1 Mary Wolinski provides a clear, succinct overview of the medieval hocket at www.the-orb.net/encyclop/culture/music/hocket.html. See also Elizabeth Eva Leach's fascinating discussion of hocketing throughout chapter 4 of Sung Birds. Leach, Elizabeth Eva, Sung Birds: Music, Nature, and Poetry in the Later Middle Ages (Ithaca and London, 2007), 175–88, 198–202, 210–37Google Scholar.

2 It is possible that the four-voice In seculum hocket discovered by Peter Jeffery dates from c.1300 and that A l'entrade d'avrillo described by Jacques de Liège in his Speculum musicae may likewise have been composed in the early fourteenth century. Neither of these pieces, however, can be said to represent the Ars Nova aesthetic; each was composed at least fifty to sixty years before Machaut's Hoquetus David. Jeffery, Peter, ‘A Colores and a Mensural Sequence in an Unknown Fragment’, Journal of the American Musicological Society, 37 (1984), 1–48CrossRefGoogle Scholar. Jacobus of Liège, , Speculum Musicae, Liber Septimus, ed. Bragard, Roger, Corpus Scriptorum de Musica, 3/7 (Rome, 1973), 70–1Google Scholar.

3 There are over thirty recordings of the complete Messe de Nostre Dame and more than twenty-five of one or more of its parts. Douce dame jolie (V4) has been recorded more than fifty times and Comment qu'a moy lonteinne (V5) twenty-four times. The Hoquetus has twenty-three recordings. For discography information up to 1994, see Earp, Lawrence, Guillaume de Machaut: A Guide to Research (New York and London, 1995), 406–7Google Scholar. For more recent data see www.medieval.org/emfaq/composers/machaut.html.

4 Leech-Wilkinson, Daniel, ‘Compositional Procedure in Machaut's “Hoquetus David”’, Royal Music Association Research Chronicle, 16 (1980), 99–109CrossRefGoogle Scholar.

5 Robertson, Anne Walters, Guillaume de Machaut and Reims: Context and Meaning in his Musical Works (Cambridge, 2002), 224–56Google Scholar.

6 ‘Elle ne présente plus, pour nous du moins, l'intérêt musical d'un motet ou de la Messe, mais apparaît plutôt comme un dictionaire de combinaisons rythmiques réalisées au moyen de trois voix coupées de pauses apparemment imprévues. C'est un jeu assez curieux.’ Machabey, Armand, Guillaume de Machault 130?–1377: La vie et l'oeuvre musical, 2 vols. (Paris, 1955), 2:134Google Scholar. Translation mine. Emphasis on musical is Machabey's.

7 While I suspect that its relative neglect in scholarship is mainly due to the lack of a known historical context for the piece until recently, as well as the fact that the genre was largely passé by the time Machaut composed it, the Hoquetus's lack of accompanying poetry may also be a contributing factor.

8 Leech-Wilkinson, ‘Compositional Procedure’, 100–1; Robertson, Guillaume de Machaut and Reims, 228, in which she identifies the motet as the ‘next-closest genre’ to the hocket; Hoppin, Richard, Medieval Music (New York, 1978), 420Google Scholar.

9 The melisma occurs at the end of the Alleluia verse Nativitas gloriose Virginis. Earp, Guide to Research, 328; Robertson, Guillaume de Machaut and Reims, 226.

10 For example, three motet tenors have thirty pitch colores and another three have forty pitches. The Hoquetus David's color has four melodic thirds, two fourths and one fifth. All but four of the twenty motets with chant-based tenors have tenors with thirds; nine of the twenty have fourths; and five of the twenty have a single perfect fifth, as in the David tenor. For a table that summarises the melodic characteristics of all twenty chant-based tenors, see Hartt, Jared, ‘The Three Tenors: Machaut's Secular Trio’, Studi Musicali, 38 (2009), 237–71, at 240Google Scholar.

11 G is Machaut's second most-selected tenor final in the motets: ten of the twenty tenor melodies conclude on F, five on G, three on D, one on c, and one on a. In Motet 22, although the chosen tenor segment concludes on D, Machaut ends the motet mid-tenor on F; for this reason, Motet 22 is included in the F category. The tenor of Motet 23 is the lone selected chant melody to conclude on a, but in this case, the contratenor sounds below on D at the work's conclusion.

12 Of Machaut's twenty chant-based tenors, in fourteen cases he divides one color into taleae, in five cases he takes two colores and divides the resulting number of pitches into equal parts, and in one case (Motet 14), he takes three colores and divides the resulting number of pitches into equal parts. A table that describes the various ways Machaut organises all of his chant-based motet tenors is provided in Hartt, , ‘Tonal and Structural Implications of Isorhythmic Design in Guillaume de Machaut's Tenors’, Theory and Practice, 35 (2010), 57–94, at 62Google Scholar.

13 In all of the motets, diminution is created by reading each note value in the tenor as the next smaller note value (e.g. a long becomes a breve, a breve becomes a semibreve, etc.), which most often leads to a reduction of each note value by one half or one third.

14 Gilbert Reaney points out that the fourteenth-century theorist Egidius de Murino identifies this as a tenor ordinatus. Reaney, Gilbert, Guillaume de Machaut, Oxford Studies of Composers 9 (New York and London, 1971), 67Google Scholar. An easily accessible example of a motet with a tenor ordinatus is Aucun vont/Amor qui cor/Kyrie, found in the Turin and Montpellier manuscripts, with an edition in Hoppin, Richard, Anthology of Medieval Music (New York, 1978), 112–14Google Scholar.

15 Although none of the motet tenors feature such a straightforward talea rhythm, it is worth noting that in Motet 6, Machaut employs a different tenor rhythm in each of the motet's two parts. As I discussed elsewhere, the second section is not a diminution of the first; rather, Machaut composes a new talea rhythm using note values that are similar to the tenor's first section. Hartt, ‘Tonal and Structural Implications’, 63.

16 There are other cadences prior to this in the Hoquetus, but, as will be discussed below, the Hoquetus's ‘major’ cadences occur when all three voices come to rest for the duration of an entire perfect long. Leech-Wilkinson points out that the simultaneous longs in the Hoquetus's first section are spaced out along the lines of an approximate 2:2:1 ratio (at bars 35, 70 and 87, and thus after thirty-five bars, after another thirty-five bars, and after seventeen bars). Leech-Wilkinson, ‘Compositional Process’, 107.

17 The most readily available editions of the Hoquetus David appear in Schrade, Leo, ed., The Works of Guillaume de Machaut, Polyphonic Music of the Fourteenth Century, 3 (Monaco, 1956), 65–7Google Scholar, and Ludwig, Friedrich, ed., Guillaume de Machaut: Musikalische Werke, Publikationen älterer Musik, 4 (Leipzig, 1943), 21–3Google Scholar. The problems found in the editions and transcriptions published to date are discussed below in Part III. The musical examples throughout this article are based on Ferrell 1 (Cambridge, Corpus Christi College, Parker Library (on loan), olim Vogüé, fol. 334v–335r), the first Machaut manuscript to contain the Hoquetus David. I thank Gill Cannell and Suzanne Paul, the sub-librarians at the Parker Library at Corpus Christi College, Cambridge, for granting me the opportunity to study Ferrell 1. The manuscript has been recently digitised and may be viewed on the Digital Image Archive of Medieval Music (DIAMM) website. In addition to ‘Ferrell 1’, I employ the following manuscript sigla throughout: MS A (BNF, fonds français 1584) and MS C (BNF, fonds français 1586).

18 For the sake of clarity, triplum, hoquetus and tenor (non-capitalised and non-italicised) are employed here when referring to specific voice parts, but Hoquetus or Hoquetus David (capitalised and italicised) are used when referring to the work as a whole.

19 Leech-Wilkinson, ‘Compositional Process’, 100. Or put another way, an upper-voice breve in the Hoquetus, for example, would be equivalent to – and notated as – an upper-voice semibreve in one of his motets.

20 As Leech-Wilkinson has shown, the composite rhythm in L₂ is one of the two most commonly employed ‘rhythmic cells’ throughout the Hoquetus, occurring nineteen times (see also L₈ and L₉ in Ex. 2). The other most frequently used rhythmic cell (employed nineteen times) occurs in L₁₀ and L₁₁ in Ex. 2. Leech-Wilkinson, ‘Compositional Process’, 104.

21 The bar numbers here and in the example captions refer to the Schrade and Ludwig editions; when bar numbering differs in the two editions, both sets of numbers are provided, as in Ex. 3b.

22 Further, the poetry in the triplum at this point, ‘And it is very clear’ (Et c'est tout cler), thus takes on double meaning!

23 Exact rhythmic correspondence does not begin until the third breve of each subsequent talea (t₂ and t₃).

24 These two passages from Motet 8 are perhaps indicative of the constant overlap discussed by the early fourteenth-century theorist Johannes de Grocheo in his description of the genre: ‘Anyone who wants to make a two-part hocket arrangement, i.e. for a first and second singer, must divide the song or tune which is to be so arranged and apportion it accordingly to each.… For in this way one overlaps the other in the manner of roof tiles, and thus they will cut each other off continually.’ (Volens autem hoquetum ex duobus, puta primo et secundo, componere debet canturn vel cantilenam, supra quod fit hoquetus, partiri et unicuique partem distribuere.… Sic enim unus iacet super alium ad modum tegularum et cooperturae domus et sic continua abscisio fiet.) Rohloff, Ernst, ed., Der Musiktraktat des Johannes de Grocheo (Leipzig, 1943), 57–8Google Scholar. Translation from Sanders, Ernest H. ‘The Medieval Hocket in Practice and Theory’, The Musical Quarterly, 60 (1974), 253Google Scholar. William Dalglish and Leech-Wilkinson also cite and provide their own translations of the passage. Dalglish, William, ‘The Hocket in Medieval Polyphony’, The Musical Quarterly, 55 (1969), 344–63, at 363CrossRefGoogle Scholar; Leech-Wilkinson, ‘Compositional Process’, 102.

25 Hoppin suggests that there are similarities between the Hoquetus David and examples of the genre from the previous century: ‘The David Hocket is archaic enough … [and] resembles the so-called instrumental motets of the Bamberg Codex’ (Medieval Music, 420). Reaney calls the Hoquetus David ‘an off-shoot of the thirteenth-century motet’ (Guillaume de Machaut, 67).

26 For a list of surviving thirteenth-century examples of the genre and sources in which they are found, see Jeffery, Peter, ‘A Four-Part “In seculum” Hocket and a Mensural Sequence in an Unknown Fragment’, Journal of the American Musicological Society 37 (1984), 5–6CrossRefGoogle Scholar, and Dalglish, ‘The Hocket in Medieval Polyphony’, 359. (See also note 2 above that lists two additional hockets that may date from c.1300.) To Jeffery's and Dalglish's lists we can now add the two Manere hockets found in Dijon, recently recovered by Mary Wolinski. For transcriptions and a discussion, see Wolinski, Mary and Haggh, Barbara, ‘Two 13th-century Hockets on Manere Recovered’, Early Music 38 (2010), 43–57CrossRefGoogle Scholar. The most recent edition of the six hockets found in Bamberg, which also contains the Portare hocket from Montpellier, is Roesner, Edward H., ed., Le Magnus Liber Organi de Notre-Dame de Paris. Les Quadrupla et Tripla de Paris, 1 (Monaco, 1993), 260–2 and 264–6Google Scholar. An older edition of the Bamberg hockets is Aubry, Pierre, ed., Cent motets du XIIIe siècle publiés d'après le manuscrit Ed. IV .6 de Bamberg (Paris, 1908), 2:221–5 and 228–32 (edition), 1:62v–64v (facsimile), 3:155–8 (commentary)Google Scholar.

27 Plicas are indicated with smaller noteheads in the examples.

28 Mary Wolinski reminds us that the notation of both Manere hockets follows the rules of Franco of Cologne, which means that ‘two unequal semibreves are in the order minor and major, having the value of one-third and two-thirds of a tempus respectively.’ Thus, although the triplum's e and d are notated as two semibreves in Dijon, it is clear that they are to be performed in a short–long pattern. Wolinski and Haggh, ‘Two 13th-century Hockets’, 45. In the Bamberg codex, however, Roesner reminds us that the notation follows Lambert's rule that unequal semibreves may proceed as minor–major or the opposite, major–minor. Roesner, Le Magnus Liber Organi, 1:353. Thus, although the semibreves would probably be rendered in a short–long pattern (since the In seculum breve is a reduction of the breve-long rhythm of the original second-mode In seculum), it is nonetheless possible for the semibreves to be rendered in the opposite fashion. As Franco's rules were definitive by the late fourteenth century, and because of the notation in Ferrell 1, it is clear that the semibreves in Machaut's Hoquetus are to be performed in a short–long pattern.

29 Some pitch correspondences are also perhaps noteworthy, though at this point, I am not sure how significant they may be, especially since there is no current evidence that Machaut knew these hockets specifically. Nonetheless, in the In seculum breve hocket, for instance, there is a recurring pitch-specific C–D–E motive found in the triplum across L₁–L₂ and again across L₃–L₄, in the hoquetus across L₁–L₂, and in the tenor across L₃–L₄. The C–D–E motive also comprises the first three pitches of the Hoquetus David's tenor, as well as its first three pitches of the triplum.

30 In more than half of the motets, at no point does an upper voice cross below the tenor. A list of occurrences that involve the motetus crossing below appears in Hartt, ‘The Three Tenors’, 254 n. 39.

31 I argue that the frequent voice crossing in the three motets with secular tenors is in part a response to the highly repetitive melodic structures of their tenors that are based on irregular virelais (Motets 16 and 20) and the rondeau (Motet 20). See Hartt, ‘The Three Tenors’, 254–7 and 260.

32 Machaut does, however, compose this type of sonority (as an a/a/a concord) at the beginning of one of his secular songs, Ballade 29, which is further made unusual by the fact that it is triple texted. See Bain, Jennifer, ‘“Messy Structure”? Multiple Tonal Centers in the Music of Machaut’, Music Theory Spectrum, 30 (2008), 195–237, at 228CrossRefGoogle Scholar.

33 These were all completed before the Hoquetus: the three-voice motets (with the exception of Motet 4) first appear in MS C, compiled c.1350, while the Hoquetus David along with the later four-voice motets (Motets 21, 22 and 23) and the Mass first appear in Ferrell 1, compiled in the 1360s.

34 ‘U’ in the examples and text denotes a unison.

35 Anna Zayaruznaya discusses the significance of crossed upper voices in Machaut's motets. Zayaruznaya, Anna, ‘“She has a Wheel That Turns…”: Crossed and Contradictory Voices in Machaut's Motets’, Early Music History 28 (2009), 185–240CrossRefGoogle Scholar.

36 By drawing upon ‘Quicumque voluerit duos contrapuncti’, a fourteenth-century treatise that addresses three-voice sonorities, as well as the work of Sarah Fuller, I have elsewhere advanced a detailed categorisation of sonority that distinguishes between intervals and their compounds, and that takes into account the quality of interval (perfect or imperfect) found in a sonority's outer voices. Hartt, , ‘Rehearing Machaut's Motets: Taking the Next Step in Understanding Sonority’, Journal of Music Theory, 54 (2010), 179–234CrossRefGoogle Scholar. Fuller, Sarah, ‘On Sonority in Fourteenth-Century Polyphony: Some Preliminary Reflections’, Journal of Music Theory, 30 (1986), 35–70CrossRefGoogle Scholar. ‘Quicumque voluerit duos contrapuncti’ appears in de Coussemaker, Edmond, ed., Scriptorum de musica medii aevi nova series a Gerbertina altera, 3 (Paris, 1869), col. 92b–93bGoogle Scholar. For a translation, see Hartt, ‘Rehearing Machaut's Motets’, 184–6.

37 Although two of the three motets with secular tenors (Motets 11 and 16) begin with different sonority types (PI and PP, respectively – Motet 20 begins with a P2 sonority), these sonorities still contain three different pitches.

38 On contrapunctus, see especially the foundational studies of Klaus-Jürgen Sachs and Ernst Apfel. The work of Sarah Fuller has been instrumental in the laying the groundwork for the application of contrapunctus theory in the analysis of Machaut's music. Margaret Bent, Elizabeth Eva Leach, and Jennifer Bain have also produced much important scholarship that has allowed for the advancement of our current understanding of the inner-workings of Machaut's music. See also my ‘Rehearing Machaut's Motets’ that draws upon and in some cases extends the work of these scholars. Klaus-Jürgen Sachs, Der Contrapunctus im 14. und 15. Jahrhundert: Untersuchungen zum Terminus, zur Lehre und zu den Quellen, Beihefte zum Archiv für Musikwissenschaft 13 (Wiesbaden, 1974). Apfel, Ernst, Diskant und Kontrapunkt in der Musiktheorie des 12. bis 15. Jahrhunderts (Wilhelmshaven, 1982)Google Scholar. Sarah Fuller, ‘On Sonority in Fourteenth-Century Polyphony’. Fuller, ‘Tendencies and Resolutions: The Directed Progression in Ars Nova Music’, Journal of Music Theory, 36 (1992), 229–58CrossRefGoogle Scholar. Eadem, ‘Organum-discantus-contrapunctus in the Middle Ages’, in The Cambridge History of Western Music Theory, ed. Christensen, Thomas (Cambridge, 2002), 477–502CrossRefGoogle Scholar. Bent, Margaret, ‘The Grammar of Early Music: Preconditions for Analysis’, in Tonal Structures in Early Music, ed. Judd, Cristle Collins (New York, 1998), 15–59Google Scholar. Eadem, Counterpoint, Composition, and Musica Ficta (New York and London, 2002)Google Scholar. Leach, Elizabeth Eva, ‘Counterpoint and Analysis in Fourteenth-Century Song’, Journal of Music Theory, 44 (2000), 45–79CrossRefGoogle Scholar. Eadem, , ‘Interpretation and Counterpoint: The Case of Guillaume de Machaut's De toutes flours (B31)’, Music Analysis, 19 (2000), 321–51Google Scholar. Bain, Jennifer, ‘Theorizing the Cadence in the Music of Machaut’, Journal of Music Theory, 47 (2003), 325–62CrossRefGoogle Scholar.

39 Although Jacobus of Liège lists the minor seventh to perfect fifth progression as an example of a cadentia, he also enumerates numerous other dissonant intervals as possibilities; for instance, the second seeking a unison, and the fourth seeking a unison or fifth as examples (among numerous others). As David Maw has recently shown, Jacobus's notion of cadentia is distinct from the idea outlined in other fourteenth-century treatises that an imperfect concord seeks a perfect concord, but is instead ‘related to an aesthetic conception of polyphony, one that developed in the thirteenth century and was distinctly different from that of the new musical order emergent at the beginning of the fourteenth.’ Maw, David, ‘Redemption and Retrospection in Jacques de Liège's Concept of Cadentia’, Early Music History, 29 (2010), 79–118, at 81CrossRefGoogle Scholar.

40 ‘Since the f cells [the simultaneous longs] stand out so strongly it is inevitable that the chords they carry will also be stressed.’ Leech-Wilkinson, ‘Compositional Process’, 107.

41 Fuller, ‘Tendencies and Resolutions’; Cohen, David, ‘“The Imperfect Seeks Its Perfection”: Harmonic Progression, Directed Motion and Aristotelian Physics’, Music Theory Spectrum, 23 (2001), 139–69CrossRefGoogle Scholar; Leach, , ‘Gendering the Semitone, Sexing the Leading Tone: Fourteenth-Century Music Theory and the Directed Progression’, Music Theory Spectrum, 28 (2006), 1–21CrossRefGoogle Scholar; Fuller, , ‘Concerning Gendered Discourse in Medieval Music Theory: Was the Semitone “Gendered Feminine?”’, Music Theory Spectrum, 33 (2011), 65–89CrossRefGoogle Scholar; Leach, , ‘Reading and Theorizing Medieval Music Theory: Interpretation and Its Contexts’, Music Theory Spectrum, 33 (2011), 90–8CrossRefGoogle Scholar.

42 This type of progression is commonplace throughout the Hoquetus (and the motets); in fact, this same voice-leading comprises the Hoquetus's first tendency progression, leading into L₃ in Ex. 5, but with b♭ to a in the lowest-sounding voice.

43 This exact progression concludes Motet 11 (again, one of the three motets with secular tenors). Motet 16, another motet with a secular tenor, concludes with a C♯¹²₋₁₀ to D¹²₈ progression.

44 If one takes the entire long (L₂) to constitute the tendency sonority, however, then the progression could be viewed as an ‘imaginary’ G⁵₋₃ sonority that resolves to an A⁵ concord. The melodic G/b♭ minor third in the triplum would then be interpreted as resolving to a in L₃.

45 A progression that can be interpreted along the same lines occurs in Motet 8 above (Example 3c): above the tenor's G in bar 51, the d/f♯ major third (of which f♯ forms a dissonant major seventh with the tenor) resolves to a c/g perfect fifth.

46 Progression e also stands out since it marks the only moment of rest that is imperfect in sound. Thus, while the rest in rhythmic activity indicates repose, the instability of the major third simultaneously yields forward motion.

47 This progression – as well as several others from Motet 4 – is discussed in detail in Hartt ‘Rehearing Machaut's Motets’, 212–25.

48 Leech-Wilkinson, Daniel, Machaut's Mass: An Introduction (Oxford, 1990), 85Google Scholar. Recently (with a journal issue date of 2003–8 but published in 2010), Roland Jackson makes a similar observation: ‘In the fourteenth century the 7th began to appear as a sonority in its own right, i.e. as an important preparatory interval leading into a cadence … By lingering momentarily on the 7th, for an S[emibreve] or even a B[reve] duration, a clear sense of tension is invoked prior to a resolution on the pure consonance of the fifth.’ While I agree with both of these points, most of Jackson's examples involving the seventh do not constitute cadences (as in phrase endings). Perhaps he was referring to cadentia when referring to the seventh as a cadential preparatory element, though he makes no mention of this. He provides several interesting internal-to-the phrase 7–5 progressions (as in Motet 20 discussed above in Example 12, and he also cites a passage from Philippe de Vitry's ‘Hugo, Hugo’), but his mention of the seventh in Motet 4 unfortunately relies on the Schrade edition, which contains an erroneous f in the motetus at the beginning of bar 5; see his Example 10b, though the triplum and motetus parts are mislabelled. The correct pitch, d, which is found in the Machaut manuscripts (see also L₃ of Ex. 11), yields a consonant fifth with the tenor's G, and only at the end of the long is a fleeting seventh to fifth progression initiated that involves the tenor and the motetus. Jackson, Roland, ‘Guillaume de Machaut and Dissonance in Fourteenth Century French Music’, Musica Disciplina, 53 (2003–8), 7–49Google Scholar, the quotation at 18.

49 Bent, Margaret, ‘The “Harmony” of the Machaut Mass’, in Machaut's Music: New Interpretations, ed. Leach, Elizabeth Eva (Woodbridge, 2003), 85Google Scholar.

50 In his brief description of the Hoquetus, Reaney comments upon this progression, in which ‘dissonances too are created … by the insertion of a note into a chord after a rest in that part, in other words by hocket’. Reaney, Guillaume de Machaut, 67.

51 Bent, ‘The Grammar of Early Music’, 27.

52 Parmi ses nombreuses compositions, on rencontre une pièce instrumentale écrite en ‘double hocquet’. Translation mine. Gastoué, Amédée, L'orgue en France, de l'antiquité au début de la période classique (Paris, 1921), 56Google Scholar.

53 In a publication from the following year, Gastoué again provides a transcription of the opening, this time with the upper voices in the correct octaves, but still with the incorrect rhythms and pitches. Gastoué, , Les primitifs de la musique française (Paris, 1922), 63Google Scholar.

54 ‘L'écriture est extrêmement recherchée et semble convenir aux instruments ou à l'orgue plutôt qu'aux voix.’ Translation mine. Machabey, Guillaume de Machault 130?–1377, 2:133.

55 Woodstra, Chris, Brennan, Gerald, Schrott, Allen, eds., All Music Guide to Classical Music: The Definitive Guide to Classical Music (San Francisco, 2005), 782Google Scholar.

56 Schrade's edition is currently the most accurate. Aside from the incorrect pitches in bar 94 (in the hoquetus voice, c and d should be d and e), the only other pitch differences between Schrade's edition and Ferrell 1 involve ficta: for example, in the triplum in bar 55 and in the hoquetus in bar 67, the ♯ symbols are notated in Ferrell 1, but are absent in MS A; editorial ficta is consequently provided above each pitch in question in Schrade's edition.

57 Gaston Allaire also furnishes a transcription of the Hoquetus David on pages 49–54 of his study that employs the Hoquetus as a vehicle through which to argue that ‘the natural and flat signs in the original manuscript sources did not indicate chromatic alterations, bu[t] they were inserted by the singers according to a certain convention to guide correct solmisation’. Allaire, Gaston, ‘Les énigmes de l'Antefana et du double hoquet de Machault: une tentative de solution’, Revue de Musicologie, 66 (1980), 27–56, at 56CrossRefGoogle Scholar. He acknowledges that his transcription is based on Ludwig's, yet he notates the triplum an octave too high in bars 49–50. Allaire's study is very useful, however, in that he provides on pages 44–5 a plate of the complete Hoquetus as found in MS A.

58 ‘Das tp. perf. erscheint bei Gruppen von 3 semibr. in Form einer Achteltriole, während 2 semibr. als einfache Achtel wiedergegeben sind, ohne die theoretisch vorgeschriebene, aber bei schneller Bewegung bedeutungslose Alteration. [Two eighth notes] lautet also in buchstäblicher Umschrift stets [triplet quaver rest-crotcher note].’ Ludwig, ed., Guillaume de Machaut: Musikalische Werke, 23.

59 Grove Music Online, s.v. ‘Hocket’ (by Ernest Sanders), www.grovemusic.com (accessed 29 August 2011). Sanders, ‘The Medieval Hocket’, 246–56.

60 Whereas Dalglish and Aubry correctly exclude In seculum viellatoris from their lists of thirteenth-century hockets, and while Roesner rightly states that ‘is it almost certainly not an instrumental piece’, other sources identify all of the In seculum works (including In seculum viellatoris) as hockets. Dalglish, ‘The Hocket in Medieval Polyphony’, 359; Aubry, Cent motets, 3:158; Roesner, Le Magnus Liber Organi, 1:352; Jeffery, ‘A Colores’, 5; Leech-Wilkinson, ‘Compositional Procedure’, 99; Robertson, Guillaume de Machaut and Reims, 225 and 384 n. 4; Sanders, ‘The Medieval Hocket’, 250.

61 Jeffery, ‘A Colores’, 15–9. See also note 2.

62 I hasten to point out that I am by no means a performance practice expert and that I see nothing inherently wrong with an instrumental performance of the Hoquetus – indeed, there are a few pleasing recordings such as David Munrow's interpretation (Music of the Gothic Era, Early Music Consort of London, DG Archiv 2723 045 (LP), 1976; also released as Musical Heritage Society MHS 525643F (CD), 1997). The Hoquetus is a frequently recorded Machaut composition, and in all but one case is performed instrumentally. I suspect that an underlying reason for both of these facts – the abundant recordings and the instrumental performance – is that the Hoquetus is untexted. Matters such as diction, pronunciation and text intelligibility do not play a role, and because of the lack of poetry, instrumentalists can feel ‘safer’ in performing it without the fear of potentially stepping on the toes of performance practice experts. Moreover, due to the paucity of notated fourteenth-century instrumental music, performers would understandably relish the opportunity to play such a work.

63 Allaire erroneously indicates the span of the triplum to be G-dd. The G was likely an oversight, as the F♯ is found in his transcription of the score in bar 86, but the incorrect dd is due to the fact that he transcribed the triplum an octave too high in bars 49–50. Allaire, ‘Les énigmes’, 51 and 54.

64 In the penultimate bar of Motet 18, Schrade notates G in the motetus (which would incorrectly extend the motetus's range to a ninth). All manuscripts indicate b. The ‘sharp’ in Motet 8 and the ‘flat’ in Motets 8 and 12 are placed in parentheses; although they are not explicitly indicated in the manuscripts, they would likely be interpolated by the singers in order to yield perfect intervals and/or for the purposes of tendency progressions.

65 Guillaume de Machaut: Ballades, rondeaux, virelais, motets, Ensemble Gilles Binchois, Harmonic Records H/CD 8825, 1988; also released as Guillaume de Machaut: Le vray remède d'amour, Cantus C 9625, 2001. Mediaeval Carols. The Mystery of Christmas Night: Words and Music from the Middle Ages, Opus Anglicanum, Herald HAVPCD 212, 1997. Guillaume de Machaut: Les motets, Ensemble Musica Nova, Zig-Zag Territoires ZZT 021002.2, 2002, also released as Aeon AECD 1108, 2011. Guillaume de Machaut: Unrequited, Liber unUsualis, Liber unUsualis 1001, 2003. Guillaume de Machault: Messe de Nostre Dame, Felix Virgo/Inviolata, Schola Gregoriana of Cambridge, Herald HAVPCD 312, 2005.

66 The Mirror of Narcissus, Gothic Voices, Hyperion A66087 (LP), 1983; also released as CD A66087 (CD), 1987. Guillaume de Machaut: Motets and Music from the Ivrea Codex, The Clerks’ Group, Signum SIGCD 011, 1999. Machaut: Motets, Hilliard Ensemble, ECM ‘New Series’ 1823, 2004.

67 Robertson, Guillaume de Machaut and Reims, 241.

68 Machaut, Messe Nostre Dame/Motets et Estampies, Obsidienne, Calliope 9318, 2002. I am unclear, however, if the ensemble opted for this method of performance based on the inclusion of the David text in each of the triplum, hoquetus and tenor parts in the manuscripts, or because David is the associated text in the chant source.

69 Leech-Wilkinson, ‘Compositional Process’, 99; Robertson, Guillaume de Machaut and Reims, 95.

70 Robertson, Guillaume de Machaut and Reims, 225 and 284–5; Leach, Sung Birds, 185.

71 The original French appears in Blomqvist, Åke, Gace de la Buigne, Le roman des deduis (Paris, 1951), 375 (lines 8076–88)Google Scholar. Translation adapted from Leach, Sung Birds, 181–2. Gace de la Buigne (c.1305–c.1384) penned Le roman des deduis as an instruction manual in hunting and ethics for the youngest son of John II the Good. The 12,210-octosyllabic-lined work was very popular, surviving in no less than twenty-one manuscripts. See also www.arlima.net/eh/gace_de_la_buigne.html for a thorough bibliography on Le roman des deduis and for a comprehensive list of manuscripts that contain the allegory.

72 Et chantent trebles et motés, / Et qu'il font bien doubles hoqués. Blomqvist, Gace de la Buigne, 415 (lines 9201–2).

73 In the process of enumerating his various genres of composition in his Prologue, Machaut writes of double hockets in the plural: ‘Doubles hoqués et plaisans lais, Motés rondiaus et virelais’. Leech-Wilkinson points out, however, that Machaut's use of the plural could be ‘for grammatical rather than for statistical reasons.’ Leech-Wilkinson, ‘Compositional Procedure’, 99.