied by a description, but has a similar stepwise tenor, and two counterpoints (see Example 7).37 The first one, given together with the tenor in score, is composed entirely in semiminimae, four notes against one (‘third species’); the second, presented as a separate part, uses only minimae (‘second species’).     35 36 37 Example 7. Species counterpoint (De preceptis, fol. 42v)
  
 

      
                
    
                          




                                                           Park, ‘De preceptis’, 95-96 (trans. 218). See also Park, ‘De preceptis’, 95, Ex. 66-1 (transcr. 218). See also Park, ‘De preceptis’, 96, Ex. 66-1 (transcr. 218). F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 229   229 6/10/14 13:36 The ‘third species’ part fills the melodic fourths and thirds of the ‘second species’ mechanically with four semiminimae. Octaves are used on every downbeat when the tenor descends, even if this produces ‘bad counterpoint’ from beat to beat.38 In this respect the example is consistent with the preceding one on syncopation, and also with Antonio da Leno’s Regulae de contrapunto, compiled into the same manuscript as De preceptis but written at least fifty years earlier.39 It remains unclear to me if da Leno’s treatise influenced De preceptis, and why they were eventually bound into the same manuscript. The treatises belong to different traditions of counterpoint pedagogy: the Regulae to the Italian, hexachord-based system of the ‘gradi’, and De preceptis to the English tradition of visualisation (the ‘sights’) and singing in parallel imperfect consonances.40 However, da Leno’s treatise, in its chapter on ‘contraponto de due notte per una’, also clearly encourages the use of octaves or fifths on a few successive downbeats of the tenor.41 It is clear that species counterpoint can play a role in the training of improvised counterpoint today. However, the earliest examples of it show a very different approach from the Fuxian species counterpoint that we tend to be familiar with. I have drawn the following conclusions from Monachus’s and da Leno’s examples for my own pedagogical practice: octaves or fifths on a few successive downbeats are an integral part of the system and may be encouraged; when singing two, three, or four notes against one, every tenor note can receive an octave or fifth as long as it is followed by some other consonance(s). It follows that independent motion between the voices is not obligatory. Finally, the counterpoint does not necessarily have to be a well-balanced or varied melody. This is because these counterpoints would be ‘finished’ at a later stage by embellishing them with standardized melodic formulas, as is illustrated in the later chapters of da Leno’s Regulae.42 The ‘fiortise’, as da Leno calls these ornamental formulas, are used to provide the necessary surface polish to the underlying note-against-note framework.43 Unfortunately, florid improvisation on a cantus firmus takes a rather long time to learn, for which reason I do not presently include it in my own teaching. It is, however, vital not to lose sight of the fact that exercises in species counterpoint are a preparation for singing florid counterpoint. Used as drilling exercises they can provide a secure knowledge of where to go next in singing on the book, but they should not be considered finished counterpoints in and of themselves.44 38 39 40 41 42 43 44 This is generally discouraged or restricted in modern counterpoint methods. See for instance Peter Schubert, Modal Counterpoint Renaissance Style (New York–Oxford, 2008), 47, ‘soft rule’ three. F. Alberto Gallo and Andreas Bücker, ‘Antonius de Leno’ in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie and John Tyrell (London, 22001). See Fuller, ‘Organum - discantus - contrapunctus’, 496. Antonio da Leno, Regulae de contrapunto, ed. Albert Seay (Colorado Springs, 1977), esp. the examples on pp. 15-18. See the examples of ‘fiortise’ in da Leno, Regulae de contrapunto, ed. Seay, 27-39. In her analysis of Petrus dictus Palma Ociosa’s examples, Sarah Fuller notes that such ornaments could be also used to ‘cover up’ underlying parallel perfect consonances; see Fuller, ‘Organum - discantus - contrapunctus’, 494-95. An early voice against this practice of disguising underlying perfect parallels is the Berkeley Treatise. See Oliver B. Ellsworth (ed. and trans.), The Berkeley Manuscript: A New Critical Text and Translation, Greek and Latin Music Theory 2 (Lincoln-London, 1984), 130-31. They may be compared to the ‘skeletons’ of improvised canons, which should be embellished later on, as Peter Schubert demonstrates in the following video, <http://www.youtube.com/watch?v=n01J393WpKk> (accessed 20 May 2014). 230 jaf_6_2.indd 230 NIELS BERENTSEN 6/10/14 13:36 1.5 Towards Free Two-Voice Counterpoint I propose the following itinerary for learning to extemporize fifteenth-century two-voice counterpoint: 1. The student learns to sing a simple gymel in thirds, above and below the cantus firmus. 2. With the help of the system of ‘sights’ the sixth and tenth above and below are introduced. 3. ‘Mixed gymel’: the student learns to alternate between these different types. 4. After some introductory exercises in contrary and oblique motion, the student learns to extemporize a short piece in discantus style, in which the use of parallel imperfect consonances is restricted to one or two at a time. 5. When the gymel and discantus techniques are combined, a florid upper voice can be extemporized on top of a metric tenor (including syncopation, ornamentation, etc.). For this final stage two-voice fifteenth-century pieces in homophonic style, such as English carols, Italian laude, or French chansons, can be used as models. In the piece quoted in Example 8, a setting of the New Year song Verbum caro factum est, the voices move from an octave to a third, using the principle of neighbouring consonances in the first bar.45 This is then followed by two bars of gymel in thirds and sixths, leading to a cadence on F. After some oblique motion in bb. 4-6, we have two bars in sixth gymel leading to a cadence on D. The tenor remains stationary in bb. 9-10, causing the upper voice to use oblique motion, followed by a gymel in thirds in bb. 11-12. When the initial cantus firmus melody comes back in b. 19, the composer has opted for a passage in tenths and sixths with an additional ornament on the word ‘parvulo’. It is not difficult to imagine how such a setting could have been obtained by extemporizing a top-part to a tenor. In fact, it is a good exercise to first extemporize counterpoint on a tenor, before singing it with its original upper voice, in order to compare the two. Example 8. Verbum caro factum est (Oxford, Bodleian Library, Ms. Canon. Misc. 213, fol. 16v)

   
   
  
                                

       
                 
      
      
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                 For a reproduction of the source see David Fallows (ed.), Oxford Bodleian Library MS. Canon. Misc. 213, Late Medieval and Early Renaissance Music in Facsimile 1 (Chicago-London, 1995). F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 231 231 6/10/14 13:36 2. Parallel Three-Voice Counterpoint Similarly to two-voice counterpoint, where different gymels can be combined successively to create a more diverse setting, two simultaneous gymels can be used to create simple kinds of three-voice polyphony. The author of De preceptis artis musicae describes two different ways to sing fauxbourdon, one with the chant in the tenor and one with the chant paraphrased by the superius. A third option, placing the chant in the middle voice, described as ‘faburden’ in English treatises, is not mentioned by Monachus. Such a faburden extemporization leads to exactly the same result as the procedure described here as the second variety of fauxbourdon: in both these versions, superius as well as contratenor paraphrase the chant, a fourth apart.46 2.1 Fauxbourdon I We encounter Monachus’s first description of fauxbourdon in chapter IV of De preceptis. This fauxbourdon is sung in three voices: superius, tenor, and contratenor.47 The superius is derived from the cantus firmus, exactly like gymel at the upper sixth. It reads lower thirds in ‘treble sight’, with a sighted unison—sounding an octave—as the initial and final notes. The contratenor starts and ends with a fifth above the cantus firmus, singing thirds in between. Essentially, we are dealing with a combination of a sixth-gymel in the superius and a third-gymel in the contratenor. This procedure is illustrated by an example that shows the contratenor and the visualized pitches of the superius in dots, along with the sounding pitches of the superius on a separate staff (see Example 9).48 Example 9. Fauxbourdon I (De preceptis, fol. 18v)


             

        
   
   

              
   
     

 

   





   

  



         The treatise provides only one example of this type of counterpoint (given above), and I do not know of any fourteenth- or fifteenth-century composition in which this model is used.49 Perhaps this technique, like simple gymel, was practised ex tempore but not considered refined enough for use in composition. 46 47 48 49 On this topic see Günther Schmidt, ‘Zur Frage des Cantus firmus im 14. und beginnenden 15. Jahrhundert’, in Archiv für Musikwissenschaft 15 (1958), 230-50. Park, ‘De preceptis’, 43-44 (trans. 159). The original—slightly unusual—name for the upper part in De preceptis is ‘suprano’. See also Park, ‘De preceptis’, 43, Ex. 45 (transcr. 159). Similarities, however, exist with the example of fauxbourdon given by Tinctoris, which uses the sequence Lauda sion as its tenor; see Tinctoris, Liber de Arte Contrapuncti, ed. Seay, 29. 232 jaf_6_2.indd 232 NIELS BERENTSEN 6/10/14 13:36 The value of this technique for teaching improvised counterpoint today lies in the fact that it can provide a smooth passage from simple two-voice singing into three-voice singing, and later to four-voice counterpoint with the tenor singing the cantus firmus. At any rate, the lack of composed examples makes it hard to go beyond the strict noteagainst-note style illustrated by the example. This is the reason I tend to focus more on the second kind of fauxbourdon described by Monachus in teaching. 2.2 Fauxbourdon II The second type of fauxbourdon, described by Monachus in chapter VI, is similar to what we see in compositions by, for instance, Dufay and Binchois. The cantus firmus is read an octave up in the superius. The tenor follows the cantus firmus in thirds above, with unisons at the beginning and at the cadences (sixths and octaves with the superius.) The contratenor ‘does as the superius’ (‘vere dicitur sicut supranus’), singing the cantus firmus a fifth up, which will result in thirds and fifths above the tenor (fourths below the superius).50 As we can see, this improvisation technique relies wholly upon visualizing intervals on a ‘ghost tenor’, a chant which is not sung at its actual pitch. This practice may explain a remarkable phenomenon we find in one of the fauxbourdon Magnificats in the manuscript Trent, Museo Provinciale d’Arte, Ms. 1374 (olim 87), where the scribe appears to have notated the superius below the tenor, on the pitch where a plainchant would typically be written (see Example 10).51 Example 10. Magnificat primi toni, excerpt (Trento, Museo Provinciale d’Arte Ms. 1374 [olim 87], fol. 110v)


           
                                      

           
    





  
                              Leaving aside the basically identical contrapuntal procedure, there are a number of differences between compositions using fauxbourdon and Monachus’s illustration of this technique (see Example 11).52 The cantus firmus in Monachus’s example moves in breves and longas, whereas composed settings seem to prefer a faster succession of chant pitches. As a consequence Monachus’s cantus firmus is broken up into fast figurations by the superius, using standardized melodic formulas reminiscent of the ‘fiortise’ 50 51 52 Park, ‘De preceptis’, ch. VI § 40, 63 (trans. 179). A reproduction of the source can be accessed through <http://www.trentinocultura.net/portal/server. pt?open=514&objID=22652&mode=2> (Accessed 6 June 2014). A similarly notated fauxbourdon was identified by Craig Wright in the second strophe of the sequence Cultor Dei memento in Cambrai, Bibliothèque municipale, Ms. 29, fol. 159. See Craig Wright, ‘Performance Practices at the Cathedral of Cambrai 1475-1550’, in The Musical Quarterly 64 (1978), 295-328, esp. 315-18. See also Park, ‘De preceptis’, 63, Ex. 54 (transcr. 178-79). F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 233 233 6/10/14 13:36 discussed earlier. Most fauxbourdon compositions use a relatively homorhythmic texture, where the upper voice is only slightly more ornate than the tenor. I assume that the contratenor, in improvising, would use the same rhythm as the tenor, rather than to try to follow the figurations of the upper voice. This kind of rhythmic treatment of the lower voices is demonstrated in another example in chapter VI.53 Example 11. Fauxbourdon II, excerpt (De preceptis, fol. 28r-v)                


    

   
 
 
            
                           
 
 

  


             
  
               
             
                Improvising a fauxbourdon using Monachus’s procedure requires a superiussinger with extensive experience of florid counterpoint. Monachus’s own ornamental formulas could be learned from the treatise and applied to this kind of improvisation. However, since the scope of my course does not allow for the teaching of florid counterpoint, this method has had limited practical use for me. I have chosen instead to combine Monachus’s method of visualization with the more homorhythmic texture of the fauxbourdon hymns by Dufay. 2.3 Improvising a Fauxbourdon Hymn Looking at Dufay’s Conditor alme siderum, we can observe that the top part consists almost entirely of alternating breves and semibreves, coinciding with the iambic meter 53 Park, ‘De preceptis’, 68, Ex. 58 (transcr. 187). 234 jaf_6_2.indd 234 NIELS BERENTSEN 6/10/14 13:36 of the text. Directly above Dufay’s setting, in its source, the chant is notated with the same rhythmical pattern in black longas and breves (see Example 12).54 Example 12. Guillaume Dufay, Conditor alme siderum (Modena, Biblioteca Estense, Ms. Alfa X.1.11, fol. 4r; plainchant values halved)


   
                 
          
     
           
        
          




                                                                  
                                                                                                                                                       In the same source we find this pattern again in the plainchant of Vexilla regis on fol. 9v, as well as in Dufay’s setting of Ad cenam agni on fol. 11r. In Ad cenam agni Dufay has used the same rhythmic principle, but this time significantly more decoration has been added to the top-part (see Example 13).55 The longa-brevis (or brevis-semibrevis) pattern can technically be applied to any chant in seven- or eight-syllable Latin poetry, such as hymns, sequences, and devotional songs, be they trochaic or iambic.56 In the case of an iambic metre, such as Ad cenam agni, one has the choice of either singing the first syllable as a perfect breve, or to treat 54 55 56 See Guillaume Dufay, Opera Omnia Tomus V: Compositiones Liturgicae Minores, ed. Heinrich Besseler, Corpus Mensurabilis Musicae 1 (Rome, 1966), No. 11. See Dufay, Opera Omnia V, ed. Besseler, No. 17. Tinctoris explains a slightly similar procedure for rhythmicizing plainchants in book 2, ch. 21 of his Liber de arte contrapuncti. Tinctoris applies a short rhythmic cell to the melody of an Alleluia, on top of which a florid counterpoint is sung. See Tinctoris, Liber de Arte Contrapuncti, ed. Seay, 108-9. On the interaction between the performance prac- F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 235 235 6/10/14 13:36 it like an upbeat, as in Dufay’s fauxbourdon. In the case of a trochaic chant, such as this trope of the sequence Veni sancte spiritus, the procedure is entirely straightforward, as one can start directly on the beat (see Example 14).57 Example 13. Guillaume Dufay, Ad cenam agni (Modena, Biblioteca Estense, Ms. α X.1.11, fol. 11r)
     
  

  
              


                                                                            
                                                                                
     
  
      
          
      

     
                
            

        tice of chant and composed polyphony see Richard Sherr, ‘The Performance of Chant in the Renaissance and its Interactions with Polyphony’, in Plainsong in the Age of Polyphony, ed. Thomas Kelly (Cambridge, 1992), 178-208. A reproduction of this item on fol. 205v-206r of the fifteenth-century chant-book Provins, Bibliothèque Municipale, Ms. 11 can be accessed through <http://bvmm.irht.cnrs.fr/> (Accessed 9 June 2014). 236 jaf_6_2.indd 236       57        
                             
           
   
   NIELS BERENTSEN 6/10/14 13:36 Example 14. Ave virgo virginum, excerpt (Provins, Bibliothèque Municipale, Ms. 011, fol. 205v-206r)


 


      
          

  
           
   
   



      
    
      
  
   



   The numerous traces of this procedure found in sources both of chant and polyphony seem to indicate that it was quite a common way to perform metric chants and devotional songs.58 More relevantly, the procedure may help us to reconsider the relation of the Dufay hymns to improvisation: if such chants possessed a rhythm known to singers—even if it was not notated—no prior communication would have been necessary for them to attain an improvisation in the flowing triple meter that is so typical of Dufay’s rendition of them. I have found that singing fauxbourdon with this kind of lightly undulating rhythm leads to a more refined result, closer to the written settings, than singing in ‘square’ equal notes. Such a rhythm also helps tremendously for singing together, because the tactus is immediately clear to all the singers. For the superius, it facilitates the use of ornaments, which can be easily adapted from Dufay’s hymns. An effective way to put this idea into practice during the counterpoint lesson is to let the students ‘improvise towards’ a composition: let students first sing a simple fauxbourdon on a hymn using this rhythm, then gradually introduce syncopations, ornamentation, etc. in such a way that the result will become close, or equivalent, to a written setting based on the same chant. 2.4 Other Parallel Three-Voice Models Besides the two types of fauxbourdon, Monachus informs us about another parallel type of counterpoint in three voices in chapter VI. This is a rather curious technique in which the upper voices simultaneously sing sixths and tenths above the tenor, creating parallel fifths between them. Monachus provides a few rules of thumb and an example for producing this kind of polyphony, which he calls ‘easy and useful’ (‘levis et utilis’; see Example 15).59 58 59 Marco Gozzi (ed.), Cantus fractus italiano: un’antologia, Musica Mensurabilis 4 (Hildesheim etc., 2012) contains many chants and simple polyphonic pieces with this rhythm. We have already encountered it in Example 8 of the present article as well. See also Park, ‘De preceptis’, Ex. 61, 72-73 (transcr. 192-93). Transcribing the example illustrating this technique poses a number of problems. First, the contratenor part is probably written a third too low from bar 10 onwards. I have corrected the parallel octaves with the tenor to sixths. Note that in Park’s transcription the syncopation in the contratenor part in bb. 2-3 is overlooked, as well as the ‘G-fa’ sign in the superius, indicating an F-sharp in b. 8 (apparently the scribe did not have a preference for musica recta in correcting diminished fifths). Second, the example does not seem to fit the tempus perfectum prolatio minor indicated in the contratenor part (see, for instance, the long, oddly placed rest in bb. 8-9). No easy solution can be found for this problem. A transcription in tempus imperfectum would show similar problems, and the final note would arrive on a weak beat. F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 237 237 6/10/14 13:36 Example 15. Sixth-tenth model. (De preceptis, 34r-34v)


        
                        
            


   
 
         
    
    

    
                                                                                                                                  
                                  However strange the parallel fifths in this example may seem to us, they are not actually at odds with fifteenth-century contrapuntal theory: counterpoint was theoretically still considered a dyadic process, in which every voice was related to the tenor only, and in this sense combined sixths and tenths are as ‘correct’ as combined thirds and sixths above a tenor such as in fauxbourdon. In fact, as Markus Jans has argued, this technique can be seen as a kind of ‘upside down fauxbourdon’, in which contratenor and superius have exchanged places.60 Nevertheless, it should be noted that this type of counterpoint would have been quite old-fashioned by the 1470s. Parallel fifths can be seen throughout the fifteenth century in cadences, but we have to go back to the fourteenth century to find pieces using them as regularly as Monachus’s example. Some late fourteenth-century English pieces show traces of this technique, such as the first bar of the Gloria trope Spiritus almefice shown in Example 16.61 60 61 Jans, ‘Alle gegen Eine’, 106, Ex. 8. See also Ernest H. Sanders, Frank Ll. Harrison, and Peter M. Lefferts (eds.), English Music for Mass and Offices I, Polyphonic Music of the Fourteenth Century 16 (Monaco, 1983), No. 31. 238 jaf_6_2.indd 238 NIELS BERENTSEN 6/10/14 13:36 Example 16. Spiritus almefice, excerpt (Brussels, Koninklijke Bibliotheek, Ms. II 266, fol. 1r)
 
 


                                              
     








 


 Markus Jans has also identified a model combining parallel sixths and tenths below an upper voice, so that parallel fifths occur between the middle and lower voices. This type of parallel fifth, which occurs frequently in the English conductus repertoire, can be observed in the Kyrie shown in Example 17.62 Example 17. Kyrie, excerpt (Durham, Cathedral Library, Ms. A.III.1, fol. 1r)
 


 
        

           
                    

    
                                              Furthermore, Jans has proposed a model in which gymels at the lower third and tenth produce parallel octaves. Whilst the system of different combinations of gymels put forward by Jans has the virtues of simplicity and elegance, it fails to take into account that in fourteenth- and fifteenth-century counterpoint the tenor is always the ‘voice of reference’ (‘Bezugsstimme’), even if it does not carry the chant. In other words, the 62 Values halved; see also Sanders et al. (eds.), English Music for Mass and Offices I, No. 1. F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 239 239 6/10/14 13:36 parallel fifths in Example 17 are real parallels, and should be interpreted as a kind of parallel organum.63 A theoretical source geographically and chronologically closer to the English fourteenth century conductus, the treatise Quator principalia musicae, provides clues to understanding this type of polyphony. The treatise talks about an ‘art in which several men appear to be singing discant, whilst in reality only one of them does’ (‘ars in qua plures homines discantare apparent, cum in rei veritate unuis tantum discantabit’).64 This technique entails the singing of a kind of organum in fifths and octaves by four or five singers, to which an expert in discant adds a voice using mainly imperfect consonances. All singers are encouraged to adorn their parts with ‘flores harmonici’. According to the author of the Quator principalia, such music can ‘strike the ear as artful, while actually being very easy’ (‘artificiosus auditui apparet, cum tamen valde levis est’). It is possible that this extemporization technique found its way into the written repertoire, as did fauxbourdon. Reduced to a three-voice setting, the common medium of composition at the time, it would take the shape of a middle voice singing a fifth above the tenor (‘fifthing’) and the upper voice singing a gymel at the tenth above, exactly as we see in Example 17. I would argue that in some English conductus we are dealing with a hybrid between parallel organum and gymel. Neither of these techniques belong to the learned tradition of discantus, but to the realm of a casual, extemporized polyphonic practice, that we can occasionally catch a glimpse of through written settings and theoretical sources. For a course like my ‘Polyphony Workshop’ at the Royal Conservatoire of The Hague, where not only Renaissance but also medieval music is practised, this organumgymel hybrid offers several didactic opportunities: The students may observe that gymel and contrary motion did not just replace the practice of parallel organum, but existed side-by-side with it for some time, sometimes even occurring in the same piece. It can also demonstrate that the rules of theorists do not always apply to the entirety of a musical repertoire, especially in genres where composition touches upon oral tradition.65 4. Conclusion De preceptis artis musicae informs us that the learning of counterpoint can start from singing simple parallel imperfect consonances, called gymel. As already pointed out by Klaus-Jürgen Sachs and others, these gymels can be combined into different types of simple three-voice counterpoint called fauxbourdon. The possibility of combining gymels in a horizontal way, alternating between them to create a more diverse two-voice counterpoint, has hitherto been overlooked. Another important element the treatise can 63 64 65 On the survival of parallel organum into the later Middle Ages and Renaissance see Sarah Fuller, ‘Discant and the Theory of Fifthing’, in Acta Musicologica 50 (1978), 214-75. Luminata F. Aluas, ‘The Quatuor principalia musicae: A Critical Edition and Translation, with Introduction and Commentary’ (Ph.D. diss., Indiana University, 1996), 519-20 (trans. 746-47). For a discussion of this ‘art’ see Fuller, ‘Organum - discantus - contrapunctus’, 494-95. This technique, for instance, clearly defies the interdiction of parallel perfect consonances, as well as the restrictions placed on parallel imperfect consonances, by continental as well as English discant treatises (including the Quatuor principalia itself). See Sylvia Kenney, ‘English Discant and Discant in England’, in The Musical Quarterly 45 (1959), 26-48. 240 jaf_6_2.indd 240 NIELS BERENTSEN 6/10/14 13:36 shed light on is the technique of ‘sighting’. By imagining a fifth or an octave as a unison with the cantus firmus, it becomes easy to visualize counterpoint on the musical staff. With the use of these elements students can quickly learn to extemporize a simple counterpoint on a given melody. Comparing Monachus’s teaching with the repertoire of the same period and earlier leads to the following three observations. Firstly, strictly parallel settings in two voices are rare; this points to the importance of contrary motion, presumably in improvisation as well as in composition. Therefore, I propose to add to Monachus’s technique of ‘mixed gymel’ the element of singing by neighbouring consonances that we find in fourteenth- and fifteenth-century discant-treatises. Secondly, Monachus’s way of organizing the rhythm of a fauxbourdon does not conform to what we find in most fauxbourdon compositions. I propose an alternative based on two hymns of Dufay, where the poetic metre dictates the rhythm of the setting. Finally Monachus’s technique of combined sixths and tenths may be contextualized by a fourteenth-century technique in which gymel is combined with parallel organum (‘fifthing’). In closing, I would like to stress that ‘cantare super librum’, as an oral tradition, can never be reconstructed or revived on the basis of historical, written sources alone. Much of the practical knowledge regarding contrapuntal extemporization was handed down from master to pupil, and every nuance of this process could not have been adequately expressed in a treatise. This practical knowledge needs to be supplied by our own know-how, learned from practising and experimenting with these techniques. Exchanging ideas with fellow practitioners and teachers of sung counterpoint has been invaluable to me in this respect. To further promote this exchange I would like to finish this essay with a few observations from my own practice. I find it most productive to let students improvise on plainchants they already know. Because there is less risk of failure, they are able to make more variations, explore different routes, make cadences in different places, etc. Having students sing counterpoint to one verse of a strophic song or chant each, creates a very helpful process of mutual imitation and emulation. The group Le Chant sur le Livre has shown that with experience one can learn to sing counterpoint even on unknown cantus firmi.66 However, I think it is rather unlikely that Renaissance musicians would ever sing counterpoint to hitherto unknown chants, because of their daily and life-long practice of chant. Using an unknown, or newly composed, cantus firmus may show an ‘unbelieving’ audience that the music is in fact created on the spot, but I do not think it is useful in a pedagogic setting. Rehearsing with one’s fellow singers is necessary to attain a satisfactory result in singing on the book, especially when a more complex music, departing from strict procedures, is aimed for. This process often takes the shape of ‘collective composition’, where certain choices are negotiated prior to, as well as during, the singing. In a counterpoint lesson we can put this concept into practice by ‘improvising towards’ a historical composition. The Dufay fauxbourdon hymns in Examples 12 and 13 are very 66 A broadcast on the Swiss radio station RTS offers an accessible discussion of the activities of Le Chant sur le Livre by the ensemble’s founder Jean-Yves Haymoz; see <http://www.rts.ch/espace-2/programmes/musique-enmemoire/4538236-musique-en-memoire-du-11-01-2013.html> (Accessed 19 May 2014). F R O M T R E AT I S E TO C L A S S R O O M jaf_6_2.indd 241 241 6/10/14 13:36 suitable for this, but this exercise can also be done in two voices using the tenor of a two-voice piece. Similarly, the writing of counterpoint exercises can start from using improvisatory models, exploring how they can be adapted, enriched and combined in composition. In this way we can use improvised counterpoint as the basis of our Renaissance music courses, in much the same way it would have been used in the fifteenth century, by, for example, Guillelmus Monachus. It provides instinctive aural and cerebral musical understanding, and, as such, I think it offers the most fruitful way to access the musical style and grammar of historical polyphony. Abstract The importance of an oral and aural understanding of counterpoint in the fifteenth century has been widely recognized by both scholars and performers of early music. In this essay I reflect on the way I have attempted to ‘reconstruct’ an itinerary for teaching the skill of extemporizing simple two- and three-voice types of fifteenth-century counterpoint, based on a close reading of Guillelmus Monachus’s treatise De preceptis artis musicae and a comparative analysis of extant compositions. De preceptis informs us that the learning of counterpoint can start from the singing of simple parallels in imperfect consonances, called gymel. These gymels can be combined into different types of simple three-voice counterpoint (fauxbourdon) or in a horizontal way, alternating between different parallels. To this technique of ‘mixed gymel’ elements of fourteenth- and fifteenth-century discantus teaching, such as singing by neighbouring consonances, may be added to achieve a freer type of counterpoint. 242 jaf_6_2.indd 242 NIELS BERENTSEN 6/10/14 13:36