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Published online by Cambridge University Press: 24 August 2009
Although medieval plainsong is known as a primarily diatonic repertory, the presence of a ‘non-diatonic’ tradition was brought to light long ago in the work of Jacobsthal, Delalande and others. This essay considers some aspects of this practice that have not been fully examined in previous studies and explores their relationship to early medieval theory and pedagogy. In the solo verses of the offertory chants, large sections are displaced from the diatonic background scale, sometimes permanently. The conception of irregular semitones presented in Scolica enchiriadis yields insight into this extensive ‘non-diatonic’ practice and has implications for interpreting variant readings of these problem spots. The final section of the essay explores some aspects of the Enchiriadis reception that point to changes in tone-system and pitch conception, shedding light on the contexts surrounding the suppression of irregular semitones.
1 G. Jacobsthal, Die chromatische Alteration im liturgischen Gesang der abendländischen Kirche (Berlin, 1897; repr. Hildesheim, 1970); D. Delalande, Vers la version authentique du Graduel grégorien: Le Graduel des Prêcheurs, Bibliothèque d'histoire dominicaine (Paris, 1949); id., ‘L'insuffisance du système d'écriture guidonien’, in Atti del congresso internazionale di musica sacra (Rome, 1950), pp. 202–6; U. Bomm, Der Wechsel der Modalitätbestimmung in der Tradition der Meßgesänge im IX. bis XIII. Jahrhundert und sein Einfluß auf die Tradition ihrer Melodien (Einsiedeln, 1929; repr. Hildesheim, 1975). The problem has been explored more recently in several studies, including C. Frasch, ‘Notation as a Guide to Modality in the Offertories of Paris, B.N. lat. 903’ (Ph.D. diss., Ohio State University, 1986); F. Praßl, ‘Chromatische Veränderungen von Choralmelodien in Theorie und Praxis’, in S. Klöckner (ed.), Cantando praedicare: Godehard Joppich zum 60. Geburtstag (Regensburg, 1992), pp. 129–55; A. Pfisterer, Cantilena Romana: Untersuchungen zur Überlieferung des gregorianischen Chorals (Paderborn, 2001); and the studies cited below (nn. 2, 4, 6, 9 and 11).
2 For more detailed discussions of Beatus servus, see Jacobsthal, Die chromatische Alteration, p. 99 ff.; C. Atkinson, ‘From Vitium to Tonus Acquisitus: On the Evolution of the Notational Matrix of Medieval Chant’, in Cantus Planus: Papers Read at the Third Meeting, Tihany, Hungary, 19–24 September 1988, ed. L. Dobszay (Budapest, 1990), pp. 181–99; id., The Critical Nexus: Tone-System, Mode, and Notation in Early Medieval Music (New York, 2008), pp. 163–7; 237; and T. Karp, Aspects of Orality and Formularity in Gregorian Chant (Evanston, Ill., 1999), pp. 197–8.
3 R. Maloy, Inside the Offertory: Aspects of Chronology and Transmission (New York, 2009).
4 Some of the same problems in the respond of this melody have been discussed in H. Rumphorst, ‘Ein schwieriges Beispiel der Melodierestitution: Das Offertorium Oravi’, Beiträge für Gregorianik, 44 (2007), pp. 49–66.
5 For circumstances surrounding the copying and dating of Pa 1121, see J. Grier, ‘The Musical Autographs of Adémar de Chabannes (989–1034)’, Early Music History, 24 (2005), pp. 125–67; and id., The Musical World of a Medieval Monk: Adémar de Chabannes in Eleventh-Century Aquitaine (Cambridge, 2007), pp. 1–96.
6 R. Hankeln, Die Offertoriumsprosuln der aquitanischen Handschriften: Voruntersuchungen zur Edition des aquitanischen Offertoriumscorpus und seiner Erweiterungen, 2 vols. (Tutzing, 1999), pp. 86–94; R. Fischer, ‘Die Bedeutung des Codex Paris, B.N. lat. 776 (Albi) und des Codex St. Gallen, Stiftsbibliothek 381 (Versikular) für die Rekonstruktion gregorianischer Melodien’, Beiträge zur Gregorianik, 22 (1996), pp. 43–73.
7 ‘Sed et in Offertorio Oravi Deum meum in duobus locis emendatione indiget, scilicet in principio et ubi est super, ut hic patet’; Johannes Affligemensis, De musica cum tonario, ed. J. Smits van Waesberghe (Rome, 1950), p. 150. For an English translation see Hucbald, Guido, and John on Music: Three Medieval Treatises, trans. Warren Babb, ed. C. V. Palisca (New Haven, 1978), p. 156.
8 Berlin, Staatsbibliothek zu Berlin, Mus. ms. 40078; Reims, Bibliothèque municipale 264; and Cambrai, Médiathèque municipale 61. These manuscripts circumvent the a♭ (an e♭ at the affinal position) with the ‘German chant dialect’: it is simply raised to f.
9 Hankeln, Die Offertoriumsprosuln, i, pp. 86–94; id., ‘Was Meint der Schreiber? Überlegungen zur Notation des Offertoriums Tui Sunt Celi im Graduale von St. Yrieix, Paris Bibliothèque Nationale, Fonds Latin 903’, in Cantus Planus: Papers Read at the 6th Meeting, Eger, Hungary, ed. L. Dobszay (Budapest, 1995), pp. 539–60.
10 The pitch level indicated in Pa 776 is also found in Ben 39; London, British Library, Harley MS 4951; Pa 780; Pa 1121; Pa 1132 and Pa 903. The pitch level of Ben 34 is matched in geographically diverse sources such as Mo 159, Ben 35, Berlin, Staatsbibliothek zu Berlin 40078, Pa 1235, Cambrai, Médiathèque municipale 61, Pa 1235, Reims, Bibliothèque municipale 264, Graz, Universitätsbibliothek 807, Trier, Stadtbibliothek 2254, Modena, Archivio capitolare 7, Rome, Biblioteca Vallicelliana 52, Pistoia, Biblioteca capitolare 120, and Turin, Biblioteca Nazionale Universitaria, sezione Musicale 18.
11 Theinred of Dover's De legitimis ordinibus pentachordorum et tetrachordorum has traditionally been dated to the thirteenth century, but John Snyder has proposed a twelfth-century origin. See J. L. Snyder, Theinred of Dover's De Legitimis ordinibus pentachordorum et tetrachordorum: A Critical Text and Translation with an Introduction, Annotations, and Indices (Ottawa, 2006), pp. 14–24; Theinred's approach to non-diatonic notes is summarised on pp. 75–87 and in id., ‘Non-diatonic Tones in Plainsong: Theinred of Dover versus Guido d'Arezzo’, in La musique et la rite: Sacré et profane. Actes du XIIIe Congrès de la Société internationale de musicologie (Strasbourg, 1986), pp. 48–67.
12 Jacobsthal, Die chromatische Alteration, pp. 269–354.
13 Atkinson, ‘From Vitium to Tonus Acquisitus’ and The Critical Nexus, pp. 128–34. See also the summary in D. Cohen, ‘Notes Scales, and Modes in the Earlier Middle Ages’, in T. Christensen (ed.), The Cambridge History of Western Music Theory (Cambridge, 2002), pp. 328–31.
14 John Caldwell has recently hypothesised that this central octave, with two disjunct tetrachords, forms an early layer of theory, expansions of which are reflected in Hucbald and the Enchiriadis treatises. See J. Caldwell, ‘Modes and Modality: A Unifying Concept for Western Chant’, in T. Bailey and A. Santosuosso (eds.), Music in Medieval Europe: Studies in Honour of Bryan Gillingham (Aldershot, 2007), pp. 35–48.
15 Peter Wagner, Joseph Smits van Waesberghe and Lawrence Gushee have taken the view that the Enchiriadis tone system is a purely theoretical construct, showing no correspondence to chant, whereas Lincoln Spiess suggests that it was created to accommodate parallel organum. P. Wagner, Einführung in die gregorianischen Melodien II: Neumenkunde. Paläographie des liturgischen Gesanges (Freiburg, 1905), pp. 228–9; L. Spiess, ‘The Diatonic Chromaticism of the Enchiriadis Treatises’, Journal of the American Musicological Society, 12 (1959), pp. 1–6; J. Smits van Waesberghe, Musikerziehung: Lehre und Theorie der Musik im Mittelalter (Leipzig, 1969), p. 104; L. Gushee, ‘Musica Enchiriadis’, in The New Grove Dictionary of Music and Musicians, ed. S. Sadie (London, 1980), xii, p. 802. Important exceptions to these trends include Jacobsthal, Die chromatische Alteration, pp. 271–3, and M. Markovitz, Das Tonsystem der abendländischen Musik im frühen Mittelalter (Bern, 1977), pp. 73–9.
16 Guido Aretinus, Regulae rhythmicae, ed. J. Smits van Waesberghe (Buren, 1985), pp. 101–2. (‘De notis Enchiriadis / Miror quattuor fecisse quosdam signa vocibus / Quasi quintae sint eaedem, quarum quaedam dissonant’); English translation in D. Pesce, Guido d'Arezzo's Regule Rithmice, Prologus in Antiphonarium, and Epistola ad Michahelem: A Critical Text and Translation (Ottawa, 1999), p. 345. Hermannus Contractus, Musica, ed. L. Ellingwood (Rochester, NY, 1936), pp. 23–4 (‘Quo in loco quidam enchiriadis musicae auctor non mediocriter errauit. Qui ipsa bina septenarum uocum quadrichorda duabus contra naturam medietatibus separans. Ipsius medietatis tropum quod impossibile est duplicauit. Et ita pro duorum naturali positione tonorum continuum tritonum incurrit. sicque totius monochordi structuram regulari eius ordine disturbato destruxit’).
17 C. Bower, ‘“Adhuc ex parte et in enigmate cernimus …”: Reflections on the Closing Chapters of Musica enchiriadis’, in A. Giger and T. Mathiesen (eds.), Music in the Mirror: Reflections on the History of Music Theory and Literature for the 21st Century (Lincoln, Nebr., 2002), pp. 21–44.
18 H. Schmid, Musica et Scolica Enchiriadis una cum aliquibus tractatulis adiunctis (Munich, 1981), pp. 62–6. For an English translation, see R. Erickson, Musica Enchiriadis and Scolica Enchiriadis (New Haven, 1995), pp. 35–8.
19 ‘At singuli horum quattuor sic sunt competenti inter se diversitate dissimiles, ut non solum acumine differant et gravitate, sed in ipso acumine et gravitate propriam naturalitatis suae habeant qualitatem, quam rursus his singulis ratum ab invicem acuminis et laxionis spacium format… . Primus qui et gravissimus Grece protos dicitur, vel archoos; Secundus deuteros, tono distans a proto; Tertius tritos, semitonio distans a deutero; Quartus tetrardus, tono distans a trito.’ Musica et scolica, ed. Schmid, p. 4; Musica Enchiriadis, trans. Erickson, p. 2.
20 Bower, ‘“Adhuc ex parte”’ and ‘The Transmission of Ancient Music Theory into the Middle Ages’, in Christensen (ed.), The Cambridge History of Western Music Theory, pp. 153–8.
21 N. Phillips, ‘Musica and Scolica enchiriadis: The Literary, Theoretical, and Musical Sources’ (Ph.D. diss., New York University, 1985), pp. 473–97; and ‘Notationen und Notationslehren von Boethius bis zum 12. Jahrhundert’, in Geschichte der Musiktheorie, iv (Darmstadt, 2000), pp. 311–14. Atkinson and Bower also tend to believe that the system was created to accommodate plainchant. See Atkinson, The Critical Nexus, pp. 130–3; and Bower, ‘The Transmission of Ancient Music Theory’, p. 156.
22 The most thorough descriptions of this pitch are in the Leipzig tonary: Quellen zur Transformation der Antiphonen: Tonar- und Rhythmusstudien, ed. H. Sowa (Kassel, 1935), pp. 81–154; and Quaestiones in musica, ed. R. Steglich (Leipzig, 1911). The relevant passages from these treatises are extensively discussed in Phillips, ‘Music and Scolica’, pp. 485–97. See also München, Bayerische Staatsbibliothek, Clm 14965b: The Tonary of Frutolf of Michelsberg, ed. R. Maloy (Ottawa, 2006), pp. 27–32.
23 For a discussion of the Byzantine parallels (phthorai), see Atkinson, The Critical Nexus, p. 117 and p. 130.
24 ‘Si aut ignavius pronuntientur aut acutius, quam oportet. Primo namque hoc vitio in humanis vocibus et sonorum qualitas et tota leditur cantilena. Quod fit, ubi, quod canitur, aut segni remissione gravescit aut non rite in sursum cogitur. Quod vitium in quibuslibet musicis instrumentis nequit fieri, eo quod disposito semel ptongorum ordine vox sua sonis singulis manet. Alia fit dissonantia, quando sonus a sono falso metitur, id est alius pro alio. Tertia dissonantia, quando sonus non respondet sono, quoto loco oportet.’ Musica et Scolica, ed. Schmid, pp. 61–2; Musica Enchiriadis, trans. Erickson, p. 34.
25 ‘Vitia nimirum sunt, sed sicut barbarismi et soloecismi metris plerumque figuraliter intermiscentur, ita limmata interdum de industria cantibus inseruntur.’ Musica et Scolica, ed. Schmid, p. 70.
26 On the grammar–music analogy, see C. Bower, ‘The Grammatical Model of Musical Understanding in the Middle Ages’, in P. Gallacher and H. Damico (eds.), Hermenutics and Medieval Culture (Albany, NY, 1989), pp. 133–45; and Atkinson, The Critical Nexus, pp. 39–46, 49–65 and 103–111. A concise summary of the medieval uses of Donatus and their relation to music is given in W. Flynn, Medieval Music as Medieval Exegesis (Lanham, Md., 1999), pp. 9–56.
27 This functional use of the dasia, I would argue, is not exceptional, as Nancy Phillips has suggested. See N. Phillips, ‘Musica and Scolica’, and ‘Notationen’. The beginning of ME establishes modal quality as fundamental to the meaning of the dasia and pitch conception of the treatises (see n. 19).
28 ‘Limmata ergo haec non plena spacia vocari solent et per ea interdum vel modus a modo transfertur vel per eadem restituitur’; Musica et Scolica, ed. Schmid, p. 69.
29 ‘si utrumque latus per haec non plena intervalla lesero rursus ad sonum, a quo coepit, redeat’; ibid.; Musica Enchiriadis, trans. Erickson, p. 40.
30 ‘Sit itaque rursus pentacordum tetrardi, cui haec vitii species subiungatur.’ Musica et Scolica, ed. Schmid, p. 70.
31 ‘Virtus ergo sonorum quattuor quaeque mela modificat. Quapropter nota nunc tibi in quattuor illis ptongis vim varietatis mirabilem et suam cuiusque faciem, qua singuli ab invicem diversitate differant et secundum se modorum faciant differentias.’ Ibid., p. 81; Musica Enchiriadis, trans. Erickson, p. 48; and ‘Demonstrandum nunc, quomodo haec quattuor ptongorum vis modos, quos abusive tonos dicimus, moderetur, et fiat dispositio talis’; Musica et Scolica, ed. Schmid, p. 13; Musica Enchiriadis, trans. Erickson, p. 7.
32 D: ‘Ergone solius soni finalis virtus quemlibet modum efficit, ut ob id tropus vel modus illius aut illius soni dicendus sit, quod in eo finis meli constiterit? M: Praecipue quidem videtur vis cuiuslibet tropi ob id in quolibet finali sono consistere, quod in eo tropus finiendo constiterit.’ Musica et Scolica, ed. Schmid, p. 82; Musica Enchiriadis, trans. Erickson, p. 48.
33 These sets of melodies, often sung with syllables such as ‘noannoeane’ and ‘noeagis’, appear in the earliest tonaries and in many treatises. They are edited in T. Bailey, The Intonation Formulas of Western Chant (Toronto, 1976). On the parallel Byzantine tradition, see J. Raasted, Intonation Formulas and Modal Signatures in Byzantine Musical Manuscripts (Copenhagen, 1966). ME and SE give versions of these melodies that differ from those found in most tonaries. See Musica et Scolica, ed. Schmid, pp. 16–20.
34 ‘Ad hunc modum consuetis utuntur modulis ad investigandam toni cuiusque vim eadem ratione compositis. Quorum principales quique a suis sonis superioribus ordientes desinunt in finales, minores vero in finalibus et inchoant et consistunt nec superiorum attingunt locum, utpote NOANNOEANE, NOEAGIS, et cetera, quae putamus non tam significativa esse verba quam syllabas modulationi attributas.’ Musica et Scolica, ed. Schmid, pp. 19–20.
35 See Bailey, The Intonation Formulas, pp. 64–6, 70–1 and 74–8. This prominent role of the tritus is somewhat humorously discussed by Guido: ‘videmus eum a Gregorio non immerito plus caeteris vocibus adamatum. Ei enim multa melorum principia et plurimas repercussiones dedit, ut saepe si de eius cantu triti .F. et .C. subtrahas, prope medietatem tulisse videaris.’ Guido Aretinus, Micrologus, ed J. Smits van Waesberghe (Rome, 1955), pp. 207–8. ‘We see that not undeservedly is the tritus beloved by Gregory more than the other notes. He assigns it to the beginnings of many melodies and most of the repeated notes, so that often, if you take away the C's and F's of the tritus from his chant, it will seem that you have removed almost half of it.’ Translation by W. Babb in Hucbald, Guido, and John, p. 79.
36 J. Chailley, Alia musica: Traité de musique du ixe siècle (Paris, 1965), p. 138. ‘Certum est, quod unaquaeque species diapason secundo suis semitoniis insignitur; quae si loca mota fuerint, totam qualitatam tropi transmutant, suo loco servata conservant.’ This remark is in the layer of the text that Atkinson attributes to author β. See the summary in The Critical Nexus, p. 176.
37 ‘atque idcirco ibidem adjuvat plurimus synemmenon tetrachordum’. Chailley, Alia musica, p. 154. This remark appears in the layer of the text that Atkinson attributes to author δ, whom he identifies as ‘the compiler of the final version’. See The Critical Nexus, p. 176 and p. 178.
38 Hucbald, De Institutione harmonica, in Scriptores ecclesiastici de musica sacra potissimum, ed. M. Gerbert, i (1784; repr. Hildesheim, 1963), pp. 112–13. The exception to octave equivalence is, of course, the b♭ of the synemmenon tetrachord, which occurs only in the central octave. A few later theorists, including Theogerus of Metz, add a synemmenon tetrachord in the lower octave. Hucbald's treatise was written between 885 and 899. See Y. Chartier, L'oeuvre musicale d'Hucbald: Les compositions et le traité de musique (Saint-Laurent, Québec, 1995), p. 76; and M. Huglo, ‘Les Instruments de musique chez Hucbald’, in G. Cambier (ed.), Mélanges à la mémoire d'André Boutemy (Brussels, 1976), pp. 183–4.
39 ‘Videlicet innumerabiles sunt cantilenarum soni. Sed quaternis et quaternis eiusdem conditionis in levando et deponendo sese consequentibus sonorum pluralitas adcrescit, id quoque me canente proba.’ Musica et Scolica, ed. Schmid, p. 63; Musica enchiriadis, trans. Erickson, p. 36.
40 Ei 169, probably from St. Gall or Reichenau.
41 A similar conflation is found in Bamberg, Staatsbibliothek, Lit. Hs. 20.
42 Most of these errors were corrected in Jacobsthal, Die chromatische Alteration, pp. 278–85.
43 Concerning the spaces between signs indicating tones and semitones. See Phillips, ‘Musica and scolica’, p. 205, and Musica Enchiriadis, trans. Erickson, pp. 39–40. This type of error is also very widespread in the sources.
44 See the facsimile in D. Torkewitz, Das älteste Dokument zur Entstehung der abendländischen Mehrstimmigkeit (Stuttgart, 1999).
45 The version of Valenciennes 337 is transmitted in Brussels, Bibliothèque Royale 10078; Bamberg, Staatsbibliothek Cod. HJ. IV 19; Mü 14649; and Kraków 1965. In two sources, Mü 14372 and Mü 18914, the last three signs are position-based. The different text families are discussed in Phillips, ‘Musica and Scolica’, pp. 44–72.
46 Munich, Bayerische Staatsbibliothek clm. 14272. Phillips notes that MSS representing all three text families were present at St. Emmeram, and all show contact with other traditions. See Phillips, ‘Musica and Scolica’, pp. 59–60. The double set of signs may have resulted from the availability of different MSS. The spaces indicating the tone are filled in with the letter ‘t’ (tonus).
47 See the critical apparatus in Musica et Scolica, ed. Schmid, p. 70. All MSS with this version of the diagram are from the simpla text family, with the exception of Ei 79.
48 Ibid., p. 38.
49 Ibid., p. 34. The discrepancy is also addressed at the end of SE. See ibid., pp. 154–6, and Musica Enchiriadis, trans. Erickson, pp. 92–3. For a penetrating study of the influence of Boethian consonance theory on organum, see D. Cohen, ‘Boethius and the Enchiriadis Theory: The Metaphysics of Consonance and the Concept of Organum’ (Ph.D. diss., Brandeis University, 1993).
50 See Musica et Scolica, ed. Schmid, p. 32. SE uses the Boethian letters A, H and P. See A. Santosuoso, Letter Notations in the Middle Ages (Ottawa, 1989), pp. 26–7.
51 The five MSS are Pa 7212, Barcelona, Archivio de la Corona de Aragon Cod. Ripoll 42; Mü 14649, Kraków, Biblioteka Jagiellońska BJ 1965, and Cesena, Biblioteca Malatestiana MS S XXVI. All these sources are from the simpla text family except for Cesena, a fifteenth-century source.
52 There are two mistakes in this series of dasia, reinforcing the impression that the signs were copied mechanically and carelessly, without an awareness of their meaning. The first dasia of the finales tetrachord is incorrect, a repetition of the tetrardus sign that precedes it in the series, and the protus and deuterus signs in the superiores tetrachord are reversed. These types of errors are not uncommon in the sources. In Example 7, the signs are transcribed without taking account of these errors.
53 This version of the example also moves in parallel motion throughout, in contrast to the correct version shown in Example 6a, where oblique and contrary motion occur at end of the passage to avoid the tritone. This same erroneous version of the example is transmitted in many sources of the simpla text family.
54 Some of these cases are mentioned in Phillips, ‘Notationen’, pp. 326–7; and explored in greater depth in B. Hebborn, Die Dasia-Notation (Bonn, 1995).
55 Cambridge, Trinity College MS 944 (R.15.22).
56 See n. 16.
57 See Hucbald, Guido, and John, ed. Palisca, pp. 96–7.
58 London, British Library, Cotton Vespasian A. II.
59 Spitta cited certain peculiarities of diagrams in some Enchiriadis sources as evidence for the same conjunction on the upper end of the scale. See Philipp Spitta, ‘Die Musica Enchiriadis und seine Zeitalter’, Vierteljahrsschrift für Musikwissenschaft, 5 (1889), pp. 443–82, at p. 481; This interpretation also made in Hebborn, Die Dasia-Notation, pp. 194–5.
60 H. Müller, Hucbalds echte und unechte Schriften über Musik (Leipzig, 1884). The currently accepted interpretation of the dasia, in Figure 1, was proposed shortly afterwards by Spitta, ‘Die Musica Enchiriadis und seine Zeitalter’.
61 Hebborn, Die Dasia-Notation.
62 For a summary of various datings of this MS, See C. Meyer, Mensura monochordi: La division du monocorde (IXe–XVe siècles) (Paris, 1996), p. lxxv.
63 On the date of Pa 7212, see ibid., p. 193. This date is considerably later than Schmid's ‘tenth or eleventh century’.
64 See Musica et Scolica, ed. Schmid, p. 29.
65 See the critical apparatus in Musica et Scolica, ed. Schmid, p. 30. This diagram is also found in a direct descendant of Pa 7212, Pa 7211, which is available in facsimile: A. Santosuosso, Paris, Bibliothèque nationale, fonds Latin 7211: Analysis, Inventory, and Text (Ottawa, 1991).
66 The gloss appears to correct some mistakes in the diagram's Greek nomenclature, but proceeds to introduce further irregularities in its names for note collections, evidently a conflation of the Guidonian ‘graves’, ‘acutae’ and ‘superacutae’ with the tetrachord names ‘finales’ and ‘excellentes’. The gloss is reproduced in Schmid's critical apparatus, Musica et scolica, p. 152.
67 Trans. based on Babb, in Hucbald, Guido. and John on Music, p. 64.
68 Ibid.
69 Bonnie Blackburn traces this progression in Guido's views on B♭ in her forthcoming essay ‘The Lascivious Career of B-flat’, in Massimo Ossi (ed.), Eros and Euterpe: Essays on Music and Eroticism from the Middle Ages to the Baroque (forthcoming). In the Regulae Guido states: ‘De synemenon / Sunt qui addunt in acutis iuxta primam alteram, / sed Gregorio vix placet patri hec lascivia’ (‘On the synemmenon. There are those who add another [b] next to the first in the high pitches, but this licence scarcely pleases Father Gregory’). Pesce, Guido d'Arezzo's Regule, pp. 348–9. And in the Epistola he says: ‘Si autem duorum vel plurimorum modorum unam vocem esse liceat, videbitur hec ars nullo fine concludi, nullis certis terminis coartari. Quod quam sit absurdum, nullus ignorat, cum semper sapientia confusa queque et infinita sponte repudiet. Quodsi quis dicat hanc vocem ideo esse addendam, ut gravis F sexta ad superquartam b possit ascendere, et eadem sexta ad subquintam descendere, illud quoque debebit recipere, ut inter sextam et septimam alia vox addatur, ut naturalis secunda gravis elevetur ad quintam et eadem acuta deponatur ad quartam. Quod quia a nemine est factum, hoc quoque a nemine est faciendum’ (‘And if one pitch is allowed to belong to two or more modes, this art will appear to be marked off by no limit, confined by no definite boundaries. That this is absurd, no one argues, since wisdom always rejects automatically everything that is confused and unbounded. But if anyone should say that this pitch ought to be added so that the sixth pitch F can ascend to the upper fourth b and the same sixth can descend to the lower fifth [B♭], he will also have to accept that between the sixth [F] and the seventh [G] another pitch may be added, so that the natural second [B] may be raised to the fifth [F♯], and the same high pitch [square ♭] may be lowered to the fourth [F♯]. But because no one has done the latter, no one ought to do the former’). Ibid., pp. 514–17.
70 This transposition occurs in Ben 34, Ben 35, and Ben 39; London, British Library, MS Harley 4951, Pa 1235, Pistoia, Biblioteca Capitolare 120, and Graz, Universitätsbibliothek 807.
71 ‘Ceterum hoc certissime novimus, quod per quorundam ignorantiam multoties cantus depravatur, quemadmodum iam plures habemus depravatos quam enumerare possimus. Quos revera non ita, ut nunc in ecclesiis canuntur, modulantium auctoritas protulit, sed pravae hominum voces motum animi sui sequentium recte composita pervertere perversaque in usum incorrigibilem deduxere, adeo ut iam pessimus usus pro auctoritate teneatur.’ Johannes Affligemensis, De musica cum tonario, p. 105. Translation is that of Warren Babb in Hucbald, Guido, and John, p. 130.
72 Karp's study of chants cited in the Berkeley MS is especially instructive in this respect. Karp, Aspects of Orality and Formularity, pp. 181–224; Snyder, Theinred of Dover's De legitimis Ordinibus, pp. 95–115.
