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The emergence of a medieval pitch concept
Published online by Cambridge University Press: 15 September 2020
Abstract
The ninth century witnessed a fundamental change in the way Western musicians thought about music. Before the Carolingians assimilated ancient music theory, they had no functional concept of how the intervals between pitches of the scale differed from one another and how those differences affected melodic structure. The transition to interval-based thinking may be traced in writings about music. The first half of Aurelian of Réôme's mid-century Musica disciplina quotes from Boethius, Cassiodorus and other ancient authors, but fails to make sense of what they say about intervals. The second half describes the rise and fall of chant melodies without reference to intervals. Treatises of the later ninth century (the Enchiriadis treatises, Hucbald's Musica) are the first to treat music in terms of individual pitches and explain how patterns of whole tones and semitones define modes and scales. However, an early draft of Musica enchiriadis, the Inchiriadon, still displays no awareness of the role that semitones played. A parallel evolution occurred in notation. Neumes, which outline melodic direction but not precise intervals, can be documented from the second quarter of the ninth century and are likely older. They lack pitch content because musicians who invented them lacked a conceptual framework for understanding pitch. Pitched notations do not appear until late in the century and their use is confined to examples in theory treatises.
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References
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16 ‘Autenti proti primitus incipit in parhypate meson genere diatoni diapente proportione. Deinde in hypate meson descendit transito semitonio. Deinde in lychanos hypaton tono transit, post hoc iterum redit tono in hypate meson. Deinde remigrat iterum in lychanos hypaton per tonum et inde se deflectit in proslambenomenos duobus tonis et dimidio.’ Glossa maior in institutione musicam Boethii, 3: 365–6.
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20 ‘Phitagoras repperit, qualiter proportionum varietas sonorum iungeretur concordie. Sint verbi causa quattuor mallei, qui subter insertos contineant numeros: xii, viiii, viii, vi. Hi igitur mallei qui xii et vi ponderibus vergebant diapason in duplo consonantiam concinebant ut hic: Antiphona Inclina Domine aurem tuam, et omnia quae in primo inveniuntur tono. Malleus xii ponderum ad malleum viiii et malleus viii ad malleum vi ponderum, secundum epitritam proportionem, diatessaron consonantiam perficiebant. Adest exemplum: Antiphona Confessio et pulchritudo, et cuncta que in tono autenti deuteri conscribuntur. VIIII vero ponderum ad vi, et xii ad viii, diapente consonantiam permiscebant, veluti hic: Antiphona Circumdederunt me, et cetera que in autentu trito inveniuntur. VIIII vero ad viii in sesquioctava proportione resonabat tonum, iuxta illud: Antiphona Puer natus est nobis, et omnia quae autenti tetrardi adscribuntur norme.’ Aurelian of Réôme, Musica disciplina 2, 62–3.
21 See Joseph Ponte, ‘Aureliani Reomensis, Musica disciplina: A Revised Text, Translation, and Commentary’, 3 vols., Ph.D. diss., Brandeis University (1961), 3: 15–17; Christian Meyer, ‘Die Tonartenlehre im Mittelalter’, in Die Lehre von einstimmigen liturgischen Gesang, Geschichte der Musiktheorie 4 (Darmstadt, 2000), 142–4; and Atkinson, The Critical Nexus, 94–6.
22 Ponte, ‘Aureliani Reomensis, Musica disciplina’, 16.
23 See McGee, Timothy J., ‘“Ornamental” Neumes and Early Notation’, Performance Practice Review, 9 (1996), 39–65CrossRefGoogle Scholar, at 44–51.
24 Glossa maior in institutione musicam Boethii, 1: 199–201.
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26 ‘Haec memorata superius quattuor principia a Pitagora inventa eadem ex semet procreant sibi coherentia.’ Aurelian of Réôme, Musica disciplina 2, 63.
27 ‘Constat autem omnis musica simphoniis sex, sonitibus quindecim, tenoribus octo.’ Ibid., 71.
28 Boethius, De institutione artithmetica 2.48, 155–8.
29 Cassiodorus, Institutiones divinarum et saecularium litterarum 2.5.7, in Cassiodori Senatoris Institutiones, ed. R.A.B. Mynors (Oxford, 1937), 144–5.
30 ‘Tonus est totius constitutionis armonicae differentia et quantitas, quae in vocis accentu sive tenore consistit.’ Ibid., 145.
31 ‘Dorius est hypolydium hemitonio, hypoaeolium tono, hypophrygium tono semis, hypoiastium ditono, hypodorium duobus semis tonis, hoc est diatessaron symphonia, praecedens.’ Ibid., 146.
32 ‘Quo autem ordine sonitus quindecim efficiant ac simphonias sex et tonos viii, hinc contemplare licebit cum inspexeris acute quantum singuli se superent, quousque altitudinem ultimi conscendant: ita ut singuli sese emitolio, id est medio tono, superent, quousque quintadecima primum octo tonis precedat.’ Aurelian of Réôme, Musica disciplina 6, 75.
33 This issue is discussed in Laurence A. Gushee, ‘The Musica disciplina of Aurelian of Réôme: A Critical Text and Commentary’, Ph.D. diss., Yale University (1962), 86–91, 138–53. See also Aurelian of Réôme, Musica disciplina, 39–41; Huglo, Michel, Les Tonaires: Inventaire, analyse, comparaison, Publications de la Société française de musicologie 3/2 (Paris, 1971), 47–56Google Scholar; and Bernhard, Michael and Ferrari, Michele C., ‘Aliquid super quibusdam regulis modulationum: Eine unbekannte musiktheoretische Schrift Aurelians von Réôme (?) in einer Mainzer Handschrift der Jahrtausendwende (Gotha, Forschungsbibliothek Memb. I 58)’, in Musik des Mittelalters und der Renaissance. Festschrift Klaus-Jürgen Sachs zum 80. Geburtstag, ed. Kleinertz, Rainer, Flamm, Christoph and Frobenius, Wolf, Studien zur Geschichte der Musiktheorie 8 (Hildesheim, 2010), 29–47Google Scholar.
34 ‘Diximus etiam octo tonis consistere in musicam per quos omnis modulatio quasi quodam glutino sibi adherere videtur. Est autem tonus minima pars musicae, regula tamen; sicut minima pars grammatice littera, minima pars arithmeticae unitas. Et quomodo litteris oratio, unitatibus catervus multiplicatus numerorum consurgit et regitur, eo modo et sonituum tonorumque linea omnis cantilena moderatur. Difinitur autem ita: tonus est totius constitutionis armonice differentia, et quantitas quae in vocis accentu sive tenore consistit.’ Aurelian of Réôme, Musica disciplina 8, 78.
35 ‘Pthongi, qui a nobis vocantur soni.’ Calcidius, In Platonis Timaeum commentarius 44, ed. and trans. John Magee, On Plato's Timaeus, Dumbarton Oaks Medieval Library 41 (Cambridge, 2016), 190–1.
36 ‘Qui plenitudinem huiusce vult nosse scientiae, ad musicam eum mittimus, et si in ipsa voluerit versari, ad consonantiam proportionum ac speculationem intervallorum necne ad certitudinem oculos vertat numerorum; et tunc nosse poterit, quam ob rem in una eademque litteratura diversus efficiatur [sonoritatis concentus].’ Aurelian of Réôme, Musica disciplina 10, 86.
37 ‘Autentus protus plures habet varietates. Denique introitum varietates insemet continet tres, quarum prima haec est: Antiphona Gaudete in Domino semper. Ad cuius initium directe finis versiculi redundat et aequatur ei, nec erigitur sursum graviter, neque deponitur deorsum. Secunda haec: Antiphona Iustus es Domine, cuius versiculi finis in altum elevatur ut queat ipsius initio iungi. Tertia haec: Antiphona Suscepimus Deus, in qua ultima versiculi pars diuscule moras agit quam in primo et secundo, extolliturque vox in sublime ut capiti possit aptari introitui.’ Ibid., 85.
38 ‘Primus siquidem in se idcirco directe finis versuum recipit, quia et in directum incoat, nec vox sinuosos decurrit per anfractus, atque in tertia tonus invenitur sillaba scilicet in TE, ut “Gaudete”.’ Ibid., 86.
39 ‘Igitur in reciprocatione introituum, si versus eiusdem XVI in se continuerit syllabas, ut est “Gloria patri et filio et spiritui sancto”, mediocriter prima initiabitur syllaba, id est “Glo-”, et secunda acuto enunciabitur accentu, videlicet “-ri-”. Ea tamen ratione, si dactilus fuerit, vel quelibet correpta syllaba; sin autem producta fuerit, fuerit tunc circumflexione gaudebit. Tercia vero, scilicet “-a”, suspensa tenebitur voce.’ Aurelian of Réôme, Musica disciplina 19, 119.
40 ‘In versibus introituum, prima syllaba, id est Glo-”, arsin pacietur exin secunda, hoc est “-ri”, diesin.’ Ibid., 126.
41 See Mittellateinisches Wörterbuch bis zum ausgehenden 13. Jahrhundert 33/4 (Munich, 2002), 605; and Lexicon musicum Latinum medii aevi, ed. Michael Bernhard, 2 vols. (Munich, 1992–2016), 2: 970.
42 Aurelian of Réôme, Musica disciplina 19, 123 and 126 (hypodorius), 126–7 (hyperlidius). See also Ponte, ‘Aureliani Reomensis, Musica disciplina’, 3: 202–3, 219–25.
43 Aurelian of Réôme, Musica disciplina 6, 75–6.
44 ‘Enimvero versus antiphonarum istius toni iunguntur sonoritati versuum autenti proti usque prope finem, excepto quod is ypodoricam plus quam prior congratulatur vocem.’ Aurelian of Réôme, Musica disciplina 19, 123.
45 ‘Nam in octava eiusdem syllaba yperlidica debet adscisci vocis melodia, videlicet in “i-” ut “ilicem” correpte dicamus.’ Ibid., 127.
46 Lexicon musicum Latinum medii aevi, 2: 213–14, 219.
47 For the dates, see Torkewitz, Dieter, ‘Zur Entstehung der Musica und Scolica enchiriadis’, Acta musicologica, 69 (1997), 156–81CrossRefGoogle Scholar; and Chartier, Yves, ed. and trans. L’Œuvre musicale d'Hucbald de Saint-Amand: les compositions et le traité de musique, Cahiers d’études médiévales, cahier special 5 (Saint-Laurent, 1995), 76–7Google Scholar.
48 ‘Primus qui et gravissimus Grece protos dicitur, vel archoos; Secundus deuteros, tono distans a proto; Tertius tritos, semitonio distans a deuteron; Quartus tetrardus tono distans a trito.’ (‘The first [dasian symbol], which is also the lowest, is called protus or archoos in Greek. The second is deuterus, a whole tone distant from the protus. The third is tritus, a semitone distant from the deuterus. The fourth is tetrardus, a whole tone distant from the tritus.’) Musica enchiriadis 1, in Musica et Scolica enchiriadis, una cum aliquibus tractatulis adjunctis, ed. Hans Schmid, Veröffentlichungen der Musikhistorischen Kommission 3 (Munich, 1981), 4. Further citations of Musica enchiriadis and Inchiriadon Uchubaldi Francigenae refer to this edition.
49 The definition to this point paraphrases Martianus Capella, De nuptiis Philologiae et Mercurii 9, 356–67, sec. 930.
50 ‘Tonus est spacii legitima magnitudo a sono in sonum. Hocque spacium musicorum sonorum, quia in sesquioctava proportione est, Greco nomine dicitur epogdous. … Semitonium non plenum toni intervallum.’ Musica enchiriadis 9, 21.
51 Musica et scolica enchiriadis, 187–205. See also Nancy Catherine Phillips, ‘Musica and Scolica enchiriadis: The Literary, Theoretical, and Musical Sources’, Ph.D. diss., New York University (1984), 96–106; and Huglo, Michel, ‘L'Inchiriadon Hucbaldi: son rapport avec la “Musica enchiriadis” et sa circulation en Italie’, Saggiatore musicale, 19 (2012), 179–98Google Scholar.
52 ‘Sed dum forte in sono aliquo dubitatur, quotus sit, tum a semitoniis, quibus constat semper deuterum tritumque disiungi, toni in ordine rimentur et mox, quis ille fuerit, agnoscetur.’ Musica enchiriadis 7, 13.
53 ‘Iuvat etiam, si dum forte in sono quolibet dubitatur, terni vel quaterni sursum seu iosum in ordine soni rimentur ab eodem sono seu ad eundem, et mox, quis ille fuerit, agnoscetur.’ Inchiriadon Uchubaldi Francigenae, ed. Schmid, 194.
54 ‘Hae quattuor descriptiunculae, dum solo ab invicem semitonio vel tono id est armonico spacio distant, eo solo a genere in genus singulae transponuntur.’ Musica enchiriadis 8, 15.
55 ‘Hae quattuor descriptiunculae solo ab invicem epogdoo vel tono, id est armonico inter cordas spacio distant, solo quoque genere in genus singulae transponuntur.’ Inchiriadon Uchubaldi Francigenae, 195.
56 ‘Verum quod in illis quattuor sonitibus, quos singulos ab invicem naturalis ratio per quadrifariam tonorum semitoniorumque positionem propria qualitate discrevit, hoc evenire nequeat, ut melos ullum eiusdem conditionis vel modi manere possit, si ab aliis ad sonos alios transponatur.… Videbisque eandem melodiae formam in transpositione sua manere non posse, sed per epogdoi vel semitonii distantiam modum unumquemque in alium transmutari.’ Musica enchiriadis 12, 48.
57 ‘Verum quod in illis quattuor sonis, quos singulos naturalis ratio ab invicem suae proprietatis qualitate discrevit, hoc evenire non possit, ut scilicet cantio aliqua eiusdem conditionis manere possit, si eadem licet intentione currens ab aliis ad sonos alios transponatur … Videbisque eandem melodiae formam in sonorum transmutatione manere non posse, sed per epogdoi distantiam in singulis ordinibus modum unumquemque in alium transmutari.’ Inchiriadon Uchubaldi Francigenae, 204.
58 Semitones are mentioned just once more, in chapter 17 (Musica enchiriadis, 48), which has no parallel in Inchiriadon.
59 Scolica enchiriadis, 146–7.
60 ‘Primus modus est, cum sibi duae uoces breuissimi spatii diuisione cohaerent, adeo ut uix discrimen inter eas sentiatur. … Secundus iam perceptibilioris est interualli.’ Hucbald, Musica 7, in L’Œuvre musicale d'Hucbald de Saint-Amand, ed. Chartier, 142.
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70 Treitler, Leo, ‘Reading and Singing: On the Genesis of Occidental Music-Writing’, Early Music History 4 (1984), 135–208CrossRefGoogle Scholar, at 142; reprinted in With Voice and Pen, 372.
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73 See Hiley, Western Plainchant, 517.
74 Ibid., 341. See also McGee, ‘“Ornamental” Neumes and Early Notation’, 56–64.