¹ Brown, H. M., ‘A Ballade for Mathieu de Foix: Style and Structure in a Composition by Trebor’, Musica Disciplina, 41 (1987), p. 77Google Scholar.

² See, for example, Reaney, G., ‘Modes in the Fourteenth Century, in particular in the Music of Guillaume de Machaut’, Organicae Voces: Festschrift Joseph Smits van Waesberghe (Amsterdam, 1963), pp. 137–43Google Scholar; ‘La Tonalité des Ballades et des Rondeaux de Guillaume de Machaut’, Guillaume de Machaut Poète et Compositeur, Actes et Colloques No. 23 (Paris, 1982), pp. 295–300Google Scholar; Hirshberg, J., ‘Hexachordal and Modal Structure in Machaut's Polyphonic Chansons’, Studies in Musicology in Honor of Otto E. Albrecht, ed. Hill, J. W. (Kassel and Basel, 1980), pp. 19–42Google Scholar; Leech-Wilkinson, D., ‘Machaut's Ros, lis and the Problem of Early Music Analysis’, Music Analysis, 3 (1984), pp. 9–28CrossRefGoogle Scholar; Fuller, S., ‘Line, Contrapunctus and Structure in a Machaut Song’, Music Analysis, 6 (1987), pp. 37–58CrossRefGoogle Scholar; ‘Modal Tenors and Tonal Orientation in Motets of Guillaume de Machaut’, Studies in Medieval Music: Festschrift for Ernest H. Sanders (New York, 1990), pp. 199–245Google Scholar. Medieval specialists have not generally endorsed Schenkerian analyses directed at discovering the roots of tonal Ursatzen in early polyphony, although they have adapted reductive procedures derived from Schenkerian teaching to illustrate pitch relationships in the lines and counterpoint of fourteenth-century music. Carl Schachter offers graphs of Landini songs that stress tonal functions (I, V, IV, VII) in ‘Landini's Treatment of Consonance and Dissonance: A Study in Fourteenth-Century Counterpoint’, Music Forum, 2 (1970), pp. 130–86Google Scholar.

³ Egidius's text is edited, without formal title, in Leech-Wilkinson, D., Compositional Techniques in the Four-Part Isorhythmic Motets of Philippe de Vitry and His Contemporaries (New York and London, 1989), pp. 18–20Google Scholar. The editor's translation and commentary appear pp. 21–4. In the absence of an authoritative title, I have designated the treatise by its incipit. In his Ars (1355), Johannes Boen similarly concerns himself with matters of color and numerical disposition, excluding tonal matters; see Leech-Wilkinson, pp. 16–17.

⁴ Beihefte zum Archiv für Musikwissenschaft 35 (Stuttgart, 1992).

⁵ ‘… diejenigen Faktoren aufzuspüren, die in jener Zeit als nicht aufzeichnungsbedürftig erachtet wurden, da sie aus der Tradition und dem Zusammenhang der Lehre heraus selbstverständlich waren’. Hexachord, Mensur, p. 17. The passage continues with a clear statement of purpose: ‘A central thrust of this study – set forth in chapter 4, ‘The Representation of the Tonal System” – is not only to describe this tradition, but to seek out its traces in the [theoretical] treatises.’ (‘Diese Tradition nicht nur zu benennen, sondern auch ihre Spuren in den Traktaten aufzusuchen, ist ein zentrales Anliegen dieser Arbeit, die das Kapitel 4: “Die Darstellung des Tonsystems” bestimmt.’) Thomas Brothers has recently urged caution about assuming unwritten performance practices (Chromatic Beauty in the Late Medieval Chanson (Cambridge, 1998), pp. 21–44Google Scholar.)

⁶ ‘Aus dieser Untersuchung ergab sich als notwendige Konsequenz die uneingeschränkte Gültigkeit der Modus-Lehre in der Musik des 14. Jahrhunderts.’ Hexachord, Mensur, p. 17.

⁷ The Greek nomenclature for the modes is Berger's and appears not only in his general linguistic usage but in the subheadings (‘Dorisch’, ‘Lydisch’, ‘Mixolydisch’) of his fourth section, where he classifies the fourteenth-century component of the Reina repertory. (It contains no ‘Phrygian’ pieces.) I find this uncritical adoption of Dorian, Lydian and Mixolydian labels for modal categories – nomenclature far more widespread in the sixteenth than in the fourteenth century – to be anachronistic in effect. Although no more than mere convenience of language might appear to be involved, the choice of terms does jar against the posture of reconstituting a fourteenth-century viewpoint. Moreover, the Greek names conjure up images of octave species divided harmonically or arithmetically (a notion Berger explicitly invokes on occasion), images incongruent with modal concepts expressed in a majority of medieval theoretical writings. Numerical designation – first mode, second, etc. – would be both more neutral and more historically apt.

⁸ Berger himself acknowledges this in the concluding paragraph of his book: ‘The theses advanced in this book have wide-reaching consequences for our image of fourteenth-century music.’ (‘Die in dieser Arbeit aufgestellten Thesen haben weitreichende Konsequenzen für unser Bild von der Musik des 14. Jahrhunderts.’ p. 262)

⁹ His theoretical exposition is concentrated in the third section of his book, ‘The Representation of the Tonal System’ (‘Die Darstellung des Tonsystems’). Its consequences for the music are explicated in the fourth section, ‘Solmisation: The Codex Reina Repertory’ (‘Solmisation: Das Repertoire des Codex Reina’). Berger adopts Carl Dahlhaus's definition of Tonsystem as ‘a musical perceptual model that allows pitch material to enter into a complex of pitch relations’ (‘eine musikalische Anschauungsform, die ein Material von Tönen zu einem Komplex von Tonbeziehungen werden läßt’: p. 86). An alternative viewpoint that regards fourteenth-century French secular song in terms of tonal types has been advanced by Lefferts, Peter in ‘Signature-Systems and Tonal Types in the Fourteenth-Century French Chanson’, Plainsong and Medieval Music, 4 (1995), pp. 117–47CrossRefGoogle Scholar. Lefferts's ideas form the basis of an extended study by Plumley, Yolanda, The Grammar of 14th Century Melody, Outstanding Dissertations in Music from British Universities (New York and London, 1996)Google Scholar. Neither addresses Christian Berger's book, but their initial premises and empirical methodology lead to conclusions quite different from his.

¹⁰ ‘Das Mittelalter hatte eine ganz spezifische, auf seine eigenen musikalischen und aufführungspraktischen Bedürfnisse hin zugeschnittene musikalische Anschauungsform … Daraus ergibt sich die Konsequenz, daß die Musik jener Zeit ohne diese musikalische Anschauungsform nicht adäquat übertragen, geschweige denn analysiert werden kann. Weiter folgt daraus auch, daß diese Anschauungsform nicht mehr allein aus den praktischen Zeugnissen entwickelt werden kann, ziehen diese doch schon weitreichende Konsequenzen aus der theoretischen Vorstrukturierung, die in dieser Anschauungsform begründet liegt.’ Hexachord, Mensur, p. 86.

¹¹ The Reina codex is formally known as Paris, Bibliothèque Nationale, fonds français nouvelle acquisition 6771; RISM siglum F-Pn n. a. fr. 6771.

¹² Here, as elsewhere in this paper, ‘modal’ with respect to notation refers to pitch constructs, not to modal elements in the mensuration system.

¹³ In concentrating on Berger's exploration of Tonsystem, the present study bypasses the topics of mensuration and text structure heralded in the title of his book. Although these topics figure in his larger project of establishing ‘elementary premises for analysis’ for late-fourteenth-century secular polyphony, the modal component merits particular attention as a core topic that permeates the study. Berger's title invokes Hexachord rather than Tonsystem. But his compact statement of purpose lists his three areas of inquiry as mensuration, text and tonal system: ‘Hence the present study wishes to make a contribution with investigation in the three realms of mensuration, text and tonal system’ (‘Dazu möchte die vorliegende Arbeit mit der Untersuchung in den drei Bereichen Mensur, Text und Tonsystem einen Beitrag leisten’: p. 23)

¹⁴ Hexachord, Mensur, p. 130. The asterisks above pitches in Examples la and lc indicate the probable continuation of a preceding accidental. This convention is followed in the subsequent examples that lack bar lines.

¹⁵ ‘Describunt autem tonum quidam dicentes eum esse regulam, quae de omni cantu in fine iudicat. Sed isti videntur multipliciter peccare. Cum enim dicunt de omni cantu, videntur cantum civilem et mensuratum includere. Cantus autem iste per toni regulas forte non vadit nee per eas mensuratur. Et adhuc, si per eas mensuratur, non dicunt modum per quem nec de eo faciunt mentionem … Temptemus igitur aliter describere et dicamus, quod tonus est regula, per quam quis potest omnem cantum ecclesiasticum cognoscere et de eo iudicare inspiciendo ad initium, medium vel ad finem … Dico etiam cantum ecclesiasticum, ut excludantur cantus publicus et praecise mensuratus, qui tonus non subiciunter.’ Die Quellenhandschriften zum Musiktraktat des Johannes de Grocheio, ed. Rohloff, E. (Leipzig, 1972), p. 152Google Scholar. (The phrases set off in italics by Rohloff, and in inverted commas in my translation, are not so distinguished in the original.) In this and the following extracts, Berger (p. 129) quotes only the fragment within angle brackets at the end of the translation.

¹⁶ “Beide betonen ohne einen konkreten Bezug zur Praxis einer Mehrstimmigkeit die Gültigkeit der Modus-Lehre für “alle Gesänge”.’ Hexachord, Mensur, p. 131.

¹⁷ ‘Et quemadmodum se habet littera ad syllabam, syllaba ad dictionem, dictio ad orationem, ita littera sive punctus ad clavem, clavis ad tonum, tonus ad cantum. Per quos tonos sive psalmi sive hymni, credo, vel gloria in excelsis, kyrie, vel prosa, vel etiam cantilena secularis, vel quaelibet alio modo cantando, vel legendo cantetur, et cum tonis accipit principium, vim, finem et fundamentum.’ Salomo, Elias, Scientia Artis Musicae, ed. Gerbert, M., Scriptores ecclesiastici de Musica (hereafter GS), vol. III, p. 20Google Scholar Partially quoted in Hexachord, Mensur, p. 131: The portion Berger cites is bracketed in my translation. For a broad-ranging study of the possible meanings of ‘clavis’ in such a context, see Dyer, J., ‘The Clavis in Thirteenth-Century Music Theory’, Cantus Planus: Papers Read at the 7th Meeting, Sopron, Hungary, September 1995, ed. Dobszay, L. (Budapest, 1998), pp. 195–212Google Scholar. I am grateful to Prof. Dyer for providing me with a pre-publication copy of his study.

¹⁸ ‘Observatio igitur et regulatio cuiuslibet toni secundum formam et modum suum in cantu naturali est finis et intention musicae: cum recte cantare secundum artem musicae nihil sit nisi quemlibet cantum secundum suum tonum recte regulare et regulariter incipere, et ducere, et finire.’ Engelbert of Admont, De Musica, GS ii, p. 331Google Scholar. Partially quoted in Hexachord, Mensur, p. 131: the portion Berger cites is bracketed in my translation.

¹⁹ Indeed, in his introductory comments, Salomo links determination of mode with church song only: ‘omnia quae communiter in ecclesia cantantur, seu cantando leguntur’ (GS iii p. 18)Google Scholar.

²⁰ At the very beginning of his treatise, Englebert has defined his main subject, musica, in terms of what we would today call ‘music theory’: ‘scientia inquirendi et discernendi’ (GS ii, p. 288)Google Scholar. In Book IV, chapter 10, Englebert does say that the octave, ‘that most perfect consonance’, suffices for ‘all musical song’ (‘omnis cantus musicus’: GS ii, p. 345Google Scholar), but that phrase must be understood as a loose commonplace of speech. Apt as it may be for expounding a modal theory based on octave species, this statement does not fit technically with the many melodies within the chant repertory that exceed an octave span. A. Rusconi has noted that Engelbert's ‘De Musica’ is solely concerned with plainchant, and that the fleeting comments on polyphonic practice are archaic in quality. He also observes that Engelbert uses no theoretical sources more recent than the later eleventh century. Rusconi, , ‘L'insegnamento del Canto Liturgico nel “De Musica” di Engelbert von Admont’, Musicam in subtilitate scrutando, Università degli Studi di Pavia, Scuola di Paleografia e Filologia Musicale – Cremona, ed. Sabaino, D. et al. (Lucca, 1994), pp. 130–1Google Scholar.

²¹ Anyone who deals with medieval theoretical writings must inevitably remove quoted passages from original contexts. What is at issue here is sensitivity to those original contexts and awareness of changes that may be effected by recontextualisation.

²² ‘Restat et nunc quidem de cantibus allis, puta motetis, baladis, et huiusmodi, de quibus tonis sive modis iudicandi fuerint aliqua declarare. Sit igitur finale iudicum omnium tonorum seu modorum cuiuslibet cantus, videlicet motetorum, baladarum, rondellorum, vireletorum, et huiusmodi istud.’ The Berkeley Manuscript, ed. Ellsworth, O. (Lincoln, Neb., and London, 1984), p. 84Google Scholar.

²³ Berger does not engage with the ontological distinction between a priori conception within a mode – mode as a guide for composition or improvisation – and post facto classification within a modal category – mode as an ideal category imposed on members of a repertory. This is a critical distinction emphasised in Power's, H. S. seminal work on mode, ‘Tonal Types and Modal Categories in Renaissance Polyphony’, Journal of the American Musicological Society, 34 (1981), pp. 433–5Google Scholar. Berger simply asserts that mode was a pervasive a priori concept not only for fourteenth-century secular song composers but also for the singers who performed their ballades, virelais and rondeaux.

²⁴ ‘De cantibus vero aliis, puta motetis et huiusdem, sciendum est quod in plagalibus eque bene potest ascendi et descendi per plures voces, sicut in autenticis dicitur; eciam tenores sequi debere naturam cantuum ecclesiasticorum.’ The Berkeley Manuscript, p. 74.

²⁵ This teacher does employ some generic distinctions, but in a loose way. These are ‘cantus ecclesiasticus’, ‘motetis et huiusdem’ or ‘huiusmodi’, ‘cantus mensurabilis’. Sometimes the ‘huiusmodi’, are defined as ballades, rondeaux or virelais.

²⁶ ‘De supradictis autem speciebus tropi sive modi qui octo sunt, originem ducunt, in quibus omnis cantus ecclesiasticus quasi in tot rotis revolvitur.’ Quatuor Principalia Musicae, ed. Coussemaker, E., Scriptorum de Musica Medii Aevi (hereafter CS), vol. iv (Paris, 1876), p. 229Google Scholar. The theorist follows this opening with a clear statement that ‘modus’ has dual meanings, one in cantus planus, the other in cantus mensurabilis; see note 35 below.

²⁷ ‘Unde tonus, prout hie sumitur, est regula de quoque cantu diiudicans in fine.’ The Berkeley Manuscript, pp. 66–8. I prefer to call this theorist Goscalcus, but since Christian Berger refers to him as ‘the Berkeley Anonymous’ I follow his designation here.

²⁸ ‘Tonus vel modus est regula quae de omni cantu in fine diiudicat.’ GS i, p. 257Google Scholar.

²⁹ This theorist mentions some modal features other than the final, but as rules to be observed, not as integral to his definition of mode.

³⁰ ‘Darüber hinaus gibt es noch eine ganze Anzahl weiterer Hinweise, die die Gültigkeit der tonus-Lehre für alle, eben auch für weltliche Gesänge, herausstellen. Nur sind sie niche da zu finden, wo von der musica mensurabilis oder von der Lehre des discantus die Rede ist, sondern in den elementaren Lehrtexten der musica plana.’ Hexachord, Mensur, p. 132. See also p. 133, top, and pp. 15–17 in the introduction.

³¹ ‘Qui igitur cantum ignorat planum, frustra tendit ad mensuratum. Prius enim in cantu plano se debet quisque fundare; dehinc ad mensurabilem potest accedere. De cantu igitur plano primo prosequamur; infra vero, libro septimo, aliquid de mensurabili tangemus.’ Speculum Musicae 6, p. 202Google Scholar. Berger (p. 132) cites only the portion shown within angle brackets in the translation, leaving out Jacques of Liège's remark that he is continuing his discussion under the banner of cantus planus.

³² ‘… die Gültigkeit der Modus-Lehre auch für die Mehrstimmigkeit.’ Hexachord, Mensur, p. 133. See also p. 17: ‘This investigation [of the relationship between musica plana and musica mensurabilis] yielded the necessary conclusion that teaching on mode was of unrestricted validity for music of the fourteenth century.’

³³ The immediate context for his remark on cantus planus as foundation for mensurabilis is, first, a discussion of ‘cantus’ that emphasises precision of pitches and intervals and knowledge of syllables and letters on the monochord and, secondly, the distinction between plain and measured cantus that stresses the two kinds of measure – that which controls distance between intervals, which pertains especially to cantus planus, and that which controls durations, one division of which pertains especially to cantus mensuratus. The remark leads into a discussion of pitch notation that begins with Isidore and Boethius and leads finally to Guidonian staff notation. Speculum Musicae 6, ch. 70–3, pp. 200–14.

³⁴ ‘Quid igitur est modus in mensurabili musica nisi conveniens ordo, dispositio vel coniunctio figurarum vel notarum musicalium, scilicet longarum, brevium et semibrevium ad invicem? Unde fit ut secundum variam dispositionem tactarum notularum inter se modi varientur, sicut in plana musica modi seu toni in cantibus variantur ex varia vocum dispositione in principio, medio et fine. Sed non est hie et ibi omnino simile.’ Speculum Musicae 7, Ch. 18, p. 40Google Scholar.

³⁵ ‘Modus autem musicae duplex est videlicet plani cantus et mensurabilis. De modis in cantu mensurabili, nihil ad praesens dicetur. Deo dante, postea. Modi autem plani cantus sunt octo.’ Quatuor Principalia, iii, ch. 19, CS iv, p. 229Google Scholar.

³⁶ ‘Sciendum est tamen quod modus armonicalis duplex est, videlicet plani cantus et mensurabilis. Planus vero cantus octo habet modos, in quibus tota versatur plana musica … Modus autem cantus mensurabilis est representatio soni longis brevibusque temporibus mensurati.’ Quatuor Principalia, IV, ch. 9, CS iv, p. 257Google Scholar.

³⁷ For instance, in Book 7, ch. 37 of the Speculum Musicae, Jacques of Liège specifically remarks that the notational figures used in musica mensurabilis are taken from musica plana and should have the same propriety of form (p. 75).

³⁸ ‘Sic igitur, in fine laboris huius de consonantiis, de cantu et tonis, ut ad musicam pertinent planam … quattuor posuimus cantus.’ Speculum Musicae 6, ch. 113, p. 316Google Scholar.

³⁹ ‘Sed iam de consonantiis, quantum ad musicam planam theoricam et practicam, de modis vel tonis et cantibus planis, quae dicta sunt sufficiant. Sicque terminetur hie liber sextus. Ad mensurabilem musicam stilus convertatur.’ Speculum Musicae 6, ch. 113, p. 317Google Scholar.

⁴⁰ Hexachord, Mensur, p. 130. This article uses Guidonian nomenclature for pitches, with capitals A-G for the lower (grave) register and lowercase a–g for the upper (acutum). Generic references to pitches without regard to register use capital letters.

⁴¹ ‘So kommt den Akzidentien als Teil der schriftlichen Aufzeichnung im Mittelalter eine Bedeutung zu, die von einer unmittelbaren, bloß indizierenden Wirkung dieser Zeichen in Form einer Erhöhung oder Erniedrigung des unmittelbar benachbarten Tones wegführt und auf andere, strukturelle Zusammenhänge verweist, nämlich auf die Hexachordstrukturen, mit deren Hilfe der mittelalterliche Sänger sein Tonsystem strukturierte.’ Hexachord, Mensur, p. 92.

⁴² ‘Die finalis des Stückes und die Akzidentien weisen auf einen B-lydischen Modus hin. Dieser Modus greift auf eine Kombination der Hexachorde über B, molle und naturale zurück, wobei der Einsatz des Hexachords über B als fa supra la den Ton as mit einbezieht. Die beiden Akzidentien in diesen ersten drei Cantus-Takten stehen vor den-jenigen Tönen, die in der Abfolge der Hexachorde Schaltstellen darstellen: das ♮ vor c' weist auf die konjunkte Kombination zweier Hexachorde hin, mit der im Rahmen dieses lydischen Modus nur die Kombination der beiden Hexachorde molle/über B gemeint sein kann, also ein c-sol/re. Das vorangegangene es' wird dadurch als ein fa supra la und das b im T[akt] 2 als ein b-fa/ut gekennzeichnet. Das ♮ vor dem f im T. 3 kennzeichnet diesen Ton als Schaltstelle zweier anderer konjunkter Hexachorde, wobei hier unter den drei möglichen Hexachorden die Kombination der Hexachorde naturale/molle gemeint sein kann, also ein f-fa-ut.’ Hexachord, Mensur, p. 133.

⁴³ In discussing passages from songs of the Reina codex, Berger does sometimes bring simultaneous vocal lines into play. See, for example, the discussion of L'ardent desier, below.

⁴⁴ This F# would be parallel to the one in bar 3 that he eradicates. The Faenza transcription is edited in Keyboard Music of the Late Middle Ages in Codex Faenza 117, ed. Plamenac, D., Corpus Mensurabilis Musicae 57 (1972), pp. 12–15Google Scholar. The Faenza codex supplies useful information because the arguments Berger puts forward for the behavior of singers would not necessarily hold for a keyboard player writing or reading a score. The Faenza arrangements drop many of the inflections found in vocal manuscripts; hence those accidentals that they do preserve have the more claim to reliability. The scribe writes Honte paour a fifth higher than the vocal version, and so renders the F# at the end of the first cantus phrase as a c#.

⁴⁵ Among them are Petrus palma ociosa (‘Ein Beitrag zur Diskantlehre des 14. Jahrhunderts’, ed. Wolf, J., Sammelbände der Internationalen Musikgesellschaft, 15 (1913–1914), p. 515)Google Scholar; Johannes de Grocheo (Musica, ed. Rohloff, E., p. 128)Google Scholar; the ‘Ars nova’ (Corpus Scriptorum de Musica 8, ed. G. Reaney, A. Gilles, J. Maillard (1964), ch. 8, pp. 32–3); Boen, Johannes (Johannes Boens Musica und seine Konsonanzenlehre, ed. Frobenius, W. (Stuttgart, 1971, p. 54)Google Scholar; the Berkeley Anonymous (The Berkeley Manuscript, p. 52).

⁴⁶ ‘Ex predictis aliqualiter incipit elucescere natura litterarum clavis presentis, videlicet quod b-fa littera signum est depressionis note sequentis in eadem clave et ♮ -mi nota elevationis. Patet etiam directa contrarietas in dictis litteris, quoniam quantum b-fa deprimit, tantum b-mi acuit, quia utraque per semitonium maius precise.’ Boen, Johannes, Musica, ed. Frobenius, , p. 54Google Scholar.

⁴⁷ ‘Dabei steht das Bemühen im Vordergrund, den Gebrauch von Akzidentien konsequent im Sinne der These Gaston Allaires als Hinweis auf eine Hexachord-Struktur aufzufassen.’ Hexachord, Mensur, p. 143. This formulation actually gives Berger full range in deciding when accidentals signal hexachord structure rather than pitch inflection. Significantly, Karol Berger's comprehensive and highly regarded study Musica Ficta: Theories of Accidental Inflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino (Cambridge, 1987)Google Scholar reports no teaching on the part of medieval theorists that accidentals signify hexachord configurations in any structural sense independent of pitch inflection.

⁴⁸ ‘In gleicher Weise tritt bei den Akzidentien die Funktion eines Hinweisen auf eine Struktur allmählich zurück zugunsten einer Funktion mit eng umrissener, unmittelbar ablesbarer Bedeutung. Dieser Umschwung deutet sich in den Theoretiker-Schriften urn die Wende zum 14. Jahrhundert mit dem Hinweis auf die neue, direkte Bedeutung den Zeichen an.’ Hexachord, Mensur, pp. 135–6. This statement stands in a contradictory relationship to his claim on p. 92 (quoted note 41 above) that at some (undefined) moment in the middle ages interpretation of accidentals shifted from signalling pitch inflection to symbolising hexachord structure. Berger never examines the contradictions between his own statements.

⁴⁹ Hexachord, Mensur, p. 106–7. The Marchettus passage, ‘Primus tonus formatur ex prima specie dyapente, que est a D gravi ad a acutum, et ex prima specie dyatessaron superius’, appears in Lucidarium, ed. Herlinger, Jan (Chicago and London, 1985), Ch. 11.4, p. 394Google Scholar.

⁵⁰ ‘'Eine Kombination dieser beiden Species ist nur in einer disjunkten Folge zweier Hexachorde möglich, also beim d-dorischen in der Kombination der Hexachorde naturale/durum.’ Hexachord, Mensur, p. 107 (Example 5 here is Berger's Ex. 7).

⁵¹ ‘Wie eng Hexachordsystem und Modi zusammenhängen, zeigt sich an den möglichen Transpositionen der Modi.’ Hexachord, Mensur, p. 108.

⁵² Lucidarium, 11.4, pp. 396–400. A doctrine linking particular hexachord combinations with specific modes would, in fact, go against Marchettus's teaching that one can end a mode ‘in any location on the hand where the species that form them can be set in the proper order above and below’ (p. 400–1). It seems odd, too, to invoke Marchettus in conjunction with French modal practices when so little is known about the origins of his ideas and their circulation outside Italy.

⁵³ Hexachord, Mensur, pp. 108–9. These theorists include Johannes Tinctoris, whose Liber denatura et proprietate tonorum (1476) is surely too late to have direct bearing on the fourteenth-century Reina repertory.

⁵⁴ See Speculum Musicae 6, ch. 75–6, pp. 216–21, and The Berkeley Manuscript, p. 84. Compare the latter with ibid., pp. 74–6, where the regular finals are cited.

⁵⁵ ‘Ohne den Modus zu kennen, ist die Entscheidung über die Auswahl der beiden unter den drei möglichen Hexachorden nicht zu treffen. Andererseits ist eine Ausführung eines Stückes, dessen Modus ich zwar kenne, ohne Kenntnis der zugehörigen Hexachorde ebenso unmöglich, vor allem angesichts der Tatsache, daß die entsprechenden Stücke im Vertrauen auf die Kenntnisse der Ausführenden ohne weitere erklärende Akzidentien aufgezeichnet worden sind.’ Hexachord, Mensur, p. 109.

⁵⁶ Hexachord, Mensur, p. 105.

⁵⁷ ‘De dictorum cantuum ♭ durali scilicet et b molli mutuis commutationibus,’ Hieronymus de Moravia O. P. Tractatus de Musica, ed. Cserba, S., Freiburger Studien zur Musikwissenschaft v. 2 (Regensburg, 1935), p. 168Google Scholar. Jerome's treatise is dated between 1272 and 1304 (Cserba, p. xxill).

⁵⁸ The first sentence reads: ‘When b-rotundum or ♭-quadratum should be introduced in a song (“cantus”) of any mode – whether authentic or plagal, and whether in a high or a low register – and when not has yet to be seen. To make this plain, note first and principally that often none of the three hexachords (“cantus”) named suffices to complete melodies within the whole corpus of any mode.’ Tractatus de Musica, p. 168.

⁵⁹ ‘Primi igitur toni in D gravi terminati melodiam, quae inclusis licentialibus extendit se a C in e acutum, duo cantus naturaliter perficiunt, scilicet naturalis primus et ♭ duralis secundus, b mollis autem, quando in hoc tono et in aliis assumitur, sequens ratio declarabit … Item quinti toni in F gravi terminati melodiam, quae inclusis licentialibus extendit se ab E gravi in g superacutum, duo cantus naturaliter efficiunt, cantus scilicet naturalis primus et secundus et cantus b mollis primus … Item quinti toni in c acuto terminati melodiam efficit cantus b duralis secundus et tertius et cantus naturalis secundus.’ Tractatus de Musica, pp. 169–70.

⁶⁰ Tractatus de Musica, p. 172.

⁶¹ Hexachord, Mensur, pp. 89–92, in a section titled ‘The System of Hexachords’.

⁶² Hexachord, Mensur, pp. 90–1. The study on which he depends is Allaire, Gaston, The Theory of Hexachords, Solmization and the Modal System, Musicological Studies and Documents 24 (American Institute of Musicology, 1972)Google Scholar. Since Allaire's study received very critical reviews from a number of respected scholars, Berger's reliance on it seems ill advised.

⁶³ ‘“Authentus tritus … constat ex tertia specie diapente <inferius> et ex tertia specie diatessaron superius.” Wie schon beim dorischen Modus ist für Jacobus von Lüttich mit dieser Bestimmung der lydische Modus in seinen wesentlichen Momenten erfaßt. Eine Kombination von dritter Quint-und Quartspecies ergibt folgendes Solmisationsschema: fa–fa/fa–fa. Eine Quinte fa–fa ist nur in einer disjunkten Folge zweier Hexachorde möglich, etwa in der Folge Hexachord naturale/durum: [example].’ Hexachord, Mensur, p. 186. The formulations for Dorian and Mixolydian are found on pages 161 and 220 respectively. Note that Jacques of Liège himself does not label the end points of the species with solmisation syllables.

⁶⁴ See quotation above, p. 83. In small print, Berger does acknowledge (in his own metaphor of hexachords) that some theorists, Jerome of Moravia among them, do accept B♭ regularly in mode 5, but he downplays this and does not recognise in this circumstance a challenge to his own claim.

⁶⁵ ‘Die Interpretation der Akzidentien im dorischen Modus ist geprägt durch das enge, einander ergänzende Zusammenwirken modaler und hexachordaler Gesichtspunkte.’ Hexachord, Mensur, p. 184. This viewpoint extends to all the modes.

⁶⁶ By an ‘ordinary’ reading I mean the common theoretical dictum that round b is to be sung as fa and square ♭ as mi. (See, for example, The Berkeley Manuscript, p. 52, and Johannes Boen, Musica, quoted note 46 above.)

⁶⁷ Transcribed by Apel, W., French Secular Compositions of the Fourteenth Century, Corpus Mensurabilis Musicae 53 (American Institute of Musicology, 1971), vol. ii, pp. 63–4Google Scholar; and Greene, G., French Secular Music: Ballades and Canons, Polyphonic Music of the Fourteenth Century (Monaco, 1982), vol. xx, pp. 168–9Google Scholar.

⁶⁸ ‘… mit dem Tritonusschritt die Beziehung zum vorigen Abschnitt unterbrochen worden war.’ ‘Abgesehen vom Tritonusschritt c'–fis' zwischen ouvert-Schluß und dem Beginn des Abgesanges liegt auch keine kontrapunktische Rechtfertigung für eine solche Erhöhung vor.’ Hexachord, Mensur, p. 152 (I have reversed the order of these statements.) Regarding the first objection, note Johannes Boen's remark (Musica, p. 52) that although the tritone is quite harsh it ought not to be rejected as despicable.

⁶⁹ For his hexachord schemes for C-Lydian, the category to which he assigns L'ardent desier, see Hexachord, Mensur, pp. 186–8. There the conjunct configuration is described as hardnatural.

⁷⁰ Hexachord, Mensur, pp. 152–3.

⁷¹ Transcribed by Apel, , French Secular Compositions, vol. ii, pp. 69–70Google Scholar; Greene, , French Secular Music, pp. 175–7Google Scholar; and Wilkins, N., A 4th-Century Repertory from the Codex Reina, Corpus Mensurabilis Musicae 36 (1966), pp. 25–7Google Scholar.

⁷² Hexachord, Mensur, p. 253.

⁷³ ‘Das ♮-durum zu Beginn des Cantus ist somit ein Hinweis auf die konjunkte Kombination der Hexachorde durum/naturale, die zur Solmisation dieses Abschnittes benötigt wird.’ Hexachord, Mensur, p. 253.

⁷⁴ ‘Sexta, scilicet tonus cum diapente, petit duplum vel quintam.’ Speculum Musicae, book 4, ch. 50, p. 123. Jacques of Liège here takes for granted that a sixth moving to an octave will be a diapente-plus-a-tone, i.e. a major sixth.

⁷⁵ See Fuller, Sarah, ‘Tendencies and Resolutions: The Directed Progression in Ars Nova Music’, Journal ofMusic Theory, 36 (1992), pp. 229–58CrossRefGoogle Scholar. There is, in addition, the question whether the contratenor G must necessarily be raised if the cantus sings c#. Apel provides no editorial ficta for the contratenor in his edition (my Example 9a).

⁷⁶ Berger's transcription of the entire song appears in Hexachord, Mensur, pp. 270–3. There he places the natural sign in front of the opening cantus d, whereas in the example on p. 253 he places it over the c in bar 2 in the position and typography of an editorial accidental. In all, he suppresses five notated c#s (bars 2, 26, 38, 57, 70), one g# (bar 21) and one f# (bar 44) in the cantus of L'escu d'amours.

⁷⁷ Transcribed by Apel, , French Secular Compositions, vol. ii, pp. 50–1Google Scholar; Greene, , French Secular Music, pp. 137–9Google Scholar; and Wilkins, , A 14th-Century Repertory, pp. 29–30Google Scholar.

⁷⁸ Berger'transcription appears in Hexachord, Mensur, pp. 264–7. The three b♮s allowed all come at primary cadence points.

⁷⁹ ‘Obwohl der Cantus kein Vorzeichen hat, gelten auch in dieser Stimme vermittels einer intellectualis transposicio die Vorzeichen b und es.' Hexachord, Mensur, p. 173 and note 21 for the subsequent discussion.

⁸⁰ One of the two definitions of coniuncta advanced by the theorist specifies it to be the mental transposition of a hexachord to some location above or below its proper one. The Berkeley Manuscript, pp. 52–4.

⁸¹ The Berkeley Manuscript, pp. 56–66. The theorist characterises five of his coniunctae as mental transpositions and four as natural ones.

⁸² ‘Septima coniuncta accipitur inter D et E acutas, et signatur in E signo b, ubi dicetur fa, et incipit eius deduccio in B acuta, finiens in G acuta, et cantatur per naturam. Nam ipsa est proprietatis seu deduccionis incipientis in C acuta ad locum inferiorem naturalis transposicio.’ The Berkeley Manuscript, p. 62.

⁸³ ‘Auch das nächste Akzidens im Cantus, ein ♮-durum auf der e-Linie des T. 9, läßt sich als Hinweis auf die Hexachord-Struktur interpretieren. Analog dem ♮-durum in T. 3 weist es darauf hin, daß der Ton es' in T. 9 ein fa supra mi des Hexachords über B ist.’ Hexachord, Mensur, pp. 174–5.

⁸⁴ The standard editions of Apel and Greene, against which Berger pits his transcriptions, do accord with the Berkeley Anonymous's teachings.

⁸⁵ Edited by Greene, , French Secular Music, pp. 140–42Google Scholar. A diplomatic transcription of the version in Vienna, Österreichische Nationalbibliothek, Cod. 2777, fols. 15’–16, may be found in Wolf, J., Geschichte der Mensural-Notation von 1250 bis 1460 (1904; repr. Hildesheim, 1965), vol. ii, pp. 142–3Google Scholar.

⁸⁶ ‘… die Auflösung dieses Strebeklanges … nicht zu einem konsonanten Klang führt’. Hexachord, Mensur, p. 155. On the concept of tendency sonority, see Fuller, ‘Tendencies and Resolutions’, pp. 230–3.

⁸⁷ ‘Auch dieser Akzidentien Hinweise für die Solmisation darstellen sollen.’ Hexachord, Mensur, p. 155.

⁸⁸ See p. 76 above, and also his outline of hexachord structure in the C-Dorian mode, Hexachord, Mensur, ex. 16, p. 172.

⁸⁹ ‘… die entsprechend dem Zeichen des T. 27 ebenfalls im Hexachord molle mit a-mi zu solmisieren sind’. Hexachord, Mensur, p. 156.

⁹⁰ See Berger's illustration, Hexachord, Mensur, p. 89.

⁹¹ ‘In his demonstratis exemplis causas fictionis musicae fictae comprehendimus, quas B et ♭ clare demonstrant; demonstrant enim B et ♭ perfectionem quam faciunt dissonantiis imperfectis et dulcem harmoniam eisdem quam tribuunt.’ Declaratio Musicae Disciplinae, ed. Seay, A., Corpus Scriptorum de Musica 7, vol. II, book 2, ch. 34, p. 47Google Scholar. Ugolino uses the terms ‘imperfect interval’ and ‘dissonance’ interchangably to designate thirds, sixths and their compounds (Declaratio, book 2, ch. 5, p. 10).

⁹² Declaratio Musicae Disciplinae, book 2, ch. 34, pp. 47–8. Not shown in the transcription is a b-fa sign before the f four notes from the end. This flat is to ensure that the f will be sung fa, in distinction to the following f[#] inflected as mi.

⁹³ ‘… ut intelligenti terminos metienti clarissime constat’. Declaratio Musicae Disciplinae, p. 47.

⁹⁴ Ugolino's insistence on propinquity between imperfect consonance and its perfect sequel evidently derives from Marchettus of Padua; see Lucidarium, ed. Herlinger, J. (Chicago, 1985), Tractatus 5, chs. 2 and 6, pp. 200–2, 206–22Google Scholar.

⁹⁵ ‘Offensichtlich sind diese Faktoren so fest in der mündlichen Aufführungstradition der Zeit verankert, daß sie selbst in diesen Theoretiker-Beispielen wirksam werden.’ Hexachord, Mensur, p. 142. Although Ugolino makes plain that book 2 of his Declaratio concerns counterpoint (ch. 1, pp. 3–4), Berger curiously opines that this example connects with the plana tradition: ‘Es sind Verdeutlichungen der Contrapunctus-Lehre, die damit zugleich ihre feste Einbindung in die Lehrtradition der musica plana unterstrichen’ (p. 142).

⁹⁶ The transcription does not show a b-fa sign inscribed in the b space before the first ligature in the lower voice, which indicates that the a-c ligature is to be solmised mi-sol. In the second example, the tenor approaches the cadence with b♭–a–G, the very change Berger introduces in his reading of the first example. Since Ugolino explicitly notates the b♭ in his second example, he would surely have notated it in the first had he considered it to be in any way necessary. Note also that Berger's reinterpretations of accidentals that contradict modal integrity consistently rest on taking them as hexachordal signs. That strategy will not work for the second Ugolino example, because the theorist himself explains the reason for and practical consequences of each notated accidental.

⁹⁷ ‘Cognovimus ergo ex praemissis musicae fictae necessitatem consonantiarum perfectionem ac dissonantiarum colorationem, harmoniarum amoenitatem producentem.’ Declaratio Musicae Disciplinae, p. 48. These summary remarks on the ficta examples contain not a hint of support for Christian Berger's notion that mode is a factor pertinent to decisions about musica ficta. In his Musica Ficta: Theories of Accidental Inflections, Karol Berger prints both of Ugolino's examples and discusses them in terms of the theorist's own observations (pp. 124–5).

⁹⁸ ‘The Historical Text as Literary Artifact’, in White, H., Tropics of Discourse: Essays in Cultural Criticism (Baltimore and London, 1978), p. 82 (emphasis in the original)Google Scholar.

⁹⁹ ‘Interpretation in History’, in Tropics of Discourse, pp. 51–80.

¹⁰⁰ ‘The Historical Text as Literary Artifact’, p. 99 (emphasis in the original).

¹⁰¹ This is, of course, not the only perspective from which the study appears flawed. It also departs from standard historical methodology, for instance in suppressing a full range of available data.

¹⁰² Gushee, L., ‘Questions of Genre in Medieval Treatises on Music’, in Gattungen der Musik in Einzeldarstellungen, ed. Arlt, W. (Bern, 1973), pp. 365–433Google Scholar, esp. 366; Fast, S., ‘Bakhtin and the Discourse of Late Medieval Music Theory’, Plainsong and Medieval Music, 5 (1996), pp. 175–91CrossRefGoogle Scholar. Fast skilfully argues the relevance of Bakhtin's categories of heteroglossia, dialogism and polyphony to interpretation of late-medieval theory texts.

¹⁰³ See S. Fast, ‘Bakhtin and the Discourse’, pp. 179–83, for Jerome of Moravia's multiplex exposition of ‘Quid sit musica’.

¹⁰⁴ So, for example, he rejects the c# in bar 1 of the Honte paour cantus as not contrapuntally motivated; not resolved on a strong beat; contrary to the e♭ ‘proper’ to the Dorian mode; and constitutive of an interval (c#–b♭,) incomprehensible within ‘categories of modal melodic design’ (‘Kategorien modaler Melodiebildung’, pp. 130–1). On the last point, he fails to notice that Johannes Boen, in a treatise dated 1357, accepts the c#-b♭), interval (Musica, p. 67).

¹⁰⁵ For parallel perfect consonances, see Fuller, S., ‘Line, Contrapunctus and Structure in a Machaut Song’, Music Analysis, 6 (1987), p. 46CrossRefGoogle Scholar, ex. 4, bars 6–7, 26–27; and idem, ‘Guillaume de Machaut: De toutes flours’, Models of Music Analysis: Music before 1600, ed. M. Everist (Oxford, 1987), pp. 51–2, ex. 3.10, bar 29, and ex. 3.11, bars 38–39. For prominent dissonances, see the edition of De toutes flours in Models of Music Analysis, between cantus and tenor bars 7, 15, 33, and the opening on a major ninth of Machaut's Ballade 30, Pas de tor, ed. Schradex, L., The Works of Guillaume de Machaut, Polyphonic Music of the Fourteenth Century, vol. iii, pp. 94–5Google Scholar.

¹⁰⁶ For remarks on this point, see Fuller, S., ‘On Sonority in Fourteenth-Century Polyphony: Some Preliminary Reflections’, Journal of Music Theory, 30 (1987), pp. 39–40Google Scholar.

¹⁰⁷ See, for example, the Quatuor Principalia, Treatise 1, chs. 13–17, CS iv, p. 205.

¹⁰⁸ For some observations on this phenomenon, see Fuller, S., ‘Modal Tenors and Tonal Orientation in Motets of Guillaume de Machaut’, Studies in Medieval Music: Festschrift for Ernest H. Sanders (New York, 1990), pp. 209–12Google Scholar. On the general issue, see Fuller, S., ‘Exploring Tonal Structure in French Polyphonic Song of the Fourteenth-Century’, Tonal Structure in Early Music, ed. Judd, C. C. (New York, 1998), pp. 59–84Google Scholar, especially 59–60, 77.

¹⁰⁹ Marchettus of Padua establishes the category of commixture to account for melodies that combine species from different modal categories (Lucidarium, 11.2, pp. 388–90). Jacques of Liège has a category of ‘cantus irregularis’ that chiefly pertains to authentic-plagal mixtures but might theoretically be extended to more problematic cases of modal identity (Speculum Musicae, book 6, ch. 77–8, pp. 221–4).

¹¹⁰ Boen, Johannes, Musica, pp. 32, 45Google Scholar. The latter passage is quoted at length in Strohm, R., The Rise of European Music 1380–1500 (Cambridge, 1993), p. 38Google Scholar.