Tonal Structure in the Music of Machaut

Plainsong and Medieval Music, 14, 1, 59–88 © 2005 Cambridge University Press DOI:10.1017/S0961137104000117 Printed in the United Kingdom Tonal structure and the melodic role of chromatic inflections in the music of Machaut* JENNIFER BAIN ABSTRACT . The interpretation of chromatic content in fourteenth-century music has been widely debated. While most studies have focused on contrapuntal necessity, this study advocates an approach that begins from the perspective of melody. Using the ballades, virelais and rondeaux of Guillaume de Machaut as a central repertory, it proposes that not only are chromatic inflections in Machaut’s monophonic songs derived melodically, but that many chromatic inflections in Machaut’s polyphonic songs also arise from melodic rather than contrapuntal requirements. Because of their implied semitone motion – arguably crucial to tonal organization – they can have an impact on the definition of tonal structure by privileging the individual pitches they decorate, particularly but not exclusively in cadential melodic formulas or progressions. Because the notational system of the music of the ars nova is so far removed from our own, decoding the musical surface is not always a straightforward task. Fourteenth- century theorists do not provide us with absolutely clear textbook instructions about how to interpret the extant manuscript sources, especially in the area of chromatic inflections, and generations of debate have concerned the interpretation of the chro- matic content of fourteenth-century song. Lucy Cross makes the insightful remark that ‘If medieval performers had been faced with the same kinds of problems about ‘‘ficta’’ that we are, we should have a far more lucid legacy from them of answers to our questions than we do.’ 1 Modern scholars and performers, anxious to determine where fourteenth-century performers would have interpolated inflections that are unsigned in the manuscript sources, have focused on contrapuntal require- ments: causa pulchritudinis ( the adjustment of thirds and sixths in order to lie closer to Email: [email protected] *I presented earlier versions of this paper at the Medieval and Renaissance Music Conference at the University of Bristol in July 2002 and at the annual meeting of the Society for Music Theory in Columbus, Ohio in October 2002. Research for this article was supported in part by the Sarah Jane Williams Award from the International Machaut Society, as well as by generous fellowships from the Que ´bec government’s Fonds pour la Formation de Chercheurs et l’Aide a ` la Recherche and the Social Sciences and Humanities Research Council of Canada. I would like to thank Sarah Fuller and my colleagues David Schroeder, Jacqueline Warwick and Steve Baur for their comments, and an anonymous reader for critiquing and engaging so deeply with an earlier version of this essay. 1 Lucy E. Cross, ‘Chromatic Alteration and Extrahexachordal Intervals in Fourteenth-Century Polyphonic Repertories’, Ph.D. diss., Columbia University ( 1990 ), 71.

Transcript of Tonal Structure in the Music of Machaut

Page 1: Tonal Structure in the Music of Machaut

Plainsong and Medieval Music, 14, 1, 59–88 © 2005 Cambridge University PressDOI:10.1017/S0961137104000117 Printed in the United Kingdom

Tonal structure and the melodic roleof chromatic inflections in the music


A B S T R A C T. The interpretation of chromatic content in fourteenth-century music has been widelydebated. While most studies have focused on contrapuntal necessity, this study advocates an approachthat begins from the perspective of melody. Using the ballades, virelais and rondeaux of Guillaume deMachaut as a central repertory, it proposes that not only are chromatic inflections in Machaut’smonophonic songs derived melodically, but that many chromatic inflections in Machaut’s polyphonicsongs also arise from melodic rather than contrapuntal requirements. Because of their implied semitonemotion – arguably crucial to tonal organization – they can have an impact on the definition of tonalstructure by privileging the individual pitches they decorate, particularly but not exclusively incadential melodic formulas or progressions.

Because the notational system of the music of the ars nova is so far removed from ourown, decoding the musical surface is not always a straightforward task. Fourteenth-century theorists do not provide us with absolutely clear textbook instructions abouthow to interpret the extant manuscript sources, especially in the area of chromaticinflections, and generations of debate have concerned the interpretation of the chro-matic content of fourteenth-century song. Lucy Cross makes the insightfulremark that ‘If medieval performers had been faced with the same kinds of problemsabout ‘‘ficta’’ that we are, we should have a far more lucid legacy from them ofanswers to our questions than we do.’1 Modern scholars and performers, anxious todetermine where fourteenth-century performers would have interpolated inflectionsthat are unsigned in the manuscript sources, have focused on contrapuntal require-ments: causa pulchritudinis ( the adjustment of thirds and sixths in order to lie closer to

Email: [email protected]*I presented earlier versions of this paper at the Medieval and Renaissance Music Conference at theUniversity of Bristol in July 2002 and at the annual meeting of the Society for Music Theory in Columbus,Ohio in October 2002. Research for this article was supported in part by the Sarah Jane Williams Awardfrom the International Machaut Society, as well as by generous fellowships from the Quebec government’sFonds pour la Formation de Chercheurs et l’Aide a la Recherche and the Social Sciences and Humanities ResearchCouncil of Canada. I would like to thank Sarah Fuller and my colleagues David Schroeder, JacquelineWarwick and Steve Baur for their comments, and an anonymous reader for critiquing and engaging sodeeply with an earlier version of this essay.1 Lucy E. Cross, ‘Chromatic Alteration and Extrahexachordal Intervals in Fourteenth-Century Polyphonic

Repertories’, Ph.D. diss., Columbia University (1990), 71.

Page 2: Tonal Structure in the Music of Machaut

the fifths and octaves that follow), and causa necessitatis ( the chromatic adjustment tomake fifths and octaves perfect).2 Even Thomas Brothers and Lucy Cross, both ofwhom devote major studies to chromaticism in the fourteenth century, concentratealmost exclusively on the relationship between chromatic inflections and counter-point.3 This issue of contrapuntal requirements is not trivial in the least: our under-standing of notated inflections and biases about the interpolation of inflections cansubstantially alter the performance and analysis of individual works.

Rather than using contrapuntal requirements as a starting point, however, I amadvocating an approach that begins from the perspective of melody. Since chromaticinflections proliferate in both monophonic and polyphonic repertories, their appear-ance cannot be ascribed to contrapuntal usage alone. Although it might be possible toargue that contrapuntal thinking underlies melodic structure in Machaut’s mono-phonic repertory – in the same way that Bach’s solo cello suites project underlyingharmonic progressions – I would suggest that the opposite is true. Not only arechromatic inflections in Machaut’s monophonic repertory derived melodically, butmany chromatic inflections in Machaut’s polyphonic repertory also arise frommelodic rather than contrapuntal requirements. Acknowledging the melodic roleof chromatic inflections may assist in the interpretation of particular contrapuntalpassages. Melodic chromatic inflections, moreover, because of their implied semitonemotion can contribute fundamentally to the projection of tonal structure in a song. Theimportance of semitone motion to the tonal structuring of a given song, however, canonly be judged by its particular musical context.

Melody, signature-systems and tonal structure

One recent theory also stresses a direct relationship (albeit in a rather different way)between melody and the new chromaticism – the conspicuous prevalence ofchromatically altered pitches beyond bX/bZ – of fourteenth-century French music.

2 Lucy Cross, Margaret Bent and Elizabeth Eva Leach, advocate that all thirds and sixths which arefollowed by fifths or octaves respectively should be adjusted chromatically to create semitone motion,whether or not semitone motion appears notationally in one of the voices. Although I agree thatinflections sometimes must be interpolated, I do not support a ‘default’ position in which all uninflectedimperfect sonorities are systematically adjusted. See Bain, ‘Theorizing the Cadence’, for further dis-cussion of my position, which follows that advocated by Klaus-Jürgen Sachs. Lucy Cross, ‘ChromaticAlteration’, see, esp. pp. 99 and 189; Margaret Bent, ‘The Grammar of Early Music: Preconditions forAnalysis’, in Tonal Structures in Early Music, ed. Cristle Collins Judd (New York and London, 1998),15–59; Elizabeth Eva Leach, ‘Guillaume de Machaut’s De toutes flours’, Music Analysis, 19/3 (2000),321–51, esp. 326, and Elizabeth Eva Leach, review of Chromatic Beauty in the Late Medieval Chanson: AnInterpretation of Manuscript Accidentals, by Thomas Brothers (Cambridge, 1997), in Music and Letters, 80/2(1999), 274–81, esp. 279–81; Jennifer Bain, ‘Theorizing the Cadence in the Music of Machaut’, Journal ofMusic Theory 47/2 (forthcoming). Klaus-Jürgen Sachs, Der Contrapunctus im 14. und 15. Jahrhundert:Untersuchungen zum Terminus, zur Lehre und zu den Quellen, Beihefte zum Archiv für Musikwissenschaft13 (Wiesbaden, 1974), esp. 103–10; and Sachs, ‘Die Contrapunctus-Lehre im 14. und 15. Jahrhundert’, inDie mittelalterliche Lehre von der Mehrstimmigkeit, ed. Frieder Zaminer, Geschichte der Musiktheorie 5(Darmstadt, 1984), 161–256, esp. 199–205.

3 Brothers, Chromatic Beauty in the Late Medieval Chanson: An Interpretation of Manuscript Accidentals(Cambridge, 1997), and Cross, ‘Chromatic Alteration’.

60 Jennifer Bain

Page 3: Tonal Structure in the Music of Machaut

With an explicit focus on the cantus line, Peter Lefferts (1995) proposed a theory oftonal types for fourteenth-century music, which was taken up and expanded byYolanda Plumley (1996), the emphasis on melody apparent even in her title: TheGrammar of 14th-century Melody: Tonal Organization and Compositional Process in theChansons of Guillaume de Machaut and the Ars Subtilior.4 As Lefferts describes it,‘the cantus line had conceptual priority over the tenor, so the composer worked ‘fromthe top down’ in making important choices about tonal behaviour.’5 Lefferts andPlumley describe the system as a priori, i.e., a pre-compositional system used bycomposers. Tonal types are identified and labelled in each song by the ‘signature-system’ of the song (XX, X, Z, Y, YY), and since the cantus has ‘conceptual priority’, tonaltypes are also identified by final cantus pitch. For instance, regardless of the final pitchin the tenor, if the cantus of a song ends on c, and an apparent BX signature appears inthe tenor part, Lefferts would label the song c-X, or if a song ends on d in the cantus andthere is no apparent signature in any voice he would label it d-Z.

Although the theory has a certain attraction because it is so systematic and gener-ates a grouping of songs into a quantifiable series of categories, I would suggest that itis fundamentally flawed for several reasons. Lefferts bases his approach on the studiesof Siegfried Hermelink and Harold Powers, both of whom systematized sixteenth-century sacred polyphony principally by cataloguing signatures (notated inflectionsat the beginning of a staff that govern the pitch content for that staff), finals and clefs.6

But unlike late sixteenth-century printed sources, fourteenth-century manuscriptsources do not embrace a standard and consistent approach to signatures, and Leffertsdoes not address this distinction. Although Leo Schrade’s and Willi Apel’s twentieth-century printed editions, on which Lefferts relies, give the illusion of systematic flatsignatures in the music of Machaut, signatures are not a consistent feature in themusic, and can only be assessed by examining the manuscripts directly.7

The distinction between a signature and an ‘accidental’ is placement: a signatureat the beginning of a line (or near the beginning of a line) might appear long beforethe first occurrence of the pitch it modifies, while an accidental will appear eitherimmediately before, or within a few notes of the pitch it modifies. More often than not,however, the situation in the Machaut manuscripts is ambiguous. For instance, in thethree-part Ballade 36, Se pour ce muir qu’Amours ai bien servi, perfect sonorities on BX

( that is, combinations of perfect octaves and fifths above a BX in the lowest voice)figure prominently, occurring frequently at the beginning or end of phrases andconcluding both sections of the song. Every B which appears in the tenor, high or low,has to be sung BX, whether notated or not, to produce perfect octaves with the

4 Peter Lefferts, ‘Signature Systems and Tonal Types in the late Fourteenth Century Chanson’, Plainsongand Medieval Music, 4/2 (1995), 117–47, and Yolanda Plumley, The Grammar of 14th-Century Melody: TonalOrganization and Compositional Process in the Chansons of Guillaume de Machaut and the Ars Subtilior (NewYork and London, 1996).

5 Lefferts, ‘Signature Systems’, 119.6 Siegfried Hermelink, Dispositiones modorum: die Tonarten in der Musik Palestrinas und seiner Zeitgenossen

(Tutzing, 1960); and Harold Powers, ‘Tonal Types and Modal Categories in Renaissance Polyphony’,Journal of American Musicological Society, 34 (1981), 428–70.

7 Lefferts, ‘Signature Systems’, 131, note 24.

Tonal structure and the melodic role of chromatic inflections in Machaut 61

Page 4: Tonal Structure in the Music of Machaut

contratenor or cantus. If signatures were used with any kind of consistency in theMachaut manuscripts, they would and should have been used in this song. Only MSE, however, uses consistent signatures for Ballade 36: all four lines of the cantus havebX signatures, while all three lines of the tenor and both lines of the contratenor havesignatures of bX and EX.8 In contrast, in MS A, only two of five cantus lines use a bX

signature, two of three contratenor lines use a bX signature, and the four lines of thetenor show no sign of consistency whatsoever. Line one of the tenor has no signature,line two has a high bX signature, line three has a low BX signature, and line four has anEX signature.9

Even when several Machaut manuscripts share the same approach to signatures ina given song, the others make it clear that there was no consensus on their usage. Forinstance, in the two-voice Ballades 1 and 14 (S’amours ne fait par sa grace adoucir and Jene cuit pas qu’onques a creature), although a bX signature appears at the beginning ofeach tenor line in MSS C, A and E, it appears much less consistently in MSS F-G and B.For Ballade 1, a possible signature occurs in only one of five tenor lines in MS F-G andin two of three tenor lines in MS B, while for Ballade 14 a possible signature occurs inonly one of four tenor lines in MS F-G and one of two in MS B. Clearly, not all scribesthought about signatures in the same way.

Moreover, when signatures do appear in the manuscripts, they usually are notconsistent between the voices of an individual song, as Ballades 1 and 14 demonstrate:the X signature in MSS C, A and E appears only in the tenor, not in the cantus.10 This

8 Manuscript sigla follow the conventional designations for the Machaut manuscripts: MS A (BNF,fonds français 1584); MS B (BNF, fonds français 1585); MS C (BMF, fonds français 1586); MS E (BNF,fonds français 9221); MS F-G (BNF, fonds français 22545–22546); and MS Vg (New York, WildensteinCollection, MS without shelfmark).

9 A closer examination of the tenor in MS A raises more questions than it answers. The first of the threeBXs in line one is notated, so perhaps it is supposed to be a signature even though it occurs later in theline rather than at the beginning. A bX signature seems to appear in the second line, although thefirst pitch is actually a b so it might simply be a coincidence, especially since the next b to appear inthat line has a X notated again for it, which should not be necessary if a signature is really in force. Thethird line has a BX signature, but again it might be an accidental rather than a signature since thesecond note is a B and another X appears later on in the line for the third B. Line four has an apparentEX signature, but the only E in the short line is the fourth note, so again, it may not be a signature butrather an accidental.

10 Numerous explanations have been given for partial or conflicting signatures, ranging from evidence ofbitonality (Apel), to an indication of modal transposition (Hoppin), or hexachordal transposition (Bent;Hughes), to necessity for cadential progressions (Lowinsky) or varied cadential sonorities (McGary), tothe sugesstion that the ‘partial’ signature is meaningless (Christian Berger). See Bent, ‘Musica ficta’, andMoll ‘Realizing Partial Signatures’ for summaries of these issues. W. Apel, ‘The Partial Signatures in theSources up to 1450’, Acta Musicologica, 10 (1938), 1–13, and 11 (1939), 40–2; Margaret Bent, ‘Musica Rectaand Musica Ficta’, Musica Disciplina, 26 (1972), 73–100; Bent, ‘Musica ficta, § 3 (ii ): Practical Applications:Signatures’, The New Grove Dictionary of Music and Musicians, 17 (New York, 2001), 447–8; ChristianBerger, ‘Hexachord und Modus: drei Rondeaux von Gilles Bincois’, Basler Jahrbuch für historischeMusikpraxis, 17 (1993), 71–87; Richard H. Hoppin, ‘Partial Signatures and Musica Ficta in Some Early15th-Century Sources’, Journal of the American Musicological Society, 6 (1953), 197–215; Hoppin, ‘Conflict-ing Signatures Reviewed’, Journal of the American Musicological Society, 9 (1956), 97–117; AndrewHughes, Manuscript Accidentals: Ficta in Focus 1350–1450, Musicological Studies and Documents 27([Rome], 1972); Edward E. Lowinsky, ‘The Function of Conflicting Signatures in Early PolyphonicMusic’, The Musical Quarterly, 31 (1945), 227–60; Thomas McGary, ‘Partial Signature Implications in the

62 Jennifer Bain

Page 5: Tonal Structure in the Music of Machaut

discrepancy between voices in terms of signature raises a serious issue for thetheoretical premise of Lefferts’ tonal types, if the cantus line is to have ‘conceptualpriority’. In his system of categories, often the final and the signature are taken fromdifferent voices, the final always from the cantus, and the signature usually fromthe tenor. His distinctions between tonal types are based on what appear to beregular inflections in only one voice, a conflict that he claims his signature categoriesdescribe:

Mapped against these signature-systems, the signatures of cantus and tenor are often conflict-ing, and if so, usually the upper voice has one flat less or one sharp more than the lower voice.11

Lefferts characterizes the signature-systems as overlapping hexachord systems inwhich upper and lower voices share two of three hexachords each, with the lowervoice extending one hexachord flatwards of the upper voice, and the upper voiceextending one hexachord sharpwards of the lower voice (see Table 1, after Lefferts).12

The implication of Lefferts’ proposed theory – which he outlines for us – is thatwithin a certain signature category the voices will reflect the signature in a similarway, with the lower voices generally flatter than the upper voices:

the usual tendency is for composers to write so that cantus and tenor stay in the pair ofoverlapping hexachords common to both hexachord systems, with alternative recta choicesbetween non-adjacent hexachords corresponding to points of tonal fluctuation. Taking thetwo-flat system for demonstration purposes, both voices would stay mainly in the BX and

Escorial Manuscript V.III.24’, The Music Review, 40/2 (1979), 77–89; and Kevin Moll, ‘Realizing PartialSignatures around 1400: Liebert’s Credo as a Test Case’, Performance Practice Review, 10 (1997), 248–54.

11 Lefferts, ‘Signature Systems’, 126.12 The idea of overlapping hexachord systems comes from Andrew Hughes, Manuscript Accidentals and

Margaret Bent ‘Musica Recta’, although Lefferts takes it much further and offers it as theoreticalexplanation rather than the practical application for interpolating inflections that Hughes and Bentpropose. Hughes, Manuscript Accidentals, esp. 46–8; and Bent, ‘Musica Recta’, esp. 98–9.

Table 1 Leffert’s example 6, ‘The signature systems as hexachords’.

Tonal structure and the melodic role of chromatic inflections in Machaut 63

Page 6: Tonal Structure in the Music of Machaut

F hexachords. The bifurcation of hexachordal pathways would fall around acute-register c; hereand above the choice would be between bX and c hexachords (with eX and e as recta alternatives);in the lower register the choice would be between EX and F hexachords (with AX and A as rectaalternatives).13

It is rare, however, for the music to behave as Lefferts suggests it does, as can be seenfrom an examination of the four Machaut songs in Lefferts c-X category. Ballade 2,Helas! tant ay doleur et peinne, is the only one to resemble Lefferts’ hexachordal schemeand distribution of recta and ficta pitches. In Lefferts’ one-flat signature-system bothvoices should share F and C hexachords with bX and b as recta alternatives in the upperregister and EX and E in the lower, and with ficta pitches fY in the upper register andb in the lower. Although a signature appears in the tenor voice of just a singlemanuscript, MS Vg,14 in MSS A and G notated bXs do appear twice in the tenor (andbZ once), while in the cantus fY occurs three times (see Table 2).15 The tenor, and thelower register, could in this case be described as flatter than the cantus.

13 Lefferts, ‘Signature Systems’, 129.14 According to Friedrich Ludwig Guillaume de Machaut, Musikalische Werke, 1: Balladen, Rondeaux und

Virelais (Leipzig, 1926), 2.15 Contrary to Schrade’s edition, no tenor signature appears in MS A. Leo Schrade ed., The Works of

Guillaume de Machaut, Polyphonic Music of the Fourteenth Century 3 (Monaco, 1956), 70–1.

Table 2 Notated chromatic inflections in Helas tant (B2), manuscripts A and G.

Table 3 Notated chromatic inflections in Il m’est avis (B22) and Une vipere (B27) and Tant doucement(R9), manuscript A.

64 Jennifer Bain

Page 7: Tonal Structure in the Music of Machaut

The other three songs in Lefferts’ c-X category (Table 3), however, do not at allreflect this kind of distribution of chromatic inflections among the voices. In Ballade22, Il m’est avis qu’il n’est dons de Nature, although bX is more frequent in the lowervoices, no signature is found in any voice in any manuscript, and an eX (not EX)appears in an upper register, in the cantus.16 The upper register in this case would beflatter than the lower, rather than sharper. The pitch cY – which for Lefferts is not a fictachoice for this category – as well as FY (both high and low) appear in lower and uppervoices. In Rondeau 9, Tant doucement me sens emprisonnés, both an upper and lowervoice (the tenor and cantus) have bXs and both an upper and a lower voice (thetriplum and tenor) have FYs ( fY and FY respectively), which should be a ficta choice forthe upper register only. In the two-voice Ballade 27, Une vipere en cuer ma dame maint,bX appears once in each of the tenor and cantus parts (except in MS G where it appearsin the tenor alone), and the only notated FY in the song occurs as an FY (not fY) in thetenor; the tenor – and the lower register – would appear to be sharper than the cantus.From these four songs, grouped together by Lefferts, it cannot be generalized thatlower voices are flatter than upper voices, or that shared ‘signature-systems’ reflect asimilar approach to chromatic content. To what extent, then, do the four songsconstitute a ‘type’ aside from their cantus endings on c?

Although Lefferts’ theory is attractive because it is systematic and providesus with an a priori system akin to tonal key signatures, his application of‘signature-systems’ does not accurately reflect what happens in the music. Moreover,by extrapolating from the X signatures, which do sometimes appear in some voices insome manuscripts, hypothetical Z and Y signatures, Lefferts takes a questionabletheoretical leap. Rather than describing chromatic content in other voices, on the fewoccasions when a signature does occur consistently in a voice part in a given song, thepurpose of the signature is to provide performance information to the singer of thatspecific voice part about how to sing that specific pitch.17

The special role of BX (and EX)

Although, as I will argue, notated chromatic inflections in the fourteenth century(such as BX, EX, AX, BZ, EZ, FY, CY and GY) can arise either contrapuntally ormelodically as tendency pitches – pitches which suggest continued motion and aparticular resolution – not all inflections are treated equally. Scholars have widelyacknowledged that in relation to other notated inflections bX has a special designationas a member of the medieval gamut, and it is described as a recta pitch rather thanficta.18 Indeed, often bX (and BX, also justified as a gamut pitch by the author of the

16 The eX appears in all of the complete works manuscripts.17 Hughes, Manuscript Accidentals, 44–6, and Bent, ‘Musica Recta’, 98–9, have posited that a X can signal a

hexachord beginning on BX, which would make EX a recta pitch in the lower voice. Cross argueseloquently (and I would agree), that ‘All the information we have indicates that flats were not to beunderstood as fixed, or even to imply their own duplication at the octave (as modern accidentals do),much less at the fifth or fourth. Such species duplication can only have a musical, not a systematic cause’;Cross, ‘Chromatic Alteration’, 130.

18 Andrew Hughes, Manuscript Accidentals, esp. 41–52; and Margaret Bent, ‘Musica Recta’, 73–100.

Tonal structure and the melodic role of chromatic inflections in Machaut 65

Page 8: Tonal Structure in the Music of Machaut

Berkeley Manuscript) is handled differently from other notated inflections. Mostobviously, it is the only inflection that is used as a final cantus and tenor pitch in anumber of secular songs by Machaut and other composers in the fourteenth century.19

Sometimes bX or BX is used as a default pitch in a song instead of b or B, whetherindicated by a signature or through ‘accidentals’ throughout.

Scholars grappling with this special treatment of bX or BX (as well as eX or EX) havedealt with it in a variety of ways. Schrade and Ludwig use BX (and EX) signaturesin their editions, Bent and Hughes describe hexachord signatures and refer totransposition of the gamut, Leech-Wilkinson describes hexachordal shifts which areused as ‘a temporary darkening of the harmonic field’, Plumley transposes the gamut‘twice flatwards’, and she and Lefferts use X signatures (among others) to designatevarious tonal types.20 Ultimately, whether or not transposition of the gamut orsignatures or hexachords are invoked, all of these writers are trying to account for thecentral rather than temporary role that BXs can play.

The notation of BX often follows the exhortations of those theorists (usually writingabout plainchant) who advocate singing BX when descending from C (to A), or whenascending from F to B, and singing BZ when ascending through B to C.21 Sometimesthis usage occurs in a contrapuntal situation as part of a directed progression(progressions from imperfect intervals to perfect intervals, for example bZ is indicatedwhen part of an imperfect interval approaching an F/c or C/c octave), while othertimes it occurs more in a melodic context ( i.e., not as part of the counterpoint). Ifmelodic rules, however, were so fixed that the choice of BX or BZ was solely dependenton melodic direction, it would never be necessary to notate either sign (and ourinterpretative job would be much simpler!).

19 Machaut’s Rondeau 1 and Ballades 3, 8, 11, 16, 19, 25, 36, and 42/RF5 (Remède de Fortune). According toLefferts also Ballades 34, 89, 105, 107, 110, 126, 133, 141, 164, Virelais 196 and 297, and Rondeau 70from Willi Apel ed., French Secular Compositions, texts edited by Samuel N. Rosenberg, 3 vols.,Corpus Mensurabilis Musicae 53 ([Rome], 1970–72); as well as Virelai 85 and Rondeau 58, fromGordon Greene ed., French Secular Music: Rondeaux and Miscellaneous Pieces, Polyphonic Music of theFourteenth Century 22 (Monaco, 1989); and Ballade 77, from Gordan Greene ed., French Secular Music:Manuscript Chantilly, Musée Condé 564, 2 vols. Polyphonic Music of the Fourteenth Century 19 (Monaco,1982).

20 Hughes, Manuscript Accidentals, 41–52; Leech-Wilkinson, ‘Machaut’s Rose, lis and the Problem of EarlyMusic Analysis’, Music Analysis, 3 (1984), 18; Plumley, The Grammar of 14th Century Melody, 8–9; andLefferts, ‘Signature Systems’. In ‘Musica Recta’, 98, Bent writes, ‘If bXs can be freely applied to a partwithout a signature, what significance can a bX signature have?’ For Bent the signature represents ahexachord transposition which allows for recta pitches unavailable in the untransposed system.Karol Berger explains flat signatures as an indication of transposed mode, and argues against therecta-preference rule suggested by Hughes and Bent. Karol Berger, Musica ficta: Theories of AccidentalInflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino (Cambridge, 1987), 58, 83–4.

21 For example, in the first treatise of the Berkeley Manuscript, the author writes: ‘note that whenever oneascends from (or from below) F-fa-ut to b-fa-Z-mi, indirectly or directly, or when one descends to F-fa-utbefore ascending to C-sol-fa-ut, he ought to sing fa on b-fa-Z-mi (by b) . . .’ (Pro quo nota quodquandocumque ab vel de sub F-fa-ut ascenditur usque ad b-fa-Z-mi mediate vel immediate, et iterumdescenditur usque ad F-fa-ut priusquam ascendatur ad C-sol-fa-ut, debet cantari fa in b-fa-Z-mi per b; ).Oliver B. Ellsworth ed. and trans., The Berkeley Manuscript, Greek and Latin Music Theory 2 (Lincoln,Nebr., 1984), 44–5.

66 Jennifer Bain

Page 9: Tonal Structure in the Music of Machaut

Some signed BXs in the repertory, however, do in fact rise to C and some signed BZsdo descend to A. When BX is the default way to sing B, it may not have a tendency tomove down by semitone to A, but rather will rise melodically to (or through) C.Melodic BXs rising to C are most prominent and easily identified in songs in whichperfect BX sonorities play a pivotal role particularly as cadential goals, such as Ballade36, Se pour ce muir qu’Amours ai bien servi (see the ascent from bX through c and d in thecantus bars 1–2 and in the tenor in bar 4 of Ex. 1). Similarly Ballade 15, Se je me pleing,je n’en puis mais, which ends on a C sonority rather than BX, is saturated with BXs (andEXs), many of which follow the pattern of BX rising to C (see the tenor in bars 29–30and the cantus in bar 34 of Ex. 2).

Particularly striking instances can occur in songs where BX plays otherwise aminimal role, as for example in the opening phrase of Ballade 28, Je puis trop bien madame comparer, in Example 3. Moving away from a unison a with the tenor, thecontratenor stops momentarily on a very dissonant bX between the consonant a/e fifthof the tenor and cantus. Since the bX continues up to c, it does not serve the functionalpurpose of increasing the tendency to a. We might first hear it as an early suggestion(or foreshadowing) of BX playing a structural role in the song, but in fact it is the onlyBX notated at any pitch level in any voice in the entire song. As an available pitch in the

Ex. 1 Se pour ce muir (B36), bars 1–5.

Ex. 2 Se je me plaing (B15), bars 29–35.

Tonal structure and the melodic role of chromatic inflections in Machaut 67

Page 10: Tonal Structure in the Music of Machaut

gamut, it is used here for aural prominence, a device all the more effective with eachrepetition of the A section of the song because of its singular use.

Just as BX sometimes functions as the default way to sing B, EX sometimes functionsas the default way to sing E. This usage is apparent by melodic approaches from EX toF (see for example the tenor in bar 31 of Ex. 2 above), and by the use of perfectsonorities on EX.22 In Ballade 8, De desconfort de martyre amoureus, for example, the firstphrase of the B section ends on an EX/bX fifth (Ex. 4).

EX, in fact, is most prevalent in songs (like Ballade 8) that end on a BX sonority.Outside this group of BX ending songs, Machaut uses EX as a notated pitch in only tenpolyphonic ballades, virelais or rondeaux.23 Of these ten, five use the inflection onlyonce or twice (Ballades 4, 12 and 22, and Rondeaux 3 and 8), while the other five, allof which end on a C sonority, have a much stronger EX presence (Ballades 15, 18, 31and 41/RF4, and Rondeau 10).24 Daniel Leech-Wilkinson brings one of these songs

22 A feature that is particular to the pitches BX and EX; rarely will an FY or CY do the reverse, i.e., descend toE and B respectively. Ballade 9 bars 4–5 and 58–9 offers an exception to this observation (FY descends toE both times), and Rondeau 2, bar 26.

23 I arrived at this count by examining the Ludwig and Schrade editions first, and then checking these tensongs against MSS A, B and C.

24 The EXs in Ballades 15, 18, 31 and 41/RF4 and in Rondeau 10 are too numerous to list here. For thoseballades and rondeaux which do not end on BX sonorities but which use an EX once or twice, the EXs canbe found in the following bars in Schrade’s edition (manuscripts included only if the inflection is not

Ex. 3 Je puis trop (B28), opening phrase.

Ex. 4 De desconfort (B8), bars 25–30.

68 Jennifer Bain

Page 11: Tonal Structure in the Music of Machaut

(Rondeau 10, Rose, lis printemps verdure) to our attention as an especially lovelyexample. As Leech-Wilkinson suggests, Rose, lis printemps verdure incorporates bothBX and EX as fundamental elements of its pitch content in some sections of the song,sections which figure all the more prominently because of their juxtaposition withsections that use EZ and BZ as default pitches (see bars 14–17, 22–25 and 32–35 inExample 8 for the sections using BX and EX).25

In addition to its special role as a fundamental element of the basic pitch material,however, EX also serves a functional, contrapuntal role in Rose, lis, printemps verdure.In terms of the larger tonal structure of the song, where D sonorities and C sonoritiesmark points of arrival ( indicated in Ex. 8 with arrows), signed EXs increase thetendency to D, while signed BZs increase the tendency to C.26 Twice, tenor EXs first areintroduced as non-tendency pitches, fleshed out with cantus octave and contratenor/triplum fifth and third, and then have a contrapuntal function a few notes later whenthe cantus forms an EX/c sixth, and the new sonority initiates a directed progressioncadentially to a D octave (Ex. 9).

This dual role of EX in Rose, lis, printemps verdure confirms that the only way to judgehow chromatic inflections relate to tonal structure is to examine precisely their usagein particular situations. In contrast to Lefferts who suggests that signature-systems inconjunction with cantus finals determine tonal categories, I would suggest that eventhe presence of default BXs and EXs, indicated either through signatures or through‘accidentals’, does not determine how an inflection will function in a given piece, orwhat its relationship to tonal structure will be.

Melodic usage of chromatic inflections

One of the ways in which inflections can contribute to the tonal structuringof individual songs is through melodic usage. Little attention has been paid tothe function of melodic (rather than contrapuntal) chromatic inflections. Melodicinflections can appear in monophonic songs plainly serving a melodic function,as well as in polyphonic settings, still serving a melodic function, but outsidethe frame of the contrapunctus. Since scholars have been particularly interested in‘harmonic’ syntax, the topic of melodic construction in fourteenth-century secularmusic has received less consideration in general, with the notable exception ofPlumley’s 1996 monograph, and Leech-Wilkinson’s articles on monophonic virelais.27

found in all three of MSS A, B and C): Ballade 4, tenor bar 3 (MSS A and B only); Ballade 12, cantus bar13 and tenor bar 15; Ballade 22, cantus bar 35; Rondeau 3, tenor bar 19 and bar 39 (in MSS A and C; MSB very clearly indicates an EZ inflection instead); and Rondeau 8, cantus bar 30 (in MSS A and B only).

25 Leech-Wilkinson, ‘Machaut’s Rose, lis’, 18. In my Ex. 5, Triplum rhythms are according to RichardHoppin, ‘Notational Licenses of Guillaume de Machaut’, Musica Disciplina, 14 (1960), 22.

26 In a forthcoming article which surveys cadential progressions in the music of Machaut, I discuss the issueof semitone tendency at length. See Bain, ‘Theorizing the Cadence’.

27 Yolanda Plumley, The Grammar of 14th Century Melody; and Daniel Leech-Wilkinson, ‘Not Just a PrettyTune: Structuring Devices in Four Machaut Virelais’, Sonus, 12/1 (1991), 16–31; and Leech-Wilkinson,‘The Well-Formed Virelai’, in Trent’anni di Ricerche Musicologiche: Studi in onore di F. Alberto Gallo, ed.Patrizia Dalla Vecchia and Donatella Restani (Rome, 1996), 125–41.

Tonal structure and the melodic role of chromatic inflections in Machaut 69

Page 12: Tonal Structure in the Music of Machaut

Ex. 5 Rose, lis (R10).

70 Jennifer Bain

Page 13: Tonal Structure in the Music of Machaut

Ex. 5 continued.

Tonal structure and the melodic role of chromatic inflections in Machaut 71

Page 14: Tonal Structure in the Music of Machaut

Correspondingly, because the topic of chromatic inflections has involved issues ofperformance practice, which mostly have focused on contrapuntal requirements, themelodic usage of chromatic inflections in fourteenth-century music has been less ofa preoccupation.28 A new focus on melodic inflections, however, could have asignificant impact on our understanding of the tonal structuring of songs.

Central to the observations that follow is the proposition that by invoking strongexpectations of linear semitone motion, chromatic inflections serve as one elementthat can establish focal pitches in the tonal organization of a phrase, a section or a song,in both Machaut’s monophony and polyphony. At least one scholar, Lucy Cross,disagrees. In her discussion of the role of chromatic inflections in fourteenth-centurypolyphony she says that:

Naturally it will happen that at most pauses, cadences or stops in polyphony there arepenultimate sharps, since a stop requires a fifth, octave, or unison, and the rules of counterpointdemand the alteration. But sharps and flats in themselves do not function, as they do in latertonal music, as the determinants of focal pitches.29

But the oft-cited contrapuntal rule to which Cross refers that thirds and sixths shouldbe major rather than minor when approaching perfect fifths and octaves respectively,reinforces the idea that semitone motion in one voice strengthens a progression andthus brings attention – focus – to the arrival sonority, and more specifically to the pitchemphasized through semitone approach. Although it may seem anachronistic toattribute to chromatic inflections a ‘leading-tone’ function, much evidence from the

28 Taking melodic usage into account, moreover, may influence judgements about performance practiceissues, such as how long an inflection has an effect on a particular pitch. Andrew Hughes, for example,makes a case for the ‘once-only’ effect of inflections (as opposed to signatures), based on a contrapuntalargument: he suggests that in most cases where it appears that an inflection has a lasting effect, it can beexplained by the rules causa necessitatis (unnotated inflections required to make imperfect fifths andoctaves perfect) and pulchritudinis (unnotated inflections required to adjust sixths and thirds in theirapproaches to octaves, fifths and unisons). This argument implicitly suggests that melodic inflections – inboth monophony and polyphony – would only ever have a ‘once-only’ effect. Some of the examples thatfollow, I will argue, suggest otherwise. Hughes, Manuscript Accidentals, 69. Although describing musicfrom later repertories, Peter Urquhart similarly suggests that melodic considerations are sometimesmore important than contrapuntal when addressing the issue of chromatic adjustments. For instance,describing Karol Berger’s suggested correction of ‘mi-against-fa discords’, Urquhart wonders ‘how suchcorrection was possible, given that a performer singing from only his own line could not tell whether aparticular diminished fifth was acceptable or not, until after he had already sung the interval. Judgingacceptability on the basis of correct resolution is possible for a score-reader, but not necessarily for asinger.’ Peter Urquhart, ‘False Concords in Busnoys’, in Antoine Busnoys: Method, Meaning and Context inLate Medieval Music, ed. Paula Higgins (New York, 1999), 361–67, esp. 380.

29 Cross, ‘Chromatic Alteration’, 189.

Ex. 6 Reductions of bars 14–17 and 22–5.

72 Jennifer Bain

Page 15: Tonal Structure in the Music of Machaut

music and the notation, taken together with commentary from coeval theory treatises,supports the notion that chromatic inflections which implicate semitone motion arecrucial to the tonal organization of French music from the fourteenth century.

Indeed the position of the semitone is critical to the notation and realization ofmedieval music in general, and hence to medieval pedagogical systems andexplication. The earliest single or double staff lines, designating F and/or c, as wellas the coloured lines within a staff, indicate to the singer the position of thesemitones. The distinction between round and square b signs serves the samefunction, first to distinguish bX from bZ, and later to inflect other pitches, i.e., tosound a pitch as a fa (with a semitone below) or as a mi (with a semitone above).The non-staff based Daseian notation relies on the position of the semitone within atetrachord as the key to its realization. Similarly, the pedagogical system of thehexachords serves to identify semitone placement, the three hexachords using mi-fato designate e-f, a-bX and b-c. This acute concern in medieval notational andpedagogical systems with the placement of semitones suggests very strongly thatthey are important to tonal organization. I would argue that, along with othermusical and textual elements, melodic semitone motion can contribute to theestablishment of focal pitches.

But I would argue further that the way in which semitone motion is important to thetonal structure of a particular song becomes apparent only through musical context.To examine the function of melodic chromatic inflections and semitone movement inthe secular works of Machaut I will focus on specific musical situations: on cadencesand the beginning of phrases in the monophonic virelais, and on two patterns thatrecur with the pitches, FY and CY in the polyphonic songs.

Monophonic cadences and chromatic inflections

Fourteenth-century theorists do little to describe formal aspects of composition suchas the musical-poetic structure of the fixed forms, or ouvert–clos organization, or howto organize a song around one or more central pitches.30 Instead, they instruct readersto begin and end a polyphonic work with perfect consonances, and they describe basicrules of note-against-note counterpoint, and progressions of two or three intervals.Discussion of monophony is restricted to chant and its modal classification. But themusic provides us with many clues. One can expect final cadences to be stable pointsof repose. The internal ouvert–clos patterning, moreover, reveals an unstable/stableor weaker/stronger set of tonal relationships produced through various musicalmeans, such as the generalized finding that ouvert cadences conclude a second orthird higher than their clos counterparts in the fourteenth-century repertory.31

30 Aegidius de Murino specifies that there are open and closed endings in ballades, rondeaux and virelais,but he does not provide details about how open and closed endings are accomplished in terms of pitchorganization. Aegidius de Murino, Tractatus cantus mensurabilis, Scriptorum de musica medii aevi novaseries a Gerbertina altera 3, ed. Edmond de Coussemaker (Paris, 1869; repr., Hildesheim, 1963), 128.

31 Lucy Cross, for example, indicates in relation to fourteenth-century ballades and rondeaux, that ‘a briefinspection of that repertory bears out our expectation at this point that the overwhelming number of

Tonal structure and the melodic role of chromatic inflections in Machaut 73

Page 16: Tonal Structure in the Music of Machaut

Although some of Machaut’s secular songs follow this pattern, a close examina-tion of both his monophonic and polyphonic fixed-form songs outlines a morecomplex situation (see Table 4). The ouvert and clos cantus pitches of Machaut’smonophony demonstrate the greatest consistency, always dropping by a second,third or fifth from ouvert to clos. In the ouvert and clos endings of the polyphonicsongs, should the cantus end lower in the clos or the final, it is always by second orthird. But frequently the cantus ends on a higher pitch at the clos cadence, by asemitone,32 a third,33 a fourth,34 and in single instances each, a sixth35 or a seventh.36

The cantus lines in the polyphonic songs clearly demonstrate a much greater varietyin the relationship between ouvert and clos cadential pitches than the cantus lines inthe monophonic songs, because the cantus line functions as only one part of apolyphonic whole. In the monophonic songs, in order to project an unstable qualityat the ouvert and a stable quality at the clos, the relationship between ouvert andclos cantus pitches must be much clearer and more predictable. In the polyphonicsongs an imperfect interval such as a third or sixth can create instability at an ouvertcadence, which might result in a less usual relationship between ouvert and closcantus pitches. For example, in a polyphonic song the ouvert might end on a G/bthird and the clos on an F/c fifth; the cantus moves up a semitone from ouvert toclos rather than down a second or third, but the weak–strong relationship is stillclear.37

This weak–strong organization is described in fact very clearly as a hierarchicalarrangement by one fourteenth-century author, Johannes de Grocheio.38 Johannes,who writes about musical practice in Paris at the beginning of the fourteenth century,

ouvert endings both in tenor and cantus parts (as these voices are usually an octave apart at the cadences)are a whole step above their respective clos’, ‘Chromatic Alteration’, 148. Acknowledging that what maybe true for Machaut, may not be true for the fourteenth-century repertory as a whole, I would suggestthat my findings for Machaut’s output warrant a more thorough examination of the rest of thefourteenth-century French repertory.

32 Significantly, all of the ballades which end a semitone higher in the clos cadence than the ouvert, end ona in the cantus at the ouvert and on bX at the clos. In Ballade 3 the cantus is the lowest voice of an a/c third,in Ballade 16 the upper voice of an FY/a third, and in Ballade 25 and Ballade 42/RF5, the fifth above D. Thecantus of Rondeau 18 ends on G with the medial on FY.

33 Ballades 29, 38, 40 and 41/RF4, and Rondeaux 1, 2, 4, 9 and 20.34 Ballades 4, 15 and 22, and Rondeaux 7 and 11.35 Ballade 30.36 Ballade 21.37 For an in-depth discussion of the role of imperfect sonorities as cadential goals see Bain, ‘Theorizing the

Cadence’.38 For further discussion of the theoretical basis for hierarchical organization in medieval music see Bain,

‘Theorizing the Cadence’.

Table 4 Relationships between ouvert and clos.

74 Jennifer Bain

Page 17: Tonal Structure in the Music of Machaut

describes the ouvert–clos organization in ductia and stantipes ( textless melodies) butwithout reference to specific pitch relationships:

The elements of the ductia and stantipes are commonly called puncta. A punctus is a structuredcollection of agreements producing euphony as they rise and fall, having two parts, similar atthe beginning, different at the end, which are commonly called ‘open’ and ‘closed’. I say‘having two parts etc.’ by analogy with two lines, one of which is longer than the other. Thegreater includes the lesser and differs from the lesser at its end.39

Johannes distinguishes between two phrases, which are related to each other but havedifferent endings. He alludes to the quality of the endings describing a hierarchicalarrangement, where the ‘closed’ ending clearly comes in the second part. Thesepoints of stability and instability prove most useful in determining other elements ofhierarchical tonal structure.40

A survey of ouvert, clos and final cadences in both refrain and couplet sections of allof Machaut’s monophonic virelais strongly suggests that semitone placement cancontribute to the strength or weakness of a cadence. While four of the 71 cadencesapproach their cadential goals from above by some combination of third and fifth(Ex. 7), all of the other cadences surveyed can be grouped through reduction intothree generalized types of melodic approach, summarized in Example 8: (a) a three-note rising figure, (b) a three-note falling figure, and (c) a three-note double

39 Christopher Page, ‘Johannes de Grocheio on Secular Music: A Corrected Text and a New Translation’,Plainsong and Medieval Music, 2 (1993), 33. ’Partes autem ductiae et stantipedis puncta communiterdicuntur. Punctus autem est ordinata aggregatio concordantiarum harmoniam facientium ascendendoet descendendo, duas habens partes in principio similes, in fine differentes, quae clausum et apertumcommuniter appellantur. Dico autem duas habens partes etc. ad similitudinem duarum linearum quarumuna sit maior alia. Maior enim minorem claudit et est fine differens a minori.’

40 These other musical elements could in turn be very useful for examining cadential organization in motetsand Mass movements, which do not use the musical and poetic schemes of the fixed-form songs.

Ex. 7 Cadences involving leaps of thirds and fifths.

Ex. 8 Three-note melodic cadential patterns.

Tonal structure and the melodic role of chromatic inflections in Machaut 75

Page 18: Tonal Structure in the Music of Machaut

neighbour figure. When semitone placement within the three-note figures is takeninto account a clear distinction arises between those figures used for unstable ouvertcadences, labelled OUV, and those used for stable medial or final cadences, labelledMED for the final cadence of the couplet and FIN for the final cadence of the refrain,which is also the final cadence of the song (see Ex. 9).

Ex. 9 Variations in semitone placement in the cadential patterns with tabulations according toMachaut’s usage in the monophonic virelais.

76 Jennifer Bain

Page 19: Tonal Structure in the Music of Machaut

For the rising and falling figures, although statistically speaking the numbers arescanty, the distribution is remarkable. Of the ten cadences that employ a rising figure,only two ascend by semitone directly to the arrival pitch and both are stable medialcadences (Virelai 5 – b-cY-d, and Virelai 22/25 – D-E-F); all but one of the rest are ouvertcadences. Of the sixteen cadences that employ a falling figure, only three descend bysemitone directly to the arrival pitch, and all three are unstable ouvert cadences(Virelai 3 – c-bX-a, and Virelais 14 and 16 – G-F-E); all but one of the rest are medial orfinal cadences. The double neighbour figure is much more prevalent (41 of the 71cadences), and again distribution by placement of the semitone is impressivelyconsistent. Of the twelve cadences that employ a double neighbour figure withdescending semitone, ten are ouvert cadences,41 while all of the sixteen doubleneighbour cadences with ascending semitones and all of the thirteen doubleneighbour cadences with no semitones are medial or final cadences.

The distribution of all of these cadences according to type and placement at weakeror stronger points within the structure of a song, suggests a continuum of stability interms of the relative tonal strength of cadential figures (see Table 5). The evidenceprovides a strong indication that a descending semitone approach (in either a doubleneighbour or a falling tone/semitone figure) – because it occurs almost exclusively atouvert cadences – renders a cadential arrival weak, while an ascending semitoneapproach (in either a double neighbour or a rising tone/semitone figure) – because itoccurs exclusively at final or medial cadences – renders a cadential arrival strong.Approaches by tone/tone or semitone/tone appear to be generally less stable whenrising and more stable when falling. Finally, the double-neighbour approach by wholetone from both above and below is on the more stable side.

Since the double-neighbour approach appears to be stable both by double wholetone and by ascending semitone (but not by descending semitone), the commonconcern about whether unnotated inflections should be applied to convert whatappear to be whole tones into semitones may not always be relevant. Certainly in mostof the cadences I have identified in the double whole tone category, Ludwig

41 I should note here that the two exceptions are found in the same song, Virelai 11, a virelai that is perhapsexceptional in many ways. It is one of only two of all of Machaut’s secular songs that has a cantus endingon a. Daniel Leech-Wilkinson describes the virelai as ‘perhaps the most difficult’ of a ‘few virelais withlittle in the way of perceptible frame or structural descent’. Leech-Wilkinson, ‘The Well-Formed Virelai’,128.

Table 5 Continuum representing relative stability of cadential approach.

Tonal structure and the melodic role of chromatic inflections in Machaut 77

Page 20: Tonal Structure in the Music of Machaut

and Schrade suggest ‘leading-tone’ adjustments in their editions, as for example inVirelai 4, Douce dame jolie.42 The virelai ends with a G-F-G figure, which occurs fourtimes melodically in the song, and no FYs are notated at any point in any of themanuscript versions (Ex. 10).

Musical elements in the song (other than FY) set up G very clearly as a tonal centre.In Douce dame jolie the opening leap of a descending fifth directs the ear immediately,setting up two focal pitches that permeate the song, d and G.43 The first phrasecontinues by circling around G, and cadences on a with a descending semitonedouble-neighbour approach. Within the context of the opening leap, the circlingaround G, and the descending semitone approach from bX, the cadential a soundsunstable. The second phrase reaffirms the centrality of G and d with an ascending leapthis time, and the phrase concludes with the same double-neighbour descendingsemitone cadential figure, again ending on an unstable a. The first four bars of thethird (and final) phrase of the refrain are almost identical to the first phrase, exceptthat G receives even more emphasis at the beginning, by its reiteration instead of d inthe opening figure. Rather than cadence on a again, just as the third phrase reaches thea, a new textual line begins and stretches out the musical phrase by three bars tofinally cadence on G. Although FY would enhance the sense of arrival of G, a wholetone double neighbour approach from F cannot undermine all of the other musicalelements that have emphasized it.44

Although in Virelai 4 the structural significance of a penultimate FY would beminimal, in Virelai 10, De bonté, de valour, the FY approach to the final G plays a criticalrole in the final cadence and in the tonal structuring of the song. In the first half of therefrain (with which the virelai begins), the rhythmic structure of the melody alignsneatly with the text to create three short (two-breve) phrases, cadencing on a, FY anda respectively (Ex. 11, cadence pitches marked above; Ex. 13 for the music and texttogether). The melodic repetition of the refrain (following the ouvert) creates some

42 Ludwig ed., Musikalische Werke, and Schrade ed., The Works of Guillaume de Machaut.43 Daniel Leech-Wilkinson aptly regards the G/d (and its octave g) as a ‘chordal drone’ in the Background

structure of the song. Leech-Wilkinson, ‘Not Just a Pretty Tune’, 20.44 Since there is no precedent in the song for an FY I would leave the F as written.

Ex. 10 Refrain of Douce dame (V4).

78 Jennifer Bain

Page 21: Tonal Structure in the Music of Machaut

asymmetry when, corresponding to the reduced syllable count of the repetition, thesecond and third phrases elide to become one three-breve phrase rather than twotwo-breve phrases, ending this time on G (see Ex. 12, again with the cadence pitchesmarked). The double neighbour with descending semitone approach renders bothcadences to a as weak (Ex. 13).

Ex. 11 First half of refrain of De bonté (V10), to the ouvert cadence.

Ex. 12 Second half of the refrain of De bonté (V10), repetition to the clos cadence.

Ex. 13 The refrain of De bonté (V10).

Tonal structure and the melodic role of chromatic inflections in Machaut 79

Page 22: Tonal Structure in the Music of Machaut

The first cadential pitch, a, typically functions as an ‘ouvert’ or secondary point ofrepose to either F or G. The cadence to FY in the second phrase, however, stronglyimplicates G as a tonal centre rather than F, an implication strengthened by theunusual approach to FY following an FZ, the two pitches separated only by a Dto create a striking aural juxtaposition. The retained FY in phrase 3 adds to thedestabilization of a in the rising semitone/tone figure that merges with thedescending semitone double neighbour cadence. FY appears twice in the first halfof the refrain, but has a similar function as an unstable cadential arrival point inphrase 2, and as a destabilizing agent of a in phrase 3. In phrase 5, however, FY takeson a new role. Rather than functioning rhythmically and textually as an arrival, itparticipates in an elision of two earlier phrases (2 and 3), to strengthen the double-neighbour approach to the long-expected G arrival in phrase 5, its impact furtherhighlighted by the striking F-D-FY figure.

Chromatic inflections as initiating device

In addition to their usage in cadential situations, chromatic inflections can have asignificant effect on the tonal structuring of songs as the initial pitch of a phrase,section or song, particularly when the initial pitch corresponds to the beginning of amensural unit at the level of the semibreve or breve.45 In general, the initial pitches oflarger musical sections function aurally and structurally as important points ofreference, most significantly because they mark the beginning of large segments of thetext, bringing attention to the musical-poetic structure. Virelai 12, Dame a qui, beginswith a three-note ascending motif, F-G-a, heard many times, that outlines two keypitches in the tonal structuring of the song: a, frequently embellished with bX through-out, functions as the ouvert cadential pitch in both sections of the song, while Ffunctions as both an initiating pitch and as a stable cadential pitch, approached by anascending semitone at the clos of both sections.

At the beginning of the couplet, however, a chromatic inflection appears, suddenlyshifting the tonal orientation (Ex. 14). After the refrain’s stable clos cadence on F, anotated bZ at the beginning of the second section introduces through a stark leap of atritone a phrase which circles around c. Although melodic tritones are generallyavoided, this one seems to be used deliberately. It is particularly effective because itoccurs not within a phrase but at the juncture between the end of one phrase (and onesection) and the beginning of the next. The following phrase parallels the ouvert

45 Even when a chromatic inflection occurs as a minim ‘pick-up’ to a semibreve or breve mensural unit, itcan sometimes contribute to the tonal structuring of the song. For instance, the signed bZ that begins Tuitmi penser, Virelai 25/28, shapes the whole of the first section of the song (the bZ inflection is found onlyin MSS Vg and G). Although a c follows the initial bZ at the beginning of a breve and ostensibly resolvesit, the repetition of the bZ at the end of a two-breve rhythmic pattern, leaves it standing unresolved untilit is picked up again an octave lower at the end of the A section and finally cadences to C. Two polyphonicvirelais 29/32 and 30/36 similarly begin with single pitches (b and E respectively), that resolve up bysemitone to a perfect sonority, a fifth on F, although only Virelai 30/36 begins also as a ‘pick-up’. Onlyin Virelai 29/32 is the pitch actually inflected, and in MS A it is only the second time through in themanuscript, after the appearance of bXs.

80 Jennifer Bain

Page 23: Tonal Structure in the Music of Machaut

and clos cadences of the refrain and returns to an orientation around the F and a,introduced in the opening motif of the song.

The initial cY of Virelai 2, Loyauté vueil tous jours maintenir, relates more directly tothe larger tonal structuring of the song, although its role is complicated by thequestion of how long the inflection lasts. My editorial suggestions in Example 15 takeinto account the fact that the second phrase begins exactly as the first (the parallel is soapparent that surely a cZ would have been indicated if a cY was not intended), and thestraightforward melodic contours: the cY remains to decorate the second d, butbecomes cZ when part of a descending pattern, and the rise to the cadence pitch fromG suggests a cZ rather than cY to avoid a sharply outlined melodic tritone at a cadentialapproach within a phrase.

In immediate terms the initial cY of Virelai 2 highlights the d that follows. Ratherthan reinforce the principal tonal focus, however, in relation to overall tonal structureits main effect seems to be to destabilize the two cadential pitches of the song, c and F.Although the first phrase begins with the cY-d figure, in my reading of the inflections

Ex. 14 Dame a qui (V12).

Tonal structure and the melodic role of chromatic inflections in Machaut 81

Page 24: Tonal Structure in the Music of Machaut

it ends on c, approached by semitone from below. With a dramatic and unusualmelodic augmented prime as a juncture between the phrases (separated by a briefrest), the second phrase immediately takes up the cY-d figure, destabilizing c andending this time on F, also approached by semitone from below.46 The two shorttextual/musical phrases of the B section reassert the importance of F and c. The firstphrase prolongs a high f through neighbour notes and descends by step to cadence onc, and the second phrase cadences on the low F again, this time in a direct approach byleap from c. Although chromatic inflections in the monophonic virelais typicallyconfirm a tonal centre, when the cY returns with the repetition of the first musicalphrase in Virelai 2 (now with new text), it shifts the tonal orientation of the song againand destabilizes c and F.

Melodic chromatic inflections in polyphony

In addition to their role in monophonic contexts, melodic chromatic inflections canhave a significant impact on tonal structure within the context of a polyphonic settingas well. These melodic chromatic inflections do not participate as functional elementsof the contrapuntal framework, but contribute to the definition of tonal structure byemphasizing particular pitches. They may serve a syntactical function structurally bycreating expectation of a goal tone through semitone movement, but contrapuntally

46 Lucy Cross discusses other (very rare) melodic augmented primes in fourteenth-century English, Italianand French sources, including examples from Marchetto’s Lucidarium and one other example fromMachaut in the Credo of his Mass, bars 192–4. Cross, ‘Chromatic Alteration’, 214–24.

Ex. 15 Loyauté (V2).

82 Jennifer Bain

Page 25: Tonal Structure in the Music of Machaut

they do not have a syntactic purpose. The final cadence of Ballade 32, Plourez, dames,plourez vostre servant, for example, demonstrates clearly the structural significance ofsuch inflections (see Ex. 16). At the final cadence of Ballade 32, the melodic cY in thecantus creates the expectation of – and achieves – a cantus d, a melodic expectation andresolution at odds with the F/c or C/c harmonic implication of the G/bZ third betweenthe tenor and contratenor.47

These structurally significant melodic chromatic inflections recur throughoutMachaut’s polyphonic repertory, and are particularly evident in two specific melodicformulas. FY often arises decoratively first and then becomes part of the counterpointin a directed progression to G, while CY appears melodically only but through itsimplication of D weakens directed progressions or cadences to E. Both FY and CY

formulas can significantly contribute to the tonal structuring of individual songs. Forexample, at the beginning of the B section in Virelai 31/37, Moult sui de bonne heure nee,the cantus fY first decorates g melodically (not harmonically since the tenor holds along G), and then plays a role in two directed progressions, the second of which is alsoa cadence (Ex. 17).

In the melodic context of the shaping of the cantus line, the fY in its emphasis of g,plays an important role structurally from its first appearance in bar 26. But contra-puntally the fY takes on structural significance only when it becomes part of a directed

47 The cantus e further supports the tenor/contratenor G/b in suggesting an F/c/f resolution, but rather thanmove up by semitone, the contratenor/cantus b/e move down by step to a/d, while the tenor, rather thanmove down by step to F instead moves down by leap to D. I discuss this passage at greater length inrelation to the larger tonal structuring of the song in: Jennifer Bain, ‘Ballades 32 and 33 and the ‘‘resdalemangne’’ ’, in Machaut’s Music: New Interpretations, ed. Elizabeth Eva Leach (Woodbridge, 2003),205–19, esp. 210–11. The G/b third suggests a resolution to either an F/c or C/c sonority. Three otherMachaut songs end with a G/b third to C/c octave progression between tenor and cantus: Ballades 22and 27, and Rondeau 19. The contratenor in both Rondeau 19 and Ballade 22 sing an E below the G/bthird, and forms a fifth in the cadential sonority; in Ballade 22 the triplum doubles the contratenor anoctave above. Ballade 30 uses the same tenor/cantus contrapuntal progression but to a D/d octave(approached by a/cY), and the contratenor in similar fashion sings an FY below the a/cY third.

Ex. 16 Final cadence of Plourez, dames (B32).

Tonal structure and the melodic role of chromatic inflections in Machaut 83

Page 26: Tonal Structure in the Music of Machaut

progression in bar 27 and then again in bar 29, where it also participates in aperfect-sonority cadence. In Ballade 22, Il m’est avis qu’il n’est dons de Nature, thepattern appears in the triplum first as melodic elaboration, and then similarlyparticipates in two directed progressions, the second of which is also a cadence (seeEx. 18). Another example occurs in Rondeau 2, Helas! Pour quoy se demente etcomplaint, in one of the very rare instances that a notated FY descends to E withoutimmediately rising to G (Ex. 19).48 A high fY first appears in the song in bar 26, adissonant seventh above the tenor G, as a melodic anticipation to the harmonically

48 As indicated in note 22 above, another occurrence appears in Ballade 9, bars 4–5 and bars 58–9 in thecantus.

Ex. 17 Moult sui (V31/37).

Ex. 18 Il m’est avis (B22), bars 33–7.

84 Jennifer Bain

Page 27: Tonal Structure in the Music of Machaut

consonant a/fY sixth of in bar 30 that initiates two successive directed progressions tothe G/g octave with which the phrase began.49

Melodic CYs contribute sometimes to the tonal structuring of a song as well. Incontrast to its strengthening role in establishing a focal pitch in Ballade 32 (Ex. 14), amelodic CY can sometimes weaken directed and/or cadential progressions by under-mining the arrival sonority. In cantus or triplum voices, cY sometimes functions as amelodic participant in a directed progression or cadence to E/e or a/e.50 By alertingthe listener to the significance of the pitch d, cY effectively destabilizes the e arrival.51

In the first phrase of Ballade 13, Esperance qui m’asseüre, for example, cY appearsboth contrapuntally as part of an a/cY third to G/d fifth directed progression, andmelodically when it continues – despite the vertical augmented second that itcreates – through the bX/d to a/e cadential progression (Ex. 20). Within this cadence toa/e, the cY confirms the privileging of d, a significant pitch in the structure of thesong.52

This cY melodic pattern occurs in monophonic contexts as well, and relates to theless stable semitone/tone rising cadential figure discussed earlier ( involving FY-G-aand b-c-d). In the first cadence of the couplet in Virelai 17, Dame, vostre dous viaire, themelody ascends from cY through d to cadence on e, and alerts the listener to the focalnature of d, by destabilizing e and giving it an ouvert quality (Ex. 21). This firstcadence of the couplet proves to be important in the tonal structuring of the song by

49 Other examples can be found in: Ballade 20 bars 9–10 in the cantus; Ballade 23 bar 9 in the triplum;Ballade 24 bars 26–8 in the cantus; Ballade 31 bars 20–1 in the contratenor; Ballade 34 bars 19–20 in CantusI ( in bar 33 the pattern returns but this time it ends most likely on fZ ( to agree with the tenor F) and nodirected progression arises involving fY); and Rondeau 9 bar 16 and bar 51, very briefly in the triplum.

50 Triplum examples can be found in Ballade 18 bars 6–7 and Rondeau 6 bar 2.51 In one occurrence of this melodic technique, the cY melodic motif appears in the context of a D/a/d

perfect sonority (embellishing the cantus d) rather than in the context of an F/d or bX/d imperfectsonority that initiates a directed progression (Ballade 21, bars 6–10).

52 The cY in the ouvert of Ballade 14 similarly begins contrapuntally and then continues melodicallythrough a directed progression to an a/e fifth. Although primarily associated with cY, one example of thismelodic technique can be found utilizing fY (rising to aa), and similarly starts contrapuntally butbecomes melodic (Ballade 30, bars 30–5; the fY would likely continue to the end of bar 33).

Ex. 19 Helas! pour quoy se demente (R2), bars 26–32.

Tonal structure and the melodic role of chromatic inflections in Machaut 85

Page 28: Tonal Structure in the Music of Machaut

implicating d firmly as a tonal centre and establishing e as an unstable pitch.53 Indeed,the ouvert phrase that follows immediately concludes again on e, this time destabi-lized by a descending semitone double neighbour cadence, and the expected d doesnot arrive until the clos cadence at the end of the repetition.

Understanding the derivation of a CY inflection as part of a melodic device couldinfluence the chromatic rendering of particular passages. For instance, in Rondeau 6(Ex. 22), both Ludwig and Schrade provide an editorial Y in bar 2 of the tenor (Ludwigtentatively includes a question mark beside the suggested Y).54 Ludwig and Schrade

53 In his discussion of Virelai 17 as one of ‘five virelais in which the final is established convincingly only inSection B’, Daniel Leech-Wilkinson argues that the final d cadence of the refrain sounds misplaced andunstable within the context of the a-centred refrain. He writes: ‘scale degree 5(a) is composed out sostrongly in Section A as to seem more final than the final, d arriving so late as to be hardly believable asthe main pitch centre for the piece.’ I would suggest that, in this case, d is not the ‘main’ pitch centre of thepiece, but rather is one of two tonal centres in a song that serves as a fine example of a work with multipletonal centres, a focal topic in my dissertation. Leech-Wilkinson, ‘The Well-Formed Virelai’, 131; JenniferBain, ‘Fourteenth-Century French Secular Polyphony and the Problem of Tonal Structure’ Ph.D. Diss.,State University of New York at Stony Brook (2001), esp. 114–51.

54 Ludwig (ed.), Musikalische Werke, 55; and Schrade (ed.), The Works of Guillaume de Machaut, 146.

Ex. 20 Esperance (B13), bars 1–4.

Ex. 21 Dame, vostre (V17), bars 13–22.

86 Jennifer Bain

Page 29: Tonal Structure in the Music of Machaut

propose the FY causa necessitatis to correct the augmented fifth and make it perfect,which results in an unusual underlying progression (see the reduction inEx. 22). The harmonic syntax becomes clearer, however, if the cY is understood as amelodic decoration and the F is left as it is to participate in the F/d sixth to E/e octavedirected progression (Ex. 23).55


Examining monophonic and polyphonic virelais, ballades and rondeaux, I haveargued that melodic semitone motion is crucial to tonal organization – to theestablishment of focal pitches – in the music of Guillaume de Machaut. The placementand direction of melodic semitone motion in three-note monophonic cadential figuresrelate directly to the projection of stability and instability at points of cadential arrival.

55 Lucy Cross and Lawrence Earp both also accept the F as it stands. Cross, ‘Chromatic Alteration’, 285; andEarp, ‘Genre in the Fourteenth-Century French Chanson: The Virelais and the Dance Song’, MusicaDisciplina, 42 (1991), 133.

Ex. 22 Proposed adjustment in tenor of Cinc, un (R6), bar 2, according to Ludwig and Schrade.

Ex. 23 Cinc, un (R6) without chromatic adjustment.

Tonal structure and the melodic role of chromatic inflections in Machaut 87

Page 30: Tonal Structure in the Music of Machaut

Moreover, semitone motion as melodic decoration in a polyphonic context cansuggest focal pitches that are unsupported by the contrapuntal environment.Although I have focused only on the music of Machaut, these conclusions could havefar-reaching consequences for the understanding of fourteenth-century French musicin general.

Medieval singers had a range of possibilities and choices that affected many areasof performance, quite possibly including the frequency and degree to which theyinterpolated chromatic inflections in particular works. Perhaps some performances ofnotated songs were highly inflected while others were not. Cross’ statement that, ‘weshould begin with the attitude that there is only one correct reading, regardless ofwhether or not we are ourselves able to determine what that is’, betrays a twentieth-century Urtext mentality inappropriate to a pre-industrial era when no two versions ofanything – shoes, pots, jewellery, books – were identical.56

In order to make sense of an individual song either through analysis or perform-ance, however, it is necessary to make firm decisions about pitch content. Rather thanfocusing on contrapuntal requirements alone as a way to determine where and whenmedieval singers might have made chromatic adjustments to notated songs, I amsuggesting that melodic considerations should be taken into account as well. Mostmedieval music, after all, appears in parts, not in score; we would do well not tounderestimate the importance of the melodic line. In contrast to Lefferts, however, Ihave argued that, rather than signalling a systematic organization of pieces into settonal categories, melodic chromatic inflections function as one of many elements inthe tonal structuring of individual works. Tonal structure is not an inherent propertyof a piece that can be read from a code, but is rather something which can beconstructed from a piece and how it actually proceeds.

56 Cross, ‘Chromatic Alteration’, 73.

88 Jennifer Bain