1 Berkeley and Los Angeles: University of California Press, 1961 (rev. 2nd edn., 1962).Google Scholar

2 Summarized by Dahlhaus as ‘the sum total of the “necessary successive or simultaneous relationships between the notes of a scale”’. The New Grove, article ‘Tonality’, citing Fétis, Traité complet de la théorie et pratique de l'harmonie (Paris and Brussels, 1844, 20th edn., 1903). Also: ‘Guido Adler's use of “tonal” as a synonym for “diastematic” was undoubtedly one of the reasons for Schoenberg's indignant rejection of the word “atonal”: in Vienna, if nowhere else, that expression meant not merely the replacement of the major-minor system but the destruction of all tonal relationships’, loc. cit.Google Scholar

3 I have not been able to consult Dahlhaus's own Untersuchungen über die Entstehung der harmonischen Tonalität (Kassel and Basel, 1968: Saarbrücker Studien zur Musikwissenschaft, ii).Google Scholar

4 Riemann, H., Vereinfachte Harmonielehre oder die Lehre von den tonalen Funktionen der Akkorde (London and New York, 1893, 2nd edn., 1903; English translation, 1896).Google Scholar

5 It is perhaps ultimately from metior ‘I measure’. Ovid says ‘modum dare remis’, ‘to give the time to the oars’. Thus the medieval rhythmic use relates to the primary meaning of the word. It is also by extension a common word for ‘tune’, like Greek tropos. Both these words could also mean a ‘way’ or ‘manner’, thus anticipating a series of European words which could mean either a ‘tune’ or a ‘type-of-tune’: Byzantine ēckas, Latin tonus and its derivatives; aer, aria, and their derivatives; and Weise and its Germanic cognates. Tropos was misused by some ancient Greek theorists to denote a scale (properly tonos, originally a stretching or tuning): hence Boethius' use of modus in the same sense. Tonus was used to translate ēchos in the early Middle Ages: thus both it and modus have a two-fold range of connotations: (1) tune or type-of-tune; (2) scale or key (cf. German Tonart: tonus and its derivatives of course also mean note or pitch, and the interval so named).Google Scholar

6 Such are the Indian raga, Arabic maqām, and the various Oriental systems of eight ‘modes’. See the magisterial article ‘Mode’ by Harold S. Powers in The New Grove, xii, 376–450, and in particular section V, ‘Mode as a musicological concept’.Google Scholar

7 For a comprehensive review see Powers, op. cit., 11, ‘Medieval modal theory’.Google Scholar

8 ‘Non enim per tonum cognoscimus cantum vulgarem’: Der Musiktraktat des Johaunes de Grocheo, ed. E. Rohloff (Leipzig, 1943), 60.Google Scholar

9 Powers, op. cit., III, ‘Modal theories and polyphonic music’, citing amongst other important writers Aaron and Zarlino. For Tinctoris see the edition by A. Seay, Corpus Scriptonan de Musica, XXII, i (American Institute of Musicology, 1975); for Glareanus, Dodecchordon (Basle, 1547), see the English translation by Clement A. Miller, 2 vols., Musicological Studies and Documents, vi (American Institute of Musicology, 1965).Google Scholar

10 Dufay's three complete settings (one alternation) are modally assigned in Modena, Biol. est., A. x. 1.11 (lat. 471, = Mod B): Optra omaia, ed. H. Besseler, I, v (Rome: American Institute of Musicology, 1966), nos. 33–35 (no. 36, incomplete, is ‘tertii et quarti toni’ in one source). The use of plainsong varies, particularly in the first, in tone 6, in which pairs of half-verses close alternately on chords of A and C respectively. Sixteenth-century settings such as those of Gombert (CMM, VI, iv), Clemens (CMM, IV, iv) or Festa (CMM, XXV, ii) are mostly rather free paraphrases of the relevant tone.Google Scholar

11 See for example Das Buxheimer Orgelbuch, 3 vols., ed. B.A. Wallner (Kassel, 1958–9, = Dos Erbe deutscher Musik, xxxvii-xxxix), nos. 24, 47, 77 (2 verses) and 248. Amongst sixteenth-century settings those published by Attaingnant (Magnificat sur les huit tons …, Paris, 1531; ed. Y. Rokseth, Publications de la Société française de Musicologie, i, 1925) consistently paraphrase the tone.Google Scholar

12 Liturgical psalm-settings were normally simpler, and therefore closer to the tone, than Magnificats. Bukofzer (Studies in Medieval and Renaissance Music, New York, 1950, pp. 181–4) drew attention to the fifteenth century double-choir settings of Modena, lat. 444–5, and printed an extract. The texture is a 3, both fauxbourdon and with overlapping tenor and contratenor, the plainchant being paraphrased in the top part. Their alternation between choirs, without overlap, was retained in twelve of the settings in Willaert and Jachet [and others], I salmi appartiacati elli vesperi (Venice: Gardane, 1550; ed. H. Zenck and W. Gerstenberg, CMM, III, viii); the other settings in this volume are for single choir in alternation with plainsong and for double choir with overlap. All are based on the relevant tone, mostly through fairly strict quotation in the tenor voice. Occasionally, however, sixteenth-century liturgical psalm-settings avoid quoting the tone literally.Google Scholar

13 Opera omnia, ed. S. Cislino and M. Luisetto, xviii (2nd edn., Padua, 1971).Google Scholar

14 The source of this title is Rome, Bibl. vat., Cap. Sist. 41. Ockeghem may have concealed under either or both of these titles an allusion to the popular song ‘Petite camusette’, used in his own chanson ‘S'elle m'amera’. (Pipelare's Mass ‘Mi mi mi’ in Jena, Urtiversitātsbibl. 21, actually appears elsewhere as ‘Petite camusette’). ‘Quarti’ rather than ‘tertii’ toni could perhaps be justified by the range of the tenor.Google Scholar

15 A strict transposition would entail the fifth mode but by a series of devices Josquin avoids quoting the high middle section of the melody in the tenor voice except in further transpostion within the new key (a fourth lower in the Kyrie, an octave lower in Agnus III). Elsewhere, this material is transferred to other voices, so that the tenor remains in mode 6 throughout.Google Scholar

16 See Appendix I.Google Scholar

17 Murray C. Bradshaw, The Origin of the Toccata (American Institute of Musicology, 1972; Musicological Studies and Documents, xxviii).Google Scholar

18 Hamburg, ND VI 3225 (lost); ‘The Tablature of Adam Ileborgh’, 1448 (Philadelphia, Curtis Institute of Music); Keyboard Music of the Fourteenth and Fifteenth Centuries, ed. W. Apel (American Institute of Musicology, 1963; Corpus of Early Keyboard Music, i).Google Scholar

19 This is an English Magnificat for organ, based on the faburden of the tone down a fifth, setting the odd-numbered verses (beginning with ‘anima mea’): Early English Church Music, vi, no. 4. See the discussion of English vocal Magnificats below, and some of the terminology of Appendix II.Google Scholar

20 Is it altogether fanciful to see the end of T.A. Walmisley's Magnificat and Nunc dimittis in D minor, composed in 1855, as the very last word in this tradition? In the liter nineteenth century the final chords were construed as an imperfect cadence and the Gloria patri of the Magnificat sometimes exchanged with that of the Nunc Dimittis (information from Dr W.J. Gatens). There is a scholarly edition of the work in The Treasury of English Church Music, iv, ed. G.H. Knight and W.L. Reed (London, 1965), 109–22. Outstanding examples from the Baroque include the Gloria from Couperin's Messe pour les parvisses and Bach's setting of ‘Kyrie, Gott Vater in Ewigkeit’ from Clavierūburg, iii.Google Scholar

21 The Gloria and Credo have no cantus firmi but share their D minor tonality with the Kyrie. The modes of the contus firmi of the last three movements are 5, 5, and 6, but the tessitura and style of each are virtually identical. For the Kyrie, see below and ex. 6. Paradoxically, as will be seen, modal definition may be more desirable in polyphonic music of the period 1450–1520.Google Scholar

22 Musica et Scolica Eachiriadis una cum aliquibus tractatulis adiunctis, ed. H. Schmid (Munich, 1981). Guido, Micrologus, ed. J. Smits van Waesberghe (Corpus Scriptorum de Musica, iv), cc. xviii-xix: see the translation by Warren Babb in Hucbald, Guido, and John on Music, ed. Claude V. Palisca (New Haven and London, 1978). Guido prefers the occursus through the tone to that straight from the ditone, and forbids it from the semiditone. Of the practical sources the Winchester troper (Cambridge, Corpus Christi College, 473: See Holschneider, A., Die Organa von Winchester, Hildesheim, 1964), being in unheighted neumes, cannot be used as evidence of the precise form of the occursus; but the major and minor third and sixth are frequent in sources from c. 1100 onwards.Google Scholar

23 Ed. M.F. Bukofzer, Musica Britannica, viii, no. 48; Denkmāler der Tonkunst in Österreich, vii (= 14–15), 197–8.Google Scholar

24 Op. cit., cc. 13 (commixtio), 22 (mixtio), 24 (polyphony). For the modern edition see note 9.Google Scholar

25 Proceedings of the Royal Musical Association, cv (1978–9), 119–20.Google Scholar

26 Contrapuntal Technique in the Sixteenth Century (Oxford, 1922), 15.Google Scholar

27 This is the reading adopted in DTÖ, vii (see note 23) and hence in some recordings. The medieval theory of musica ficta is discussed by Margaret Bent, ‘Musica Recta and Musica Ficta’, Musica Disiplina, xxvi (1972), 73–100.Google Scholar

28 London, British Library, Sloane 1210, f. 140, first printed by F. LJ. Harrison, Music in Mediveal Britain (London, 1958; 4th edn., Buren, 1980), 150–1. For obvious reasons, any written specimen will normally introduce at least minor elaborations of the technique. In the present instance, the cadential treatment seems to confirm that the contus firmus is in the middle voice, transposed up a fifth, rather than in the top voice, transposed up an octave.Google Scholar

29 But Erasmus in the sixteenth century, writing of ‘Fauburdum’, says that it ‘neither gives forth the pre-existing melody nor observes the harmonies of the art’ (cited by Clement A. Miller in The Musical Quarterly, lii (1966), 339).Google Scholar

30 Antiphonale Sarisburiense, ed. W.H. Frere (London, 1901–24), plates s, r, s.Google Scholar

31 ed. A. Smijers, Werken van Josquin des Pres, Motetten, ii, 11–19. The sexta vox (called by Smijers ‘Altus prima vox’), though present in Petrucci's Motetti de la corona, libro tertio (1519) and other sources, is absent from three important manuscripts and appears to be a later addition by an inexpert hand. The note d′ in the cantus firmus in bar 94 is a misprint for b (flat). The text is a panegyric on ‘Amor’, in elegiac couplets, put in the mouth of Christ as he hangs on the cross. W. Elders has pointed out that the scheme of ‘Huc me sydereo’ is exactly paralleled in his six-part ‘Ave nobilissima creatura’, based on the almost identical antiphon ‘Benedicta tu in mulieribus’: see E.E. Lowinsky (ed.), Jasquin des Prez (London, 1976), 526–7 and the further references there given. Josquin has retained not merely the cantus firmus but its metrical layout, except that the proportions of the three statements are changed from 6:3/2:1 to 6:6/4:2 (the irregular diminution of statement 2 being in both cases the consequence of a change from triple to duple mensuration). Even the cadential chords in each part are retained. Nevertheless in my view this is not so much a question of a ‘motet cycle’ (Elders) as of a somewhat less appropriate re-use of an existing successful scheme, the texture being enlarged to six voices and the length greatly increased by the changed proportions.Google Scholar

32 See Appendix II.Google Scholar

33 Ludford's Magnificat ‘Benedicta’ appears to be unique in having an alien cantus firmus (not the tone) at its basis. Taverner's first and third Magnificats revert to the tone itself.Google Scholar

34 Aplin, J., ‘A Group of English Magnificats “Upon the Faburden”’, Soundings, vii (1978), 85–100, esp. pp. 99–100, and ‘The Survival of Plainsong in Anglican Music: Some Early English Te-Deum Settings’, Journal of the Amman Musicological Society, xxxii (1979), 247–75, esp. pp. 274–5. The main thrust of Aplin's work, of course, has been to demonstrate the actual retention of faburdens and plainsong in the works discussed.Google Scholar

35 72 Versetl sammt 12 Toccaten (Vienna, 1726).Google Scholar

36 ‘argutus’, bright or clear-toned, has connotations of ‘sharpness’: cf. ‘acutus’. Whether or not the sharpening of the sixth and seventh degrees of the scale can be regarded as ‘chromaticisrn’, even in the modern sense, its effect here, enhanced as it is by the quasi-parallel movement of the first two chords, is absolutely stunning and out of all proportion to the simplicity of the means employed. For a recent study, See Teo, K.S., Chromaticism in the English Madrigal (diss. University of Oxford, 1983).Google Scholar