1 By ‘Ars Nova’ I mean here motets of French provenance from the first two-thirds of the fourteenth century, and not those larger and more notationally complex works that survive only in sources from the final decades of the century.

2 These counts include introitus sections (if any) and final longs. Petre/Lugentium is in fact considerably longer than Beatius/Cum humanum since it is written with perfect tempus and major prolation.

3 Petre/Lugentium was written in late 1342 or early 1343, and Christe/Veni has been dated to late 1359 or early 1360. The range of dates of c.1340 to 1360 for Beatius/Cum humanum is consistent with its intricate hockets as well as the source situation (see Appendix 2); a possible terminus ante quem is suggested by Joachim Lüdtke, who dates the Würzburg fragment to c.1365–75; ‘Kleinüberlieferung mehrstimmiger Musik vor 1550 in deutschem Sprachgebiet IV: Fragmente und versprengte Überlieferung des 14. bis 16. Jahrhunderts aus dem mittleren und nördlichen Deutschland’, Nachrichten Der Akademie Der Wissenschaften in Göttingen Philologisch-Historische Klasse, 6 (2001), 420–87, at 436. On the dating of Petre/Lugentium, see Wathey, Andrew, ‘The Motets of Philippe de Vitry and the Fourteenth-Century Renaissance’, Early Music History, 12 (1993), 119–50, at 133–5CrossRefGoogle Scholar. On the dating of Christe/Veni, see Robertson, Anne Walters, Guillaume de Machaut and Reims: Context and Meaning in His Musical Works (Cambridge and New York, 2002), 192–206 Google Scholar.

4 On the relevance of the term ‘introitus’ to reduced-voice openings of motets, see Anna Zayaruznaya, ‘[I]ntroitus: Untexted Beginnings and Scribal Confusion in the Machaut and Ivrea Manuscripts’, Digital Philology, forthcoming.

5 Impudenter/Virtutibus is edited in Leo Schrade, ed., The Roman de Fauvel; The Works of Philippe de Vitry; French Cycles of the Ordinarium Missae, Polyphonic Music of the Fourteenth Century 1 (Monaco, 1956), 91–6; for O canenda/Rex, see ibid., 106–9; and for Pictagore/O terra, Günther, Ursula, ed., The Motets of the Manuscripts Chantilly, Musée condé, 564 (olim 1047) and Modena, Biblioteca estense, a. M. 5, 24 (olim lat. 568), Corpus mensurabilis musicae 39 (Rome, 1965), 33–9Google Scholar.

6 I thank Anne Walters Robertson for the suggestion that a retrograde procedure might have been built into the tenor – that the standard bipartite two-color model with second color in diminution ran forwards and then backwards, mirroring pitches and/or rhythms after the midpoint of the hocket section – and that such a prograde–retrograde procedure might have resonated with the moral content of the texts.

7 A later analogue to such repetitive hocketing, though on a smaller scale, can be found in some of the texted hockets (bb. 40–5) of Comes Flandriae/Rector creatorum, a political motet from Bruges with texts about music which Reinhard Strohm dates to 1381. See his Music in Late Medieval Bruges (Oxford, 1985), 103–5 on the texts and dating, 204 for the edition.

8 The appendix and music examples below are not diplomatic transcriptions, but editions using a form of Ars Nova notation. Ligatures have been silently broken up to allow for notation in score, but have been taken into account for purposes of text underlay. Dots of division are not represented where bar lines do their work.

9 Anna Zayaruznaya, ‘Hocketing with the Times: Evidence of Reworkings in Ars nova Motets’, paper presented at Reworkings: Musical Re-Elaboration and Cultural Context, Schola Cantorum, Basel (November 2014), and forthcoming in the Basler Jahrbuch für historische Musikpraxis.

10 Jacobi Leodiensis Speculum musicae, ed. Roger Bragard, Corpus scriptorum de musica 3, vol. 7 ([Rome]: American Institute of Musicology, 1973), 89. A parallel passage uses ‘inserunt’: ‘a se repellunt cantus antiquos organicos, conductos, motellos, hoketos duplices, contraduplices et triplices, nisi quod aliquos illorum inserunt in motetis’ (ibid., 25). Previously I had interpreted these references as merely pointing to the hockets that appear near the ends of the taleae of many Nova, Ars motets (‘Hockets as Compositional and Scribal Practice in the ars nova Motet – A Letter from Lady Music’, Journal of Musicology, 30 (2013), 461–501, at 490)Google Scholar. I am now inclined to think that they may instead, or additionally, refer to more extreme insertions.

11 Chrétien appears in Machaut's Aucune/Qui (Motet 5) and Joseph of Exeter in the Fauvel motet Tribum/Quoniam.

12 Strubel, Armand, ed., Le roman de Fauvel (Paris, 2012), 666 Google Scholar. When not otherwise indicated, translations are my own.

13 Bent, Margaret, ‘Polyphony of Texts and Music in the Fourteenth-Century Motet: Tribum que non abhorruit/Quoniam secta latronum/Merito hec patimur and Its “Quotations”’, in Hearing the Motet: Essays on the Motet of the Middle Ages and Renaissance, ed. Pesce, Dolores (New York and Oxford, 1997), 82–103 Google Scholar.

14 Cf. bars 82–7 in Schrade's edition (The Roman de Fauvel, 60–3 [no. 30]), which is barred by longa. To facilitate comparison with Beatius/Cum humanum, Firmissime/Adesto has been edited here from the Brussels Rotulus, where it is notated with minims. The G in triplum bar 166 follows F-Pn 146, and the second minim tail in triplum bar 169 has been editorially supplied. While the possibility of a common source for both quotations cannot be dismissed out of hand, the scenario of Beatius/Cum humanum quoting Firmissime/Adesto is by far the more likely one, given the mensural nature of the quoted tune and its identical position in each triplum text. The quotation seems to be limited to the triplum voice. The motetus's pitches in Beatius/Cum humanum only accord with those of the motetus in Firmissime/Adesto during bars 203–6, making it unlikely that the lower-voice pitches were similar in the two passages.

15 Plumley, Yolanda, The Art of Grafted Song: Citation and Allusion in the Age of Machaut (Oxford and New York, 2013)CrossRefGoogle Scholar.

16 With primary focus on textual quotations, Boogaart, Jacques, ‘Encompassing Past and Present: Quotations and their Function in Machaut's Motets’, Early Music History, 20 (2001), 1–86 CrossRefGoogle Scholar. Wathey, Andrew, ‘Auctoritas and the Motets of Philippe de Vitry’, in Citation and Authority in Medieval and Renaissance Musical Culture: Learning from the Learned, ed. Clark, Suzannah and Leach, Elizabeth Eva (Woodbridge and Rochester, 2005), 67–78 Google Scholar.

17 Several citations in the upper voices have also been noted: Plumley (The Art of Grafted Song, 231–46) suggested that the Ivrea motet Mon chant/Qui doloreus quotes several songs. Loose melodic correspondences within and between motets and songs are discussed in Tamsyn Rose-Steel, ‘French Ars Nova Motets and their Manuscripts: Citational Play and Material Context’, Ph.D. diss., University of Exeter (2011), 60–1, 99, 145–8.

18 Margaret Bent (‘Polyphony of Texts and Music’, 96) has argued that the mid-point of Tribum/Quoniam constitutes ‘a clearly audible musical quotation of the beginning of Garrit Gallus/In nova fert’ which ‘involves all three parts, changing their roles and applying light camouflage’; see her Example 4.5, bottom two systems. Note the temporal transformation involved in the camouflaging: three breves in the middle system correspond to six in the bottom one. And an anonymous reader kindly brought to my attention that there is a correspondence of text and rhythm – but not pitch – connecting the words ‘musicorum collegio’ when they appear in Musicorum/In templo Dei and Apollinis/Zodiacum. Harrison, Frank Llewellyn, ed., Musicorum collegio: Six Fourteenth-Century Musicians’ Motets (Monaco, 1986), nos. 1 and 2Google Scholar.

19 ‘Modus perfectus dicitur esse, quandocumque ita est, quod aliquis modus desinit per talem quantitatem vel per talem modum sicut per illam, qua incipit’. Reimer, Erich, ed., Johannes de Garlandia: De mensurabili musica, kritische Edition mit Kommentar und Interpretation der Notationslehre, Beihefte zum Archiv für Musikwissenschaft 10–11, 2 vols. (Wiesbaden, 1972), 1:39Google Scholar.

20 Ibid. , 1:49–51.

21 That is, assuming that Franco wrote in c.1280, and Lambertus in the 1270s; see Frobenius, Wolf, ‘Zur Datierung von Francos Ars cantus mensurabilis ’, Archiv für Musikwissenschaft, 27 (1970), 122–7CrossRefGoogle Scholar.

22 For ‘longior longa’ see de Moravia, Hieronymus, Tractatus de musica, ed. Meyer, Christian and Lobrichon, Guy, Corpus Christianorum, Continuatio Mediaevalis 250 (Turnhout, 2012), 177 Google Scholar. For the longa ‘ultra mensuram’, see Reimer’annes de Garlandia, 36–8.

23 ‘The imperfect [long] does not know how to be made except through the following or preceding breve . . . because the long and the breve [together] (and vice versa) always make one perfection’ (‘unde considerandum est quod imperfect fieri nequit nisi . . . brevi sequente seu precedente, quoniam longa et brevis et econverso semper unam perfectionem faciunt’), Meyer, Christian, ed., and Desmond, Karen, trans., The ‘Ars musica’ Attributed to Magister Lambertus/Aristoteles (Farnham and Burlington, 2015), 70–1Google Scholar. For an argument against this part of Lambertus's treatise and an assertion that the two-breve long deserves to be called ‘perfect’ see Yudkin, Jeremy, ed. and trans., De musica mensurata: The Anonymous of St. Emmeram; Complete Critical Edition (Bloomington, IN, 1990), 102–7Google Scholar.

24 See discussion in Meyer, The ‘Ars musica’, xxv (trans. Barbara Haggh-Huglo).

25 de Colonia, Franco, Ars cantus mensurabilis, ed. Reaney, Gilbert and Gilles, André, Corpus scriptorum de musica 18 ([Rome], 1974), 29–30 Google Scholar; trans. Wegman, modified.

26 See also the discussion of these passages from Franco and Lambertus in Tanay, Dorit, Noting Music, Marking Culture: The Intellectual Context of Rhythmic Notation, 1250–1400 (Holzgerlingen, 1999), 42–5Google Scholar. The anonymous of St Emmeram links the Trinity and the perfection of the number three to several aspects of music including the three consonances and the kinds of notes (longs, breves and semibreves), but interestingly he does not mention the perfect longa in this context; see Yudkin, De musica mensurata, 76.

27 Maw, David, ‘Redemption and Retrospection in Jacques de Liège's Concept of Cadentia ’, Early Music History, 29 (2010), 79–118, at 104Google Scholar.

28 It is instructive that the avoidance of this very circumstance was one of the arguments Lambertus made against those who call perfect longs ‘ultra mensuram’: ‘This is false, because if it were true then a natural song could be made from all imperfects, because they say that the imperfect [i.e. the duple] is perfect [i.e. is complete, being recta]’ (‘quod falsum est, quia si verum esset, tunc posset fieri cantus naturalis de omnibus imperfectis, quoniam imperfectam dicunt esse perfectam’). Mayer, The ‘Ars musica’, 70–1 (translation modified).

29 Siena, Biblioteca comunale, l.v.30, 129r; ed. and trans. Karen Desmond at www.arsmusicae.org/. The Seville source for the treatise (Seville, Biblioteca capitular y colombina, sign.: 5–2–25) has this text in a more prefunctory form: ‘Numerus vero ternarius perfectus est assumptus a Trinitate etcetera’.

30 Jacobi Leodiensis Speculum musicae, 7:2. Translations are by Rob Wegman and can be accessed at https://princeton.academia.edu/RobCWegman/Translations.

31 ‘For between good and perfect deeds and bad and imperfect [deeds] there is a great difference, great variation, as compared to each other and to God. For he approves and rewards the former, and punishes and reproves the latter, since he is the cause of good things, and not of bad things’ (‘Est tamen inter actus bonos et perfectos et inter malos et imperfectos magna distinctio, magna variatio, ut inter se et ad Deum conferuntur. Hos enim approbat et remunerat, illos punit et reprobat, quia ipse causa bonorum, non malorum existit’), Jacobi Leodiensis Speculum musicae, 7:61.

32 Perhaps he is thinking of Augustine's discussion of the harmonia of the proportion of 1:2 in De trinitate, iv.4.

33 Firmissime/Adesto must have been in existence by c.1317–19, when it was copied into F-Pn 146. The 1324/5 dating of the Speculum is based on faulty reasoning about its relationship with the Docta sanctorum, and the treatise could as easily be a product of the 1330s as the 1320s; see Desmond, Karen, ‘New Light on Jacobus, Author of Speculum musicae ’, Plainsong and Medieval Music, 9 (2000), 19–40, at 35Google Scholar.

34 Maw, ‘Redemption and Retrospection’, 106. Maw's analysis of the passage discussed here focuses on the light it can shed on Jacobus's theorisation of imperfect concord and cadentia.

35 Although tempus was also characterised by the words ‘perfect’ and ‘imperfect’ in Ars Nova theory, Jacobus's objections are limited to imperfect modus, since he supported the Petronian division of the breve. Neither did he link prolation with the Trinity, perhaps because it was called ‘minor’ or ‘major’ rather than imperfect or perfect, and was often framed as a quality or subset of tempus.

36 ‘Quociens uero due pluresue reperiuntur pause inmediate quarum duo ualeat tempora modus est imperfectus ut in moteto Adesto sancta trinitas’. Paris, Bibliothèque Nationale, lat. 14741, fol. 4v. Transcribed in the Thesaurus Musicarum Latinarum, www.chmtl.indiana.edu/tml/14th/ANOQUAE_MPBN1474.html. In some cases the citations were too short to include ‘trinitas’.

37 Ibid .

38 Strubel, Roman de Fauvel, 137–8.

39 Vetter, Eddie, ‘Philippe de Vitry and the Holy Trinity: An Early Manifesto of the Ars Nova’, in Liber amicorum Chris Maas – Essays in Musicology in Honour of Chris Maas on his 65th Anniversary, ed. Wegman, Rob C. and Vetter, Eddie (Amsterdam, 1987), 4–14, at 8Google Scholar.

40 Robertson, Anne Walters, ‘Which Vitry? The Witness of the Trinity Motet from the Roman de Fauvel ’, in Hearing the Motet: Essays on the Motet of the Middle Ages and Renaissance, ed. Pesce, Dolores (Oxford, 1997), 52–81, at 53Google Scholar.

41 Ibid. , 53.

42 Ibid. , 56.

43 The length of Beatius/Cum humanum and the style and notation of its unusual central section suggest that it post-dates not only Firmissime/Adesto, but probably also the Speculum musicae.

44 Jacobi Leodiensis Speculum musicae, 7:95; translation reproduced from Page, Christopher, Discarding Images: Reflections on Music and Culture in Medieval France (New York, 1993), 70 Google Scholar.

45 Colla/Bona is edited in Schrade, The Roman de Fauvel, 85–7; Lerch, Irmgard, Fragmente aus Cambrai: Ein Beitrag zur Rekonstruktion einer Handschrift mit spätmittelalterlicher Polyphonie, Göttinger musikwissenschaftliche Arbeiten 11, 2 vols. (Kassel, 1987), 2:155–60Google Scholar. For Zolomina/Nazarea, see Frank Llewellyn Harrison, ed., Motets of French Provenance, Polyphonic Music of the Fourteenth Century 5 (Monaco, 1968), 62–5.

46 See Clark, Alice, ‘Listening to Machaut's Motets’, The Journal of Musicology, 21 (2004), 487–513 CrossRefGoogle Scholar.

47 On hockets introduced partway through motets (almost always with the start of a diminution section), see Zayaruznaya, Anna, The Monstrous New Art: Divided Forms in the Late Medieval Motet (Cambridge, 2015), 79–80 CrossRefGoogle Scholar.

48 For Impudenter/Virtutibus see Schrade, The Roman de Fauvel, 91–6.

49 That is, if the original talea were sixty-six breves, its diminished or renotated version would relate to it in the ratio of 3:1 or 2:1, depending on whether it was in perfect or imperfect modus to begin with.

50 See Zayaruznaya, The Monstrous New Art, 227–34.

51 For example, Robertson notes that the first color of Firmissime/Adesto is three times as long as the second; she also turns our ear to the bigger groupings suggested by maximodus. ‘Which Vitry’, 53–6.

52 It is unlikely that Machaut was responsible for Beatius/Cum humanum or Firmissime/Adesto, since neither motet is present in any of the books we refer to as his collected works.

53 On Vitry and the theoretical tradition, see below. The author of the 1351 Quatuor principalia refers to ‘pluribus motetis quos composuit praedictus Philippus, flos quidem musicorum’; see Luminita Florea Aluas, ‘The Quatuor Principalia Musicae: A Critical Edition and Translation, with Introduction and Commentary’, Ph.D. diss., Indiana University (1996), 421. On Vitry and attribution more broadly, see Bent, Margaret and Wathey, Andrew, ‘Vitry, Philippe de’, The New Grove Dictionary of Music and Musicians, ed. Sadie, Stanley (London, 2001), 26:806–12Google Scholar.

54 The arguments for Vitry's authorship of Firmissime/Adesto are summarised in ibid., 811. It should, however, be noted that treatise citations are no longer considered valid evidence for attributing works to Vitry.

55 Desmond, Karen, ‘Did Vitry Write an ars vetus et nova?’, Journal of Musicology, 32 (2015), 4 CrossRefGoogle Scholar.

56 Similarities in diction between Tuba/In arboris and Firmissime/Adesto have been noted by Kügle, Karl, The Manuscript Ivrea, Biblioteca capitolare 115: Studies in the Transmission and Composition of Ars Nova polyphony (Ottawa, 1997), 107 Google Scholar, note 59; those between Firmissime/Adesto and Le chapel des trois fleurs de lis in Robertson, ‘Which Vitry?’, 56; those between Cum statua/Hugo and O creator/Phi millies in Zayaruznaya, The Monstrous New Art, 131–41.

57 Anna Zayaruznaya, ‘The Late Works of Philippe de Vitry’, paper delivered at All Souls College, Oxford (March 2015), publication in preparation.

58 I thank Karl Kügle for the suggestion that this motet could also have been written in honour of Pierre Roger's elevation to cardinal in 1338. While Beatius/Cum humanum spends more time criticising than lauding, Vitry's Petre/Lugentium mixes praise of its dedicatee (here certainly Pierre Roger as Clement VI) with criticism of his subjects.

59 On the attribution of these comparanda to Vitry, see Bent and Wathey, ‘Vitry, Philippe de’, 810. On Vitry and untexted hockets, see Zayaruznaya, ‘Hockets as Compositional and Scribal Practice’.

60 The motetus closes ‘scribere non posse; possit super ethera scribi’. F-Pn 2444, fol. 48v.

61 The triplum closes ‘O Maria virgo parens / meum sic ure spiritum / quod amori tuo parens / amorem vitem irritum!’; see Kügle, The Manuscript Ivrea, 121.

62 This can be fruitfully related to the sonic intensity dubbed ‘supermusical’ by Emma Dillon, who discusses a motet ‘rendered speechless’ by a ‘supermusical excess of language’ as ‘a sonorous equivalent of [Mary's] wordless sob’ at the foot of the cross. Dillon, Emma, The Sense of Sound: Musical Meaning in France, 1260–1330 (Oxford and New York, 2012), 326–7CrossRefGoogle Scholar. In the present case it is not verbal excess but rhythmic, with a similar effect: ‘a kind of music in which sound asserts itself through and beyond words’ through notational ‘translations of sounds regarded as ineffable or unruly’ (ibid., 327–8).

63 Gilbert Reaney transcribed the incipit in Manuscripts of Polyphonic Music (c. 1320–1400), RISM B/IV, vol. 2, 199–200. Reaney does not note the concordance with Trémoïlle.

64 The motet's presence in this source was first noted in Lerch-Kalavrytinos, Irmgard, ‘Ars Nova-Fragmente in Würzburg’, in Borderline Areas in Fourteenth- and Fifteenth-Century Music/Grenzbereiche in der Musik des 14. und 15. Jahrhunderts, ed. Kügle, Karl and Welker, Lorenz (Münster and Middleton, 2009), 119–30Google Scholar. Lerch-Kalavrytinos based her transcription of the motet's opening thirty breves on Paris 2444 due to the illegible nature of the folio at that time. Between Lerch's announcement of the source and the publication of her findings another report on the Würzburg fragments was published in Joachim Lüdtke, ‘Kleinüberlieferung mehrstimmiger Musik vor 1550 in deutschem Sprachgebiet IV: Fragmente und versprengte Überlieferung des 14. bis 16. Jahrhunderts’, Nachrichten der Akademie der Wissenschaften in Göttingen: Philologisch-Historische Klasse (2001), 429–36.

65 Lerch-Kalavrytinos, ‘Ars Nova-Fragmente in Würzburg’, 124; Lüdtke, ‘Kleinüberlieferung mehrstimmiger Musik’, 436.

66 The identification was published on 23 May 2012 on http://jjstoessel.wordpress.com/. Additional information on this fragment by Alexander Rausch is published in Klugseder, Robert, ed., Quellen zur mittelalterlichen Musik- und Liturgiegeschichte des Klosters Mondsee, Codices Manuscripti Supplementum 7 (Purkersdorf, 2012), 232–40Google Scholar. The full digitised fragment can be viewed at www.cantusplanus.at/en-uk/fragmentphp/fragmente/indexNEU.php.

67 See Rausch's discussion in Klugseder, ed., Quellen zur mittelalterlichen Musik- und Liturgiegeschichte des Klosters Mondsee, 232–40.

68 Bent, Margaret, ‘A Note on the Dating of the Trémoïlle Manuscript’, in Beyond the Moon: Festschrift Luther Dittmer, ed. Dittmer, Luther A., Gillingham, Bryan and Merkley, Paul (Ottawa, 1990), 217–42, at 222Google Scholar.

69 Wright, Craig, Music at the Court of Burgundy 1364–1419: A Documentary History, Musicological Studies 28 (Henryville, PA, 1979), 140–9Google Scholar. See also Bent, ‘A Note on the Dating’, 218f.

70 Sources: A-Wn 123a, 2v (V), D-WÜf 10a, 2bv (W), F-Pn 2444, 49v (P). Variants: 1 liberat] liberet V; 2 pugiles] pugilles P; superat] separat P; 4 humanitas que] conieci, humanitasque codd.; potest] possunt P; 5 mundiali] mundialis W; abuti gloria] habitu glorie V; 6 post coacta add. ieiunia postea expunctum P; abstinencia] astinencia P, abstinentie V; 7 subdita] subobit (uid.) P; obediencie] obediencia P; 8 ut false cedat] WP, ut false cedunt V, fortasse corrigendum pro caesura post quartam syllabam: false cedat ut; 9 querit] queret V; 10 christi tamen] iusti tantum (uid.) P, illeg. W; languendo] langwendo V; 11 que inpia] conieci, quempiam V, quem quepiam W, quemque piam P; 12 subdendo] cedendo PW; 13 cedit] cedet V; 15 qua] quam P; est] om. P; abitum] conieci, habitum VW, habitura P; 16 cum nitamur] conieci (cf. Ovid, Amores 3.4.17), coniunctamur V, coniuntamur W, cum amur (uid.) P; semper] om. P; 18 unitatem] uni- hic desinit P

71 Cf. Ovid, Amores 3.4.17: ‘nitimur in vetitum semper cupimusque negata’.

72 Sources: A-Wn 123a, 2v (V), D-WÜf 10a, 2bv (W), F-Pn 2444, 49v (P). Variants: 3 vitare] victare P; hic desinit V; 7 nature] natura P; 8 obedientia] hic desinit W; 12 habet] conieci, habent P.