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Franco of Cologne on the rhythm of organum purum*

Published online by Cambridge University Press:  05 December 2008

Charles M. Atkinson
The Ohio State University


Thanks in part to a fine translation by Oliver Strunk, the Ars cantus mensurabilis of Franco of Cologne is a treatise we all think we know. It is perhaps for this reason that Franco's treatise has been all but ignored in most of the recent discussions of the rhythm of Notre Dame organum. The one noteworthy exception to this is Fritz Reckow's discussion of organum purum in his dissertation on Anonymous iv and in his various articles on organum and related topics in the Handwörterbuch der musikalischen Terminologie, in the Schrade Gedenkschrift, and elsewhere. But for Reckow, and presumably for most other scholars as well, Franco's description of organum is strongly coloured by his theories of mensuration, appearing to place even organum purum under the heading of ‘mensurable music’. This in turn seems to distance Franco from the earliest layer of organum composition at Notre Dame, rendering his ideas of little value in arriving at an interpretation of the rhythmic character of this music.

Research Article
Copyright © Cambridge University Press 1990

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1 Strunk, O., Source Readings in Music History (New York, 1950), pp. 139–59Google Scholar.

2 The interest of scholars has been focused more upon the ideas of Johannes de Garlandia, Anonymous iv and the St Emmeram Anonymous, among the Notre Dame theorists of the mid- to late thirteenth century, or upon the de la Fage Anonymous or the Vatican Organum Treatise in the earlier part of the century. See, for example, Roesner's, E. discussion of ‘Johannes de Garlandia on organum in speciali’, Early Music History, 2 (1982), pp. 129–60CrossRefGoogle Scholar, and his The Performance of Parisian Organum’, Early Music, 7 (1979), pp. 174–89CrossRefGoogle Scholar. (Roesner's discussion of Franco's term floratura will be reviewed later in this study.) See also Sanders, E. H., ‘Consonance and Rhythm in the Organum of the 12th and 13th Centuries’, Journal of the American Musicological Society, 33 (1980), pp. 264–86CrossRefGoogle Scholar; Yudkin, J., ‘The Rhythm of Organum purumThe Journal of Musicology, 2 (1983), 355–76CrossRefGoogle Scholar; idem, ‘Notre Dame Theory: A Study of Terminology, including a New Translation of the Music Treatise of Anonymous iv’ (Ph.D. dissertation, Stanford University, 1982)Google Scholar; Fuller, S., ‘Theoretical Foundations of Early Organum Theory’, Acta Musicologica, 53 (1981), pp. 5284CrossRefGoogle Scholar; and Immel, S., ‘The Vatican Organum Treatise Re-examined’, Abstracts of Papers Read at the Fiftieth Annual Meeting of the American Musicological Society (Philadelphia, 1984), p. 18Google Scholar. For a more complete listing and assessment of recent scholarship on organum, see Yudkin's ‘Notre Dame Theory’, in particular his Introduction and Chapter 1 (pp. 1–48).

3 Reckow, F., Der Musiktraktat des Anonymus 4, Beihefte zum Archiv für Musikwissenschaft 4 and 5 (Wiesbaden, 1967)Google Scholar; Proprietas und perfectio: Zur Geschichte des Rhythmus, seiner Aufzeichnung und Terminologie im 13. Jahrhundert’, Acta Musicologica, 39 (1967), pp. 115–43CrossRefGoogle Scholar; ‘Organum’, Handwörterbuch der musikalischen Terminologie (Wiesbaden, 1971)Google Scholar; Die Copula: Über einige Zusammenhänge zwischen Setzweise, Formbildung, Rhythmus und Vortragsstil in der Mehrstimmigkeit von Notre Dame, Akademie der Wissenschaften und der Literatur zu Mainz: Abhandlungen der geistes- und sozialwissenschaftlichen Klasse, Jg. 1972, Nr. 13 (Wiesbaden, 1972)Google Scholar; ‘Das Organum’, Gattungen der Musik in Einzeldarstellungen: Gedenkschrift Leo Schrade, 1. Folge, ed. Arlt, W., Lichtenhahn, E. and Oesch, H. (Bern, 1973), pp. 434–96Google Scholar; ‘Organum’, sections 1–5, The New Grove Dictionary of Music and Musicians, ed. Sadie, S., 20 vols. (London, 1980), xiii, pp. 796803Google Scholar.

4 See the discussion of this issue below, pp. 6–10. In his article ‘Organum’ for the Handwörterbuch, Reckow shows Franco as placing organum under the genus ‘musica mensurabilis’, stating: ‘Bei Franco spielt der rhythmische Charakter bei der Mehrstimmigkeits-Klassifikation gar keine Rolle mehr, da für ihn alle Mehrstimmigkeit (von den Tenor-Haltetönen abgesehen) als rhythmisch-proportional gemessen gilt’ (op. cit., pp. 9–10). In Der Musiktraktat des Anonymus 4, ii, pp. 40–5Google Scholar, Reckow hypothesises that Franco must already have been dealing with manuscript settings of organum purum in which the upper voice was written in modal, or perhaps even mensural notation: ‘[Franco's] Regelung setzt die Anwendung eines vom Zusammenklang zunächst völlig unabhängigen Rhythmisierungsverfahrens im Duplum voraus, und dieses Verfahren kann nur die modalrhythmische Lesung der Melismen sein eventuell bereits nach mensuraler Umschrift’ (op. cit., p. 40).

5 Franco's remarks on organum purum – a type of music that formed an important part of Leonin's Magnus liber – seem to form a sharp contrast with those of other thirteenth-century theorists. Whereas writers such as Johannes de Garlandia emphasise consonance or dissonance with the given tenor as the determinant of long and short note values in organum purum, Franco's stating that in organum purum ‘Whatever is written as a longa simplex is long; as a breve, short; as a semibreve, still shorter’, and ‘Whatever is long requires concord with respect to the tenor,’ does indeed seem to suggest that he was dealing with a later version of this type of music, just as Reckow hypothesised.

6 See the works cited in nn. 2 and 3 above.

7 ‘Proponimus igitur ipsam mensurabilem musicam sub compendio declarare; bene dictaque aliorum non recusabimus interponere, erroresque destruere et fugare; et si quid novi a nobis inventum fuerit, bonis rationibus sustinere et probare’; Franconis de Colonia Ars cantvs mensvrabilis, ed. Reaney, G. and Gilles, A., Corpus Scriptorum de Musica [hereafter CSM] 18 ([Rome], 1974), p. 24Google Scholar. All translations are mine unless otherwise indicated.

8 The division and numbering of chapters is that given in CSM 18.

9 Jerome's version reads: ‘Mensura est habitudo quantitatem, longitudinem et brevitatem cujuslibet cantus mensurabilis manifestans’. For the complete text see Hieronymus de Moravia O.P.: Tractatus de musica, ed. Cserba, S. O.P., Freiburger Studien zur Musikwissenschaft 2 (Regensburg, 1935)Google Scholar.

10 For the parallel passages in Johannes de Garlandia see Reimer, , Johannes de Garlandia, Beihefte zum Archiv für Musikwissenschaft 10 (Wiesbaden, 1972), p. 35Google Scholar, lines 1–3 (musica mensurabilis), and p. 36, sent. 5–8, and p. 37, Sent. 16–20 (mensura); for Anon. iv, see Reckow, , Der Musiktraktat des Anonymus 4, i, p. 22Google Scholar, lines 3–6 (mensura). In Anon. iv, see also p. 76, lines 12–35, and p. 77, lines 1–6. Somewhat surprising, given his dependence upon Johannes de Garlandia for certain aspects of his theory, is the fact that the St Emmeram Anonymous also uses the word ‘quantitas’ to distinguish between non-mensurable and mensurable music: ‘Et nota, quod inmenourabilis est illa, ubi non sunt longe uel breues uel aliqua quantitas temporum sub certo numero distributa. Mensurabilis est illa, in qua sua quantitas temporum reperitur’, Sowa, H., ed., Ein anonymer glossierter Mensuraltraktat 1279, Königsberger Studien zur Musikwissenschaft 9 (Kassel, 1930), p. 5Google Scholar (my italics).

11 In his famous essay on Gothic Architecture and Scholasticism (Cleveland and New York, 1957)Google Scholar E. Panofsky pointed to the importance of the Scholastic summa as a conceptual model that could operate in architecture just as in the various types of philosophical, scientific and theological writings that were its primary manifestation. Its principal attributes were: (1) totality (sufficient enumeration), (2) arrangement according to a system of homologous parts and parts of parts (sufficient articulation), (3) distinctness and deductive cogency (sufficient interrelation) (see Panofsky, p. 31). In the summa, as in other Scholastic writing, the commanding ideal was a mode of expression that would make the orderliness and logic of the author's thought palpably explicit and clear. Although I would not go so far as to characterise Franco's Ars cantus mensurabilis as a ‘summa’ in the sense of Aquinas's Summa theologica, Franco himself refers to his work as a ‘compendium’, and it does exhibit a number of traits (e.g. its striving to be comprehensive, the logical, hierarchical arrangement of its parts, and the clarity and specificity of its treatment) that place it squarely in the Scholastic tradition as Panofsky and others have characterised it. (The classic treatment of Scholasticism is of course Grabmann's, M.Geschichte der scholastischen Methode, 2 vols. [Freiburg, 19091911; repr. 1957]Google Scholar, and the subject is treated in almost any work on medieval intellectual history. Two recent treatments are those of De Wulf, M., An Introduction to Scholastic Philosophy, trans. Coffey, P. [New York, 1956]Google Scholar and Pieper, J., Scholasticism [London, 1960].)Google Scholar

12 ‘Notandum quod tam in discantu quam in triplicibus etc. inspicienda est aequipollentia in perfectionibus longarum, brevium et semibrevium, ita quod tot perfectiones in tenore habeantur quot in discantu vel in triplo etc., vel e converso, computando tam voces rectas quam obmissas usque ad penultimam, ubi non attenditur talis mensura, sed magis est organicus ibi punctus’ (CSM 18, p. 75; my italics).

13 The relevant sentences in chapter i are sentences 9 and 11. See Excerpt 2 above.

14 Cf. the description of organum purum (=organum speciale) in the St Emmeram Anonymous's discussion of the four-note ligature with perfection and with opposite propriety: ‘Ipsa figura quaternaria figurata per oppositum et perfecta semper in dispositione organi specialis nascitur sibi esse; id est quociensconque in cantu aliquo ordinatur, supra burdonem tenoris edificari cernitur a natura et sub dispositione organi specialis.’ (‘This quaternary figure, written per oppositum and perfect, always arises in the disposition of organum speciale; that is, whenever it is disposed in some melody [cantus] it is perceived to be erected over a burdo of the tenor by the nature and under the disposition of (organum speciale’.) Sowa, , ed., Ein anonymer glossierter Mensuraltraktat, p. 53Google Scholar, lines 2–6; my italics.) Franco's use of the phrase in unisono in this passage has a direct parallel in the treatise of Johannes de Garlandia. In his discussion of organum cum alio, Johannes states: ‘eius aequipollentia tantum se tenet in unisono usque ad finem alicuius puncti, ut secum convenit secundum aliquam concordantiam’ (‘its equivalence is maintained in unisono [i.e. over a single pitch sustained in the tenor] as far as the end of a section, so that it might come together with it in some consonance’; Reimer, , Johannes de Garlandia, i, pp. 88–9; my italics.) See also the discussion below, pp. 1516Google Scholar.

15 On the translation of the pharse ‘omne id quod accidit’ in this passage and the significance it holds for the interpretation of Johannes's ideas, see Sanders, E., ‘Consonance and Rhythm in the Organum of the 12th and 13th Centuries’, Journal of the American Musicological Society, 33 (1980), pp. 269–71CrossRefGoogle Scholar, and the Communications of Professors Reckow and Sanders, ibid, 34 (1981), pp. 588–91. On Johanne's ‘rules of consonance’ themselves, see Apel, W., ‘From St. Martial to Notre Dame’, Journal of the American Musicological Society, 2 (1949), pp. 145–58CrossRefGoogle Scholar, and Waite, W., ‘Discantus, Copula, Organum’, Journal of the American Musicological Society, 5 (1952), pp. 7787CrossRefGoogle Scholar, and The Rhythm of Twelfth-Century Polypony (New Haven and London, 1954), pp. 120–2Google Scholar. Both of these authors based their discussion on Coussemaker's edition (de Coussemaker, E., ed., Scriptorum de musica medii aevi nova series [herafter CS], i, pp. 97117 and 175–85)Google Scholar. Reckow, F. (Der Musiktraktat des Anonymus 4, ii, pp. 35–9, 45)Google Scholar arrived at a new interpretation of Garlandia in part through a series of astute text-critical observations. He demonstrated clearly that the text in Coussemaker was faulty, and that a new edition was needed. For treatments based on the new edition by Reimer, (Johannes de Garlandia, iii)Google Scholar, see Sanders, ‘Consonance and Rhythm’, pp. 267–74, and Yudkin, ‘The Rhythm of Organum Purum’.

16 As both Reckow and Roesner point out, Garlandia's second and third rules are ‘codicils’ to the first, addressing specific instances in which the general rule does not apply. The import of the second rule, in Roesner's words, is that ‘the modal pattern takes precedence over the first rule at the ends of phrases’ (Roesner, ‘Johannes de Garlandia’, p. 154). In Franco, the ‘rule of the figura’ has become the first one, and presumably applies anywhere in the course of the duplum melody.

17 On this point see Hughes, A., ‘Franco of Cologne’, The New Grove Dictionary, vi, pp. 794–7Google Scholar, and Apel, W., The Notation of Polyphonic Music 900–1600, 5th edn (Cambridge, MA, 1953), pp. 310–15Google Scholar. On the relationship of Franco's treatise to others in the thirteenth and early fourteenth centuries see Arlt, W. and Haas, M., ‘Pariser modale Mehrstimmigkeit in einem Fragment der Basler Universitätsbibliothek’, Forum Musicologicum, Basler Studien zur Musikgeschichte 1 (Bern, 1975), pp. 231–41Google Scholar.

18 The example illustrating these rules, however, is written in modal, not mensural, notation in all manuscripts of the treatise except Paris, Bibliothèque Nationale, MS fonds lat. 16663. Cf.Reckow, , Der Musiktraktat des Anonymus 4, ii, p. 40 n. 9Google Scholar, and Cserba, , ed. Hieronymus de Moravia, p. 258Google Scholar.

19 Roesner, ‘The Performance of Parisian Organum’, p. 176.

20 Reckow, , Der Musiktraktat des Anonymus 4, ii, p. 41 n. 9Google Scholar.

21 As pointed out in n. 18 above, the example is written in modal notation in all manuscripts of the treatise except Paris, BN, fonds lat. 16663. Cf. the notation of Iudea et Iherusalem in Wolfenbüttel, Herzog August Bibliothek, MS 628 Helmst. (W1), fol. 13, and Florence, Biblioteca Medicea-Laurenziana, MS Plut. 29.1, fol. 65, both readily available in Parrish, C., The Notation of Medieval Music (New York, 1959)Google Scholar, plates xxviia and xxviib. The version in W1 is particularly striking, since it begins with what looks like a Franconian ternaria without propriety and with perfection, but is in fact a longa simplex followed by a binaria. Although the sources for the Magnus liber show that singers were not willing to go so far as to follow Franco's suggestion of changing the notes of the plainchant in order to create a consonance with a newly composed duplum, there is nonetheless some evidence in practical sources to show that the successive e's in the duplum of the first phrase of Iudea et Iherusalem did indeed create a problematic dissonance with the F in the tenor. Reckow, (Der Musiktraktat des Anonymus 4, ii, p. 41 n. 9)Google Scholar found that in a setting of Benedicamus domino on fol. 24v of the Las Huelgas manuscript – one with the same opening phrase as Iudea et Iherusalem – the last binaria of the phrase (with the pitches e–c) had been changed to a ternaria with the pitches f–d–c, followed by a longa simplex on c. Thus, instead of having an e of three tempora against the F in the tenor, the Las Huelgas setting forces the e of the penultimate ligature to sound for only one tempus.

22 In Reckow's words: ‘Infolgedessen [the statement quoted in n. 4 of the present article] kann sich die Einschränkung, daβ das Organum purum ein cantus non in omni parte sua mensuratus sei …, nicht auf “Teile” (Abschnitte) der Oberstimmen-Melismen – diese sind nach Franco insgesamt rhythmisch streng festgelegt –, sondern nur auf die Tenor-“Stimme” und ihre Haltetöne selbst beziehen; denn diese allein sind (wenn auch nur der Schreibweise nach, nämlich als einfache longae) in ihrem Wert für Franco noch nicht exakt “gemessen”.’; (Der Musiktraktat des Anonymus 4, ii, p. 41)Google Scholar.

23 Anon. vii: ‘tenor est fundamentum motelli et dignior pars’ (CS i, p. 379b); St Emmeram Anonymous: ‘tenor … eo quod sit dignior pars’ (Sowa, , ed., Ein anonymer glossierter Mensuraltraktat, p. 92, lines 19f)Google Scholar; Johannes de Grocheio: ‘Tenor autem est illa pars, supra quam …’ (Rohloff, E., Der Musiktraktat des Johannes de Grocheo, Media Latinitas Musica 2 [Leipzig, 1943], p. 57, line 12)Google Scholar; Pseudo-Johannes, de Muris: ‘dum…pars una multum ascendit, reliqua vero multum descendit …’ (CS iii, p. 240b)Google Scholar. These are cited after Reckow, , Der Musiktraktat des Anoymus 4, ii, p. 41 n. 11Google Scholar.

24 Roesner, ‘The Performance of Parisian Organum’, p. 176.

25 ibid.

26 ibid.

27 I shall refer to the author of this supplement as ‘Pseudo-Garlandia’.

28 Reimer, , Johannes de Garlandia, i, p. 95Google Scholar.

29 For Jerome's discussion of the flos harmonicus, see Cserba, , Hieronymus de Moravia, pp. 183–8Google Scholar. It is clear from Jerome's description of the flos harmonicus that it is indeed performed as Roesner (‘The Performance of Parisian Organum’, p. 177) states. What is not so clear is its connection with Pseudo-Garlandia's florificatio vocis. Roesner is convinced that the connection is close, and that the florificatio vocis ‘is not an attempted graphic representation of some medieval ancestor of the early Baroque trillo’ (p. 177). From his study of the term and concept of color in the thirteenth and fourteenth centuries, Voogt, R. (‘Repetition and Structure in the Three- and Four-Part Conductus of the Notre Dame School’ [Ph.D. dissertation, The Ohio State University, 1982], pp. 2367, esp. pp. 3448)Google Scholar is equally convinced that the florificatio vocis is in fact what Roesner says it is not – namely, a series of repetitions of a single pitch, which in performance would probably sound rather like the Baroque trillo. Voogt feels that the model for Pseudo-Garlandia's florificatio vocis may have been the repercussive neumes of plainchant, examples of which also appear in the Aquitanian versus (cf.Voogt, Repetition and Structure', p. 40, and Fuller, S., ‘Aquitanian Polyphony of the Eleventh and Twelfth Centuries’ [Ph.D. dissertation, University of California at Berkeley, 1969], III, nos. 20–4)Google Scholar.

30 Roesner, ‘The Performance of Parisian Organum’, p. 177. For Jerome's description of the reverberatio see Cserba, , Hieronymus de Moravia, pp. 183–7Google Scholar.

31 ‘Nota procellaris in cantu fieri debet cum apparentia quidem motus absque tamen soni vel vocis interruptione’ (Cserba, , Hieronymus de Moravia, p. 185)Google Scholar; translation from Roesner, ‘The Performance of Parisian Organum’, p. 177.

32 Roesner, ‘The Performance of Parisian Organum’, p. 177.

33 Cserba, , Hieronymus de Moravia, pp. 189–94Google Scholar, and CS I, pp. 94b–97; translated by Knapp, Janet in ‘Two XIII-Century Treatises on Modal Rhythm and the Discant’, Journal of Music Theory, 6 (1962), pp. 200–16CrossRefGoogle Scholar.

34 The word nota had, since Antiquity, carried the meaning of a ‘graphic sign’, ‘mark’ or ‘character’, and was used from late Antiquity (cf. Boethius, De institutione musica, bk IV, ch. 3) through the Middle Ages (cf. Jacques de Liège. Speculum musicae. bk VI. ch. 72) as the standard designation for the graphic signs representing music. For further discussion and bibliography see Huglo, M., ‘Les noms des neumes et leur origine’, Études Grégoriennes, 1 (1954), pp. 5367Google Scholar; Bautier-Régnier, A.-M., ‘A propos du sens de neuma et de nota en latin médiéval’, Revue Belge de Musicologie, 18 (1964), pp. 19CrossRefGoogle Scholar; Stäblein, B., Schriftbild der einstimmigen Musik, Musikgeschiche in Bildern, iii: Musik des Mittelalters und der Renaissance, Lfg 4 (Leipzig, 1975), pp. 68, 19, 26, 30Google Scholar, and Corbin, S., Die Neumen, Paläographie der Musik, i/3 (Cologne, 1977), pp. 3.13.5Google Scholar.

35 ‘Figura, ut hic accipitur, est signum denotans sonum vel sonos secundum suum tempus longitudinis atque brevitatis’ (Cserba, , Hieronymus de Moravia, p. 197)Google Scholar.

36 Franco and Johannes de Garlandia are not alone among thirteenth-century theorists in using the term figura in this way. Cf. the St Emmeram Anonymous: ‘Cum ergo figura sit causa et principium omnis cantus, que et sub certa diminutione temporis seu temporum mensurata compositioni huius artis fons esse dicitur et origo’ (Sowa, , Ein anonymer glossierter Mensuraltraktat, p. 13, lines 9–12)Google Scholar. What is unusual about this is that figura should have been used at all as a designation for a notational sign. As mentioned in n. 34, the standard medieval designation for the graphic signs used to represent music was nota, not figura. The most common use of the term figura in earlier treatises on music is to indicate a diagram (e.g. Aribo, , De musica [c. 1070], ed. van Waesberghe, J. Smits CSM2 [Rome, 1951], pp. 15Google Scholar; the Quaestiones in musica [c. 1120] attributed to Rudolf of St Trond [1070–1138], ed. Steglich, R., Publikationen der Internationalen Musik-Gesellschaft, Beihefte, ii/10 [Leipzig, 1911], p. 18)Google Scholar, although it is sometimes used to designate pitches, particularly in conjunction with the measurement of the monochord (e.g. , Pseudo-Odo, Dialogus in musica, ed. Gerbert, M., Scriptores Ecclesiastici de Musica, i [St Blasien, 1784; repr. Milan, 1931], p. 253bGoogle Scholar; Guido, , Micrologus, CSM 4 [1955], pp. 91–5Google Scholar; Wilhelm, of Hirsau, , Musica, ed. Harbinson, D., CSM 23 [1975], p. 74)Google Scholar. As far as I have been able to determine, the earliest use of figura as a term designating practical notational signs seems to be in the thirteenth century, in treatises dealing with mensurable music. Although it is sometimes equated with nota, as in both Anon, vii and Anon, iv (cf.Reckow, , Der Musiktraktat des Anonymus 4, i, pp. 40–1)Google Scholar, figura – especially when used by itself- carries with it the connotation of a precise, measurable value. This usage must derive from its long tradition as a technical term in mathematics. (Cf. Bede's, De temporum ratione, ed. Jones, C. W., Bedae opera de temporibus [Cambridge, MA, 1943], p. 181Google Scholar, lines 76–82, or the various mathematical works either by or attributed to Gerbert of Aurillac [later Pope Silvester ii], ed. Bubnov, N., Gerberti… Opera mathematica (972–1003) [Berlin, 1899]Google Scholar, passim [see Index].) Its association with mathematics may likewise have had something to do with use of figura in the theory of metrics, although the term already had a connection with poetry via rhetoric. (See, for example, the poem on metrical theory attributed to Walahfrid Strabo, ed. Huemer, J., Neues Archiv der Gesellschaft für ältere deutsche Geschichtskunde, 10 [1885], pp. 166–9Google Scholar, where figura seems to be synonymous with ‘verse’. On rhetorical figures, see Arbusow, L., Colores rhetorici [Göttingen, 1948]Google Scholar, Faral, E., Les arts poétiques du xiie et du xiiie siècle [Paris, 1924]Google Scholar, and Murphy, J., Rhetoric in the Middle Ages [Berkeley, 1974].)Google Scholar It is worth noting here that the author of the Summa musicae (c. 1300), attributed to Johannes de Muris, comments that ‘nota idem operatur in cantu, quod figura in metro’, and goes on to say that ‘Est enim intentio actoris in cantu & actoris in metro una in genere, scilict ut vox cum materia dictaminis sui (concordet)’ (Gerbert, , Scriptores, iii, p. 234b)Google Scholar. A terminological study of figura is still lacking; when done, it should provide fascinating insights into the relationships between music and its sister artes in the Middle Ages. Appel's, M.Terminologie in den mittelalterlichen Musiktraktaten (Berlin, 1935), p. 9Google Scholar, and Gysin, H. P.'s Studien zum Vokabular der Musiktheorie im Mittelalter (Amsterdam, 1958), pp. 98–9, 104Google Scholar, are useful starting-points. I offer the above references – whose list is by no means complete – as a small additional contribution to such a study. I should here like to thank Dr Theresia Payr of the Mittellateinisches Wörterbuch and Dr Michael Bernhard of the Lexicon musicum latinum (both-in Munich), and Dr Christoph von Blumröder of theHandwörterbuch der musikalischen Terminologie (Freiburg im Breisgau), for permission to work in their respective archives during the summers of 1982 and 1986 in preparation for this essay.

37 ‘Ligatura est plurium notarum invicem conjunctarum ligatio, quae quidem in unisono fieri non debet’ (Cserba, , Hieronymus de Moravia, p. 190Google Scholar; my italics). The translation is by Janet Knapp (‘Two XIII-Century Treatises’, p. 203).

38 This interpretation is advanced by both Voogt (‘Repetition and Structure’, pp. 40–3) and Roesner (‘The Performance of Parisian Organum’, p. 176) in their respective interpretations of the passage in question here.

39 See Cserba, , Hieronymus de Moravia, p. 259Google Scholar.

40 Cf. n. 14 above.

41 See, for example, the works cited in n. 15 above.

42 CSM 18, pp. 81–2.

43 Strunk, , Source Readings, p. 159Google Scholar.

44 Roesner, ‘The Performance of Parisian Organum’, p. 176.

45 Cf. Boethius, , De institutione musica libri quinque, ed. Friedlein, G. (Leipzig, 1867), i, 3, p. 189Google Scholar, lines 15–19, 22–3, and i, 31, p. 222, lines 6–12; Cassiodorus, , Institutiones, ed. Mynors, R. A. B. (Oxford, 1937), ii, 5Google Scholar, sections 6 and 7, also in Gerbert, , Scriptores, i, pp. 1617Google Scholar; Isidore, , Etymologiarum sive Originum libri xx, ed. Lindsay, W. M., 2 vols. (Oxford, 1911)Google Scholar, bk iii, section 22, also in Gerbert, , Scriptores, i, pp. 23–4Google Scholar.

46 For a treatment of these terms in Antiquity, see Wagner, R., ‘Der Berliner Notenpapyrus, nebst Untersuchungen zur rhythmischen Notierung und Theorie’, Philologus, 77 (1921), pp. 256310, esp. pp. 301–7Google Scholar.

47 Percutitur vero versus anapaestus praecipue per dipodian, interdum et per singulos pedes. est autem percussio cuiuslibet metri in pedes divisio.’ Victorinus, Marius, Artis grammaticae libri iii, in Keil, H., Grammatici latini, 8 vols. (Leipzig, 18551880), vi, p. 75Google Scholar, lines 26–9 (my italics).

48 ‘Nam cum sint numeri plures, iambum et trochaeum frequentem segregat ab oratore Aristoteles, Catule, vester; qui natura tamen incurrunt ipsi in orationem sermonemque nostrum, sed sunt insignes percussiones eorum numerorum e minuti pedes.’ Cicero, , De oratore, ed. and trans. Rackham, H. H. (Cambridge, MA, 1942), iii, 182–3, pp. 144–5Google Scholar (my italics; the translation is a modified version of Rackham's). See also De oratore, iii, 185–6Google Scholar, and Orator, ed. and trans. Hubbell, H. M. (London, 1952), 198–9Google Scholar.

49 ‘Trimetrum et senarium promisce dicere licet, sex enim pedes, tres percussiones habet.’ Quintilian, Institutio oratoria, ed. and trans. Butler, H. E. (London, 1953), ix, 4, 75, pp. 548–9Google Scholar (my italics). See also Institutio oratoria ix, 4, 51–2, and xi, 3, 108–9Google Scholar.

50 ‘Jambicus autem, cum pedes etiam dactylici generis adsumat, desinit iambicus videri, nisi percussioneita moderaveris, ut, cum pedem supplodes, iambum ferias; ideoque illa loca percussionis non recipiunt alium quam iambum et ei parem tribrachyn, aut alterius exhibuerint metri speciem.’ Rufinus, , Commentarium in metra Terentiana, in Keil, , Grammaticilatini, vi, p. 555Google Scholar, lines 23–7 (my italics).

51 Edition and French translation by Finaert, G. and Thonnard, F.-J., De musica libri sex, Oeuvres de Saint Augustin, lresérie: Opuscules, vii: Dialogues philosophiques, iv: La musique (Bruges, 1947)Google Scholar; English translation by Taliaferro, R. C. in Writings of Saint Augustine, ii, Fathers of the Church 4 (New York, 1947)Google Scholar.

52 Since there is no Index Verborum for the edition, I provide a list of these references here, listed by book, chapter, and section: Percutio: I, i, l; II, xi, 20; II, xiii, 24; IV, i, 1; IV, vii, 8; IV, v, 11; VI, viii, 20. Percussio: II, xi, 20; II, xi, 21; IV, ii, 2; IV, xiv, 24; VI, x, 25. Plaudo: I, v, 10; I, xiii, 27; II, x, 18; II, xiii, 24; II, xiii, 25; II, xiv, 26; III, iv, 9; III, vii, 15; III, vii, 16; IV, ii, 2; IV, xi, 12; IV, xvi, 30; IV, xvi, 33; V, xi, 24; VI, i, 1; VI, x, 27; Plausus: I, vi, 11; I, xiii, 27; II, xi, 20; II, xiii, 24; II, xiii, 25; II, xiv, 26; III, iii, 5; III, iii, 6; III, iv, 7; III, iv, 8; III, iv, 9; III, iv, 10; III, v, 11; III, v, 12; III, vii, 15; III, viii, 18, IV, i, 1; IV, ii, 2; IV, vii, 8; IV, xvii, 35; V, XI, 24; VI, x, 27; VI, xiv, 47. Ictus: I, iv, 9.

53 ‘Intende ergo et aurem in sonum, et in plausum oculos: non enim audiri, sed videri opus est plaudentem manum, et animadverti acriter quanta temporis mora in levatione, quanta in positione sit.’ Augustine, , De musica, II, xiii, 24; Taliaferro translation, p. 233Google Scholar.

54 ‘Vehementer admiror quomodo eo percuti potuerint illi pedes, quorum divisio simpli et dupli ratione constat.’ ibid.; my italics.

55 ‘M. Quantum ergo silendum est, dum repetitur? D. Unum tempus, quod est unius brevis syllabae spatium. M. Age, jam percute hoc metrum, non voce, sed plausu. D. Feci. M. Percute etiam hoc modo anapaestum. D. Et hoc feci.’ Augustine, , De musica, IV, i, 1; Taliaferro, p. 260Google Scholar.

56 Franco defines the perfect long as follows: ‘(6) Longa perfecta prima dicitur et principalis. (7) Nam in ea omnes aliae includuntur, ad eam etiam omnes aliae reducuntur. (8) Perfecta dicitur eo quod tribus temporibus mensuratur’ (CSM 18, p. 29; my italics). His justification for this new concept of the long is: ‘Est enim ternarius numerus inter numeros perfectissimus pro eo quod a summa trinitate, quae vera est et pura perfectio, nomen sumpsit’ (CSM 18, pp. 29–30; my italics). I would posit that the source of this justification was Augustine. Cf. Augustine's statement on the perfection of the number three in I, xii, 20 of De musica: ‘Quare in temario numero quamdam esse perfectionem vides, quia totus est: habet enim principium, medium et finem’ (Finaert and Thonnard, p. 70; my italics).

57 On Bacon, see Emden, A. B., ‘Bacon’, A Biographical Register of the University of Oxford to A.D. 1500, i (Oxford, 1957), pp. 87–8Google Scholar. The principal source of biographical material for Emden's article is Easton, S. C., Roger Bacon and his Search for a Universal Science (New York, 1952)Google Scholar. See also Brewer, J. S., ed., Fr. Rogeri Bacon opera quaedam hactenus inedita, Rerum Britannicarum Medii Aevi Scriptores (Rolls Series) 15 (London, 1859; repr. Frankfurt, 1964)Google Scholar, Preface, , and Burke, R. B., trans., The Opus majus of Roger Bacon (New York, 1928; repr. 1962)Google Scholar, Introduction. For the place of Bacon's work within the intellectual life of the thirteenth century, see Kibre, P., ‘The Quadrivium in the Thirteenth Century Universities’, Arts libéaux et philosophie au moyen âge: Actes du quatrième congrès international de philosophie médiévale, 1967 (Montreal, 1969), pp. 175–91Google Scholar, and Ellinwood, L., ‘Ars musica’, Speculum, 20 (1945), pp. 290–9CrossRefGoogle Scholar. The starting-point for any study of John of Garland must be Paetow, L. J., The Morale Scolarium of John of Garland, with an Introduction to his Life and Works, Memoirs of the University of California, iv/2 (Berkeley, 1927)Google Scholar. See also Paetow, 's The Arts Course at Medieval Universities, with Special Reference to Grammar and Rhetoric, The University of Illinois: The University Studies, iii/7 (Urbana-Champaign, 1910)Google Scholar, and Lawler, T., The Parisiana Poetria of John of Garland, Yale Studies in the History of English 182 (New Haven, 1974)Google Scholar, Introduction.

58 Opus majus, ed. Bridges, J. H., The ‘Opus majus’ of Roger Bacon (London, 1900; repr. Frankfurt, 1964)Google Scholar; Opus tertium, ed. Brewer, , Fr. Rogeri Bacon opera quaedam hactenus inedita, pp. 1310Google Scholar. According to Easton, , Roger Bacon, p. 153Google Scholar, the two works were composed in the same year. Bacon's own remarks in the Opus tertium (e.g. ‘Nam secundum quod exposui in Opere Majori…’, Brewer, , Opus tertium, p. 228)Google Scholar make it clear that the, Opus majus was the earlier of the two works.

59 Gilson, E., History of Christian Philosophy in the Middle Ages (New York, 1955), p. 294Google Scholar. This remark was made specifically with regard to the Opus majus, but certainly pertains to its companion work as well. On the relationship of these two works to each other and to Bacon's Opus minus, see Easton, , Roger Bacon, pp. 144–66Google Scholar.

60 Cf. Waite, , The Rhythm of Twelfth-Century Polyphony, p. 36Google Scholar. The fact that Boethius plays such an important role in Bacon's discussion of arithmetic, but a distinctly secondary role in his discussion of music, is not mentioned by Waite, but it further buttresses his own case for the influence of Augustine on the development of the system of the rhythmic modes (ibid., pp. 29–39).

61 ‘Illa enim est pars necessaria musicae, sicut Augustinus docet secundo Musicae, dicens quod plausus necessarius est, quia non solum est delectatio auditus necessaria, sed visus.’ Bacon, , Opus tertium, cap. lxiv, ed. Brewer, , Opus tertium, pp. 267–8Google Scholar (my italics). Cf. the passage quoted from Augustine, ii, xiii, 24, cited in n. 53 above.

62 Cf. Paetow, , Morale scolarium, pp. 95–6Google Scholar. See also Lawler, , Parisiana poetria, p. xiGoogle Scholar.

63 Among the many works attempting to answer this question, see in particular Machabey, A., ‘Jean de Garlande, compositeur’, Revue Musicale, no. 221 (1953), pp. 20–2Google Scholar; Waite, W., ‘Johannes de Garlandia: Poet and Musician’, Speculum, 35 (1960), pp. 179–95CrossRefGoogle Scholar; Rasch, R. A., lohannes de Garlandia en de ontwikkeling van de voor-Franconische notatie, Musicological Studies 20 (Brooklyn, 1969)Google Scholar, and most recently Reimer, , Johannes de Garlandia, i, pp. 117Google Scholar. Reimer feels that John of Garland the poet and Johannes de Garlandia the author of De mensurabili musica are not the same person.

64 Ed. Lawler, Parisiana poetria. For a study of the relationship of John's Parisiana poetria to the contemporaneous Parisian sequence and, in turn, to the theory and practice of rhythm in the late twelfth and thirteenth centuries, see Fassler, M., ‘The Role of the Parisian Sequence in the Evolution of Notre-Dame Polyphony’, Speculum, 62 (1987), pp. 345–74CrossRefGoogle Scholar. Like the present author, Fassler underscores the importance of the beat or ictus, which John of Garland describes with the term percussio (see in particular pp. 358–61 of Fassler's study).

65 ‘Est autem ductia sonus illitteratus, cum decenti percussione mensuratus. Dico … cum recta percussione, eo quod ictus eam mensurant et motum facientis et excitant animum hominis ad ornate movendum secundum artem, quam ballare vocant, et eius motum mensurant in ductiis et choreiis.’ Johannes, de Grocheio, [De musica], ed. Rohloff, E., Der Musiktraktat des Johannes de Grocheo, Media Latinitas Musica 2 (Leipzig, 1943), p. 52Google Scholar, lines 38–44, and Rohloff, , ed., Die Quellenhandschriften zum Musiktraktat des Johannes de Grocheio (Leipzig, n.d.), p. 136Google Scholar, lines 13–20.

66 ‘Componere ductiam et stantipedem est sonum per puncta et rectas percussiones in ductia et stantipede determinare.’ Rohloff, , Der Musiktraktat, p. 53Google Scholar, lines 23–4; Die Quellenhandschriften, p. 136, lines 147–8.

67 The lexica and glossaries consulted include the following: Arnaldi, F., Latinitatis italicae medii aevi … lexicon imperfectum (Brussels, 1939)Google Scholar; Bartal, A., Glossarium mediae et infimae latinitatis regni hungariae (Leipzig, 1901; repr. Hildesheim, 1970)Google Scholar; Baxter, J. H. and Johnson, C., Medieval Latin Word List from British and Irish Sources (Oxford, 1934)Google Scholar; Blaise, A., Lexicon latinitatis medii aevi, Corpus Christianorum, Continuatio Medievalis (Turnhout, 1975)Google Scholar; Castro, A., Glosarios latino-españnoles de la edad media (Madrid, 1936)Google Scholar; Diefenbach, L., Glossarium latino-germanicum mediae et infimae aetatis (Frankfurt, 1857)Google Scholar; Du Cange, C., Glossarium mediae et infimae latinitatis (Niort, 18831887; repr. Graz, 1954)Google Scholar; Forcellini, A., Totius latinitatis lexicon (Padua, 18641898)Google Scholar; Glossarium mediae latinitatis sueciae (Stockholm, 1968)Google Scholar; Latham, R. E., Revised Medieval Latin Word List from British and Irish Sources (Oxford, 1965)Google Scholar; Lexicon mediae et infimae latinitatis polonorum (Wroclaw, Warsaw, Kraków and Gdańsk, 1975)Google Scholar; Maigne d'Arnis, W.-H., Lexicon manuale ad scriptores mediae et infimae latinitatis (Paris, 1866)Google Scholar; Niermeyer, J. F., Mediae latinitatis lexicon minus (Leiden, 1976)Google Scholar; Souter, A., A Glossary of Later Latin to 600 A.D. (Oxford, 1949)Google Scholar; Thesavrvs lingvae latinae (Leipzig, 1940–)Google Scholar.

68 de Liège, Jacques, Speculum musicae, ed. Bragard, R., Jacobi Leodiensis Specvlvm mvsicae, CSM 3 (1973), bk viii, cap. ii, pp. 78Google Scholar. The edition reads ‘fḻoraturis’ instead of ‘fḻoraturis’. For the passage in question, however, both of the manuscripts containing it (Florence, Biblioteca Medicea-Laurenziana, Plut. 29.16, fol. 122v, and Paris, Bibliothèque Nationale, fonds lat. 7207, fol. 275v) have ‘floraturis’, with ‘1’, not ‘i’, in the first syllable. I wish to thank Dr Anna Lenzuni, of the Biblioteca Medicea-Laurenziana, and Dr François Avril, of the Bibliothèque Nationale, for their assistance in confirming these readings. I should also like to thank Professor Peter Lefferts for informing me (in a letter of 30 November 1988) of two further references to floritura/floratura. The first is in maxim 11 of rubric XIII of Robertus de Handlo's Regule, in which Handlo gives examples of the types of music exhibiting the fifth of Franco's rhythmic modes, consisting of breves and semibreves (I quote from the draft text of Professor Lefferts's forthcoming edition of the treatise): ‘Abhoc siquidem modo proveniunt hoketi omnes, rundelli, ballade, coree, cantifractus, estampete, floriture,…’ (cf. CS i, p. 402b)Google Scholar. The second reference occurs in both versions of the quartum principale of the Quatuor principalia (CS iii, p. 354b= CS iv, p. 278a): ‘Discantus enim sic dividitur … alius est copulatus qui dicitur copula, id est floritura.’ As Lefferts points out, this passage is a gloss on Franco's initial mention of copula as a type of discant in chapter 2 of the Ars cantus mensurabilis (CSM 18, p. 26). As both of these references would suggest, the relationship between copula and floritura is one that deserves a thoroughgoing treatment. (I should note here that the quartum principale, glossing the first sentence of Franco's chapter on organum purum, says ‘organum proprie sumptum mensuram non retinet’ [CS iii, p. 363b = CS iv, p. 297a], but does not mention floratura in this context; indeed, it does not treat of sentence 7 of the chapter at all.)

69 ‘Sed si forte in fine clausulae in ultima aut in penultima dictionis sillaba, ut discantus pulchrior et facetior habeatur et ab auscultantibus libentius audiatur, aliquos organi modulos volueris admiscere licet facere.’ Seay, A., ed., ‘An Anonymous Treatise from St. Martial’, Annales Musicologiques, 5 (1957), pp. 742Google Scholar; passage quoted from p. 33 (my italics).

70 CSM 18, p. 75 (my italics); cf. n. 12 above.

71 Cf. n. 22 above. There is yet a further interpretation of Franco's statement that should at least be mentioned here as a hypothesis. As discussed earlier in this paper, some parts of organum purum seem in Franco's view to involve a duplum whose notation is rhythmically fixed – ‘rhythmisch streng festgelegt’, in Reckow's words. It may be no accident that the musical example manifesting this conception is the opening section or ‘pars’ of ludea et Iherusalem, which in both the practical sources and the manuscripts of Franco's treatise is written in a clear first-mode pattern. It was this example and the ‘rules of consonance’ connected with it that led Reckow to hypothesise that Franco might have been working with settings of organum written in modal notation or perhaps even rewritten in mensural notation. Evidence that would support this view has been offered by Roesner, who points out (‘Johannes de Garlandia on organum in speciali’, p. 159 n. 85) that in the manuscript Berlin, Staatsbibliothek der Stiftung Preussischer Kulturbesitz, lat. 4° 523, material notated in modus non rectus in other sources has been re-notated mensurally. Reckow's hypothesis thus seems quite plausible. Under such circumstances it could well be that the one ‘part’ of organum purum still being performed in its original manner in Franco's time was that ‘on penultimates’, which – even if notated in figurae suggesting fixed rhythmic values – was to be performed in a rhythmically free fashion.

72 With this point in mind, one contemplating an edition of this music would be well advised to read the remarks by Zaminer, F., Der vatikanische Organum-Traktat (Ottob. lat. 3025): Organum-Praxis der frühen Notre Dame-Schule und ihrer Vorstufen, Münchner Veröffentlichungen zur Musikgeschichte 2 (Tutzing, 1959), pp. 99100Google Scholar, and Eggebrecht, H. H., ‘Organum purum’, Musikalische Edition im Wandel des historischen Bewußtseins, ed. Georgiades, T. (Kassel, 1971), pp. 93112, esp. pp. 110–12Google Scholar. See also J. Yudkin, ‘The Rhythm of Organum Purum’, especially pp. 374–6.

73 ‘Organum autem non aequalitate punctorum sed infinita multiplicitate ac mira quadam flexibilitate cantui suo concordat in aliqua, ut dictum est, consonantiarum, aut cum cantu debet incipere et inde modulando vel lasciviendo, prout oportuerit et organizator voluerit, vel ascendere superius vel inferius descendere, tandem vero in diapason aut cum cantu terminum ponere’ (Seay, ‘An Anonymous Treatise’, p. 35, sent. 11). On the treatise itself, and specifically on this passage and its significance, see Eggebrecht, H. H., ‘Die Mehrstimmigkeitslehre von ihren Anfängen bis zum 12. Jahrhundert’, Die mittelalterliche Lehre von der Mehrstimmigkeit, Geschichte der Musiktheorie 5 (Darmstadt, 1984), pp. 987, esp. pp. 5966Google Scholar. Eggebrecht points out that the edition by Seay needs to be revised to incorporate readings from Barcelona, Biblioteca Central, MS 883, and Parma, Biblioteca Paltina, MS parm. 1158. My translation is a modified version of that by E. Sanders (‘Consonance and Rhythm’, p. 265).

74 Seay, ‘An Anonymous Treatise’, p. 35, sent. 13.

75 ‘Quodsi plures quam quatuor fuerint, tune quasi regulis non subjacent, sed ad placitum proferuntur. Quae etiam ad organum et conductum pertinent singulariter’ (Cserba, , Hieronymus de Moravia, p. 190Google Scholar; my italics). Translation by Janet Knapp (‘Two XIII-Century Treatises’, p. 203).

76 On Kilwardby, who taught in Paris c. 1240, see pp. xi–xvii of the Introduction to the edition of De ortu scientiarum by A. G. Judy O.P., Auctores Britannici Medii Aevi 4 (Oxford and Toronto, 1976) and Haas, M., ‘Studien zur mittelalterlichen Musiklehre I: Eine Übersicht über die Musiklehre im Kontext der Philosophic des 13. und frühen 14. Jahrhunderts’, Forum Musicologicum, 3 (Winterthur, 1982), pp. 323456, esp. pp. 403–8Google Scholar. According to Judy (op. cit., pp. xvii–xxxi), the supplement is contained in the manuscripts Munich, Bayerische Staatsbibliothek, clm 28186, fols. 258r–259v; Florence, Biblioteca Medicea-Laurenziana, Plut. xxvii, dext., cod. 9, fol. 143v–145r; and Kraków, Biblioteka Jagiellońska 754, fols. 42, 43v, 44r. It has been discussed briefly by F. Reckow on p. 283 of his ‘ “Ratio potest esse, quia …”: Über die Nachdenklichkeit mittelalterlicher Musiktheorie’, Die Musikforschung, 37 (1984), pp. 281–8Google Scholar. I am very grateful to Professor Reckow for information about the treatise and the forthcoming edition of its text.

77 The quotations are from the draft text of the edition of the ‘Kilwardby Anonymous’ now being prepared by Dr Ulrike Hascher-Burger. I am most grateful to Dr Hascher-Burger for allowing me to quote from her text before its publication.

78 Cf. n. 11 of this study.

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