Portions of this article were presented in papers read at the Fourth National Conference of the Society for Music Theory (1981) and the Thirteenth Congress of the International Musicological Society (1982) I am grateful to Profs Theodore Karp and Robert Lynn for reading earlier versions of this article and offering many helpful suggestionsGoogle Scholar

1 ‘Das Grundgebilde der antiken Musiktheorie ist das Tetrachord.’ Michael Markovits, Das Tonsystem der abendlandischen Musik im fruhen Mittelalter, Publikationen der Schweizerischen musikforschenden-Gesellschaft, 2/30 (Berne and Stuttgart, 1977), 73Google Scholar

2 See also Palisca, Claude V, ‘Theory, theorists’, §5, The New Grove Dictionary of Music and Musicians (London, 1980), xviii, 744–6, and Anicius Manlius Severinus Boethius, The Fundamentals of Music, trans with Introduction and Notes by Calvin M Bower (New Haven, 1989) Before proceeding, a summary of terminology may be helpful The terms ‘pentachord’ and ‘tetrachord’ indicate diatonic segments spanning a perfect fifth and perfect fourth respectively They are often replaced by the terms ‘diapente’ and ‘diatessaron’ Other commonly encountered spans include the ‘diapason’ (octave), ‘ditone’ (major third) and ‘semiditone’ (minor third) Still other spans are created by combining smaller ones, always conjunctly ‘bis diapason’ (double octave), ‘diapente cum tono’ (fifth plus a tone, i e major sixth), etc It is useful to note that some spans may be variously constructed, Theinred distinguishes between the ‘diapente cum semiditono’ and the ‘bis diatessaron’ (minor seventh), because these constructions lead to differing internal arrangements of the tones and semitones (cf Tabulae III–9 and III–10)Google Scholar

3 Boethius, De institutione musica, ed. Godofred Friedlein (Leipzig, 1867), §§iv 14 (pp 337–41) and iv 17 (pp 343–8), The Fundamentals of Music, 148–52 and 157–60 As Palisca points out (‘Theory’, 746), Boethius used these letters originally as points in the division of the monochordGoogle Scholar

4 Hucbald, De harmonica institutione, ed Martin Gerbert, Scriptores ecclesiastici de musica sacra potissimum (Sankt Blasien, 1794, repr Milan, 1931), i, 110, trans Warren Babb, Hucbald, Guido, and John on Music, Music Theory Translation Series, 3, ed Claude V Palisca (New Haven, 1978), 23–4Google Scholar

5 Dialogus de musica, ed Gerbert, Scriptores, 1, 252–63 It will be simpler to refer to the anonymous author of this treatise, and of the Musica artis disciplina (Scriptores, 1, 265–84) also formerly attributed to Odo or Oddo, as ‘pseudo-Odo‘Google Scholar

6 Berno of Reichenau Prologus in tonarium cum tonario, ed Gerbert, Scriptores, ii, 67–8Google Scholar

7 Aribo De musica, ed Joseph Smits van Waesberghe, Corpus scriptorum de musica, 2 (Rome, 1951).Google Scholar

8 Prologus in tonarium, ed Gerbert, Scriptores, ii, 69–70, see also Palisca, Theory', 747Google Scholar

9 Pesce, Dolores, The Affinities and Medieval Transposition (Bloomington, 1987), 14Google Scholar

10 Liber specierum, ed Joseph Smits van Waesberghe, Expositiones in Micrologum Guidonis Aretini (Amsterdam, 1957)Google Scholar

11 Palisca, ‘Theory’, 747, speaks of Berno and his school as being ‘fond of speculating with the antique species of 4ths, 5ths and octave and of dividing their gamut into tetrachords‘Google Scholar

12 'Obwohl die Gattungen fur die mittelalterliche Musikpraxis entbehrlich sind, werden sie aus Traditionsliebe bewahrt, und sie stutzen die neue, auf antike Grundlagen gestellte Lehre durch ihr Ansehen als alte Kulturguter Markovits, Das Tonsystem, 81Google Scholar

13 Apel, Willi, Gregorian Chant (Bloomington, 1958), 152–3Google Scholar

14 Musica artis disciplina, ed Gerbert, Scriptores, i, 274, see also Apel, Gregorian Chant, 164 and n 29Google Scholar

15 For treatments of this topic, see Jacobsthal, Gustav, Die chromatische Alteration im liturgischen Gesang der abendlandischen Kirche (Berlin, 1897, repr Hildesheim, 1967), Dominique Delalande, ‘L'insuffisance du système d'écriture guidonien, ou l'existence de plusieurs notes mobiles dans le système grégorien’, Atti del Congresso internazionale di musica sacra (Tournai, 1952), 202–6, Apel, Gregorian Chant, 162ff., and Pesce, The AffinitiesGoogle Scholar

16 Pesce, The Affinities, 2–3, 36, 38 and passimGoogle Scholar

17 Burney, Charles, A General History of Music, repr ed Frank Mercer (New York, 1935). i, 675, says, among other things, that Book III of Theinred's treatise ‘contains Diagrams and Scales innumerable of different species of Octave’ (a remark that the reader will appreciate more fully by the end of this article), he complains of the ‘barbarism and obscurity of the Latin’ and concludes, ‘now, since the theory of Sound is so much better understood and explained by the writings of Galileo and many others, our old countryman, Theinred, may henceforth remain peaceably on his shelf, without much loss to the art or science of Music’ For a survey of the errors and other indignities to which other historians and bibliographers have subjected Theinred, see John L Snyder, ‘The De legitimis ordinibus pentachordorum et tetrachordorum of Theinred of Dover’ (Ph D dissertation, Indiana University, 1982), chap 1 One recent error should be noted here in Andrew Hughes, ‘Theinred of Dover’, The New Grove Dictionary, xvii, 731–2, the title of Theinred's treatise is given incorrectly Prof Hughes has informed me (private correspondence, 1981) that the erroneous title was inserted after proofs had been corrected Unfortunately, this error has been repeated in Michel Huglo, Bibliographie des éditions et études relatives à la théorie musicale du moyen âge'. Acta musicologica, 60 (1988), 264Google Scholar

18 MS Bodley 842 appears in Bodleian catalogues after the middle of the seventeenth century, its date has been variously reported as ‘late-fourteenth’ or ‘early-fifteenth’ century (Falconer Madan and H H E Craster, A Summary Catalogue of Western Manuscripts in the Bodleian Library (Oxford, 1922), i/1,433, C C J Webb, ‘Tenred of Dover’, English Historical Review, 30 (1915), 658) Mr M B Parkes, of Keble College, Oxford, has kindly examined the manuscript at my request, and has expressed the opinion that it dates from the very end of the fourteenth century or the very beginning of the fifteenth, and that, furthermore, a date later rather than earlier in this span may be supported by the fact that the manuscript seems to have been copied away from London (Yorkshire or Eastside), where older styles of script would have remained longer in use (private correspondence, 1980)Google Scholar

19 Snyder, ‘The De legitimis’, ii Spelling has been normalized, except for a few characteristically medieval terms, the capitalization and punctuation of the manuscript (which are quite haphazard) have been freely emended Some errors in my previous version of the text have been silently corrected for this article I wish to acknowledge the assistance given me with the manuscript and the text by Hans Tischler and Ian Thomson of Indiana University, and by Mark Edward Clark of the University of Southern Mississippi, final responsibility for the reading of the text and the translation thereof rests of course with the authorGoogle Scholar

20 Reaney, Gilbert, ‘Transposition and “Key” Signatures in Later Medieval Music’, Musica disciplina, 33 (1979), 29–30, argues for a thirteenth-century date, but see also Snyder, ‘The De legitimis’, chaps 1 and 2 I presented a paper on this issue, ‘Dating Theinred of Dover's De legitimis ordinibus pentachordorum et tetrachordorum A Review of the Evidence’, at the Fiftieth Annual Meeting of the American Musicological Society (Philadelphia, 1984), an article is in preparationGoogle Scholar

21 See Snyder, , ‘The De legitimis’, i, 39–41 For Theinred's views on consonance, see idem, ‘Theinred of Dover on Consonance A Chapter in the History of Harmony’, Music Theory Spectrum, 5 (1983), 110–20Google Scholar

22 The term is Apel's (Gregorian Chant, 162), he also used the expression ‘semitonal group‘Google Scholar

23 See Klaus-Jürgen Sachs, Mensura fistularum (Stuttgart, 1970), 48–51, and Snyder The De legittmis', ii, 126–7Google Scholar

24 Snyder, 'The De legitimis, 1, 52–3, ii, 45, 115–18 It is instructive that Theinred's central error in treating the genera stems from confusion concerning whether he is dealing with an ascending or a descending systemGoogle Scholar

25 One wonders whether the correct reading of the chapter heading should not be ‘De speciebus convenientiarum’, which would be much more logical in context. Indeed, given the sentence that follows, it would have been understandable for a scribe to have substituted ‘consonantiarum’ for ‘convenientiarum’, consciously or otherwise, this could also represent a slip or a little carelessness on Theinred's part. In any case, the manuscript reads ‘consonantiarum’ unambiguously, and that reading has been allowed to stand for the present.Google Scholar

26 Snyder, ‘Theinred of Dover on Consonance’, 112Google Scholar

27 If Theinred actually thought of the ‘b quadratum’ as ‘h’, the use of ‘b’ (= ‘b rotundum’) would seem more logical in terms of alphabetical order Theinred often refers, however, to ‘b quadratum’, just as he refers to ‘e rotundum’ and ‘e quadratum’, so that this hypothesis does not hold up It is worth noting that the legitimacy of the B♭ was one of the points of contention between Guido (and his followers) and Berno (and his followers) – see Pesce, The Affinities, 14–22 Theinred comes down solidly on the side of the B♭, and thus, if not with Berno, at least squarely against Guido, his use of the B♭ in so conspicuous a fashion in presenting his theory may be simply a way of underscoring this pointGoogle Scholar

28 These letters have some relationships with intervallic letter notations, particularly with the system found in Tractatuli IX and X of Oxford, Bodleian Library, MS Rawl C 270 (Codex Oxoniensis Bibl Bodl Rawl C 270, pars B XVII tractatuli a quodam studioso peregrino ad annum MC collecti, ed Joseph Smits van Waesberghe, Divitiae musicae artis, ser A, vol xb (Buren, 1980)), see especially Smits van Waesberghe's discussion, pp 44–64 There are also obvious connections with the system set out by Hermannus Contractus, Musica Hermanni Contracti, ed Leonard Ellinwood, Eastman School of Music Studies, 2 (Rochester, 1936), 9–11Google Scholar

29 A brief explanation of the notations employed in the manuscript is in order here Theinred's majuscule/minuscule system, discussed above, is used in Tabula III–2 and several places in the text, in the remaining tabulae, a substitute system has been used This system indicates all pitches with minuscule letters, and adds to the ‘e’ an ornament (e~) to indicate E♭ Unfortunately, the minuscule ‘e’ of many scripts of the era was prone to have a ‘hook’ due to the properties of quill pens and/or the mechanics of the calligraphy, e and e are both common forms, and the latter could plausibly be mistaken for the ornamented character here under discussion – or vice versa. It is therefore not surprising that the tabulae contain many errors concerning E♭: Theinred did not really explain his original system, and the scribe who created the substitute system did so without any comment at all, the scribe of Bodley 842 must have been confronted with a most difficult situation While he may therefore be forgiven somewhat, the fact is that his failure to copy all of the strange markings in front of him with complete accuracy has left the only surviving copy of the treatise in a virtually nonsensical state It may also be noted that the ornament (‘flat sign’) of the substitute notation greatly resembles the abbreviation for ‘-is’ (genitive case), which is similarly attached to letters in the notation of the Robertsbridge Codex (and in German letter keyboard tabulatures), but there with the effective meaning ‘sharp’ (see Thurston Dart and John Morehen, ‘Tablature’, The New Grove Dictionary, xviii, 508) For a discussion of what little is known of the manuscript tradition of this treatise, see Snyder, ‘The De legitimis‘, i, 22–35Google Scholar

30 It is interesting that the Greater Perfect System likewise covered a fourteenth in four tetrachords, but descending from a’ to B; this required an additional note – proslambanomenos – to complete the double octave (Proslambanomenos means ‘added note’, see Michaelides, Solon, The Music of Ancient Greece An Encyclopedia (London, 1978), 273) It is curious that medieval theory incorporated proslambanomenos into its species system, and then created its own, extra-species ‘added note’, the gamma The gamma was in turn incorporated into the system of hexachords, and additional notes at both ends of the range were regarded as musica ficta, being extra manu Theinred was not concerned with a finite gamut, his system needs no ‘added’ notes, and is thus arguably the most logical pitch system developed in the Middle AgesGoogle Scholar

31 Theinred thus anticipates the later development of the concept of an infinite scale, on which see Hughes, Andrew, ‘Solmization’, §1, The New Grove Dictionary, xvii, 458–61, and Snyder, ‘The De legitimis‘, i, 97–8Google Scholar

32 The other two methods are closely bound up with Theinred's treatment of plainsong, and will require separate articles (now in preparation) An overview of Theinred's theory and its application to plainsong may be found in John L Snyder, ‘Non-Diatonic Tones in Plainsong Theinred of Dover versus Guido d'Arezzo’, La musique et le rite sacré et profane, Actes du XIII^e Congrès de la Société internationale de musicologie (Strasbourg, 1986), ii, 49–67Google Scholar

33 Pesce, The Affinities, 20.Google Scholar

34 Ibid., 16–18Google Scholar