1 For a general account of this problematic, see the collection of essays edited by Binding, Günther and Speer, Andreas, Mittelalterliches Kunsterleben nach Quellen des 11. bis 13. Jahrhunderts (Stuttgart-Bad Cannstatt, 1993)Google Scholar . In order to give this non-aesthetical discipline a name, some people use the term ‘kallistics’, already mentioned by Hegel, Georg Wilhelm Friedrich, Vorlesungen über die Ästhetik, vol. 1, ed. Moldenhauer, Eva and Michel, Karl Markus, Werke 13 (Frankfort, 1986), 13Google Scholar .

2 The original version dates from 1959 under the title Sviluppo dell'estetico medievale (Milan: Marzorati editore)Google Scholar . An English translation was published by Yale University in 1986 as Art and Beauty in the Middle Ages (and 2nd edn, 2002). After the English translation had been published, Eco revised the book substantially and borrowed the title from the English translation of the earlier version: Arte e bellezza nell'estetica medievale (Milan, 1987)Google Scholar ; the chapter on music is found on pp. 41–4. This book has been repeatedly re-edited and, obviously, read. The latest edition of the German translation appeared in 2007 (Munich). The 1987 version has not been translated into English.

3 Musical Quarterly, 82 (1998), Special Issue: Music as Heard, ed. Rob C. Wegman.

4 Such sources have, for example, been used by Page, Christopher, The Owl and the Nightingale: Musical Life and Ideas in France 1000–1300 (London, 1989)Google Scholar and by Tammen, Björn, Musik und Bild im Chorraum mittelalterlicher Kirchen 1100–1500 (Berlin, 2000)Google Scholar .

5 Some evidence for sensuous elements in music theory have been collected here and there. See Crocker, Richard, ‘Discant, Counterpoint, and Harmony’, Journal of the American Musicological Society, 15 (1962), 1–21CrossRefGoogle Scholar ; Reckow, Fritz, ‘Rectitudo – pulchritudo – enormitas. Spätmittelalterliche Erwägungen zum Verhältnis von materia und cantus’, Musik und Text in der Mehrstimmigkeit des 14. und 15. Jahrhunderts, ed. Günther, Ursula and Finscher, Ludwig, Göttinger Musikwissenschaftliche Arbeiten 10 (Kassel et al., 1984)Google Scholar , 1–36; idem, ‘Processus und structura. Über Gattungstradition und Formverständnis im Mittelalter’, Musiktheorie 1 (1986), 5–29; idem, ‘Pictoribus atque poetis licet incipere quod volunt: Interdisziplinäre Voraussetzungen für das Verständnis mittelalterlicher Musik’, Zusammenhänge, Einflüsse, Wirkungen, ed. Fichte, Joerg O. et al. (Berlin and New York, 1986), 117–129Google Scholar ; and Fuller, Sarah, ‘Delectabatur in hoc auris: Some Fourteenth-Century Perspectives on Aural Perception’, Musical Quarterly, 82 (1998), 466–477CrossRefGoogle Scholar (see above, n. 3).

6 De musica VI, xiii, 38. The most recent critical edition of book six is Jacobsson, Martin, Aurelius Augustinus: De musica liber VI, Acta Universitatis Stockholmensis. Studia Latina Stockholmensia 47 (Stockholm, 2002)Google Scholar . Until a complete critical edition is published, the edition by Finaert, Guy and Thonnard, F.-J. should be used for the remaining five books: La musique, De musica libri sex, Bibliothèque augustinienne, Œuvre de Saint Augustin 7/4 (Paris, 1947)Google Scholar . Jacobsson's edition also contains an English translation of book six. For the first five books, see Augustine, , On music, translated by Taliaferro, R. Catesby (Annapolis, MA, 1939)Google Scholar .

7 De musica VI, xiv, 44: ‘Quid ergo facile est? An amare colores et voces et placentas et rosas et corpora leniter mollia?’

8 Augustine discusses rhythms by means of ratios in De musica I, vii, 13–I, x, 17. The idea of equality remains implicit but in fact provides an important criterion for the classification of ratios. In book six, Augustine clearly states the significance of equality and gives examples of how equality controls metrical feet (De musica VI, x, 26–7).

9 For an account of the pedagogical context, see Marrou, Henri-Irenée, Saint Augustine et la fin de la culture antique (Paris, 1958)Google Scholar ; O'Connell, Robert J., Art and the Christian Intelligence in St. Augustine (Oxford, 1978)Google Scholar ; Hadot, Ilsetraud, Arts libéraux et philosophie dans la pensée antique, Études Augustiniennes, (Paris, 1984)Google Scholar ; and eadem, ‘Erziehung und Bildung bei Augustin’, Internationales Symposion über den Stand der Augustinus-Forschung vom 12. bis 16. April 1987 im Schloß Rauischholzhausen der Justus-Liebig-Universität Gießen, ed. Mayer, Cornelius and Chelius, Karl Heinz (Würzburg, 1989), 99–130Google Scholar .

10 We do not know what the original sixth book looked like because it survives solely in a version Augustine revised twenty years later. The book was requested by an otherwise unknown bishop named Memorius, for whom Augustine might have revised the book, but there is no way of reaching a reliable conclusion. See Marrou, Saint Augustine, 580–3; O'Connell, Art, 178–88.

11 De musica VI, x, 28; VI, xii, 34; VI, xiv, 44.

12 De musica VI, xii, 34: ‘Aequalitatem illam, quam in sensibilibus numeris non reperiebamus certam et manentem, sed tamen adumbratam et praetereuntem agnoscebamus, nusquam profecto appeteret animus, nisi alicubi nota esset; hoc autem alicubi non in spatiis locorum et temporum, nam illa tument, et ista praetereunt. Ubi ergo censes? Responde, quaeso, si potes! Non enim in corporum formis putas, quas liquido examine aequales numquam dicere audebis, aut in temporum intervallis, in quibus similiter, utrum sit aliquid aliquanto quam oportet productius vel correptius, quod sensum fugiat, ignoramus. Illam quippe aequalitatem quaero, ubi esse arbitreris, quam intuentes cupimus aequalia esse quaedam corpora vel corporum motus, et diligentius considerantes eis fidere non audemus.’ (We cannot find exact and enduring equality in sensible numbers, we only recognise it as suggested and transitory. Therefore, the mind would definitely never strive after equality were it not known from somewhere. That ‘somewhere’, however, does not exist in space or time because space expands or shrinks and time passes. So where do you assume [does it exist]? Answer, I ask you, if you can! You certainly do not expect it in corporeal forms which after accurate scrutiny you would never dare to call equal, neither do you expect it in time intervals where we cannot know whether something is faster or slower than it should be. For this escapes sensory perception. Thus, I ask where do you think equality exists, which we desire if we observe that certain bodies or corporeal motions are equal, although we do not dare to trust them if we consider it carefully.)

13 Ibid.: ‘Ibi puto, quod est corporibus excellentius, sed utrum in ipsa anima an etiam supra animam, nescio.’ (I think in a place more excellent than the corporeal sphere. Whether, however, in the soul itself or even beyond the soul I don't know.)

14 These things are well known; see for instance Plato, Phaidon, 74asqq., and Aristotle, Posterior Analytics, 77a5sqq., respectively.

15 For example, De musica VI.II.2: ‘ut a corporeis ad incorporea transeamus’.

16 While it has usually been acknowledged that medieval texts on music theory were pedagogically motivated, it is only recently that Max Haas, using the Musica enchiriadis as an example, demonstrated how deep the resulting impact could really have been. See his Musikalisches Denken im Mittelalter (Bern et al., 2005), 279–344Google Scholar . In the case of Augustine, the pedagogical impact is different because the text did not address young children. Yet it still clearly determines the intention and the consequent manner of argumentation.

17 De musica VI, xii, 36: ‘Unde ergo credendum est animae tribui, quod aeternum est et incommutabile, nisi ab uno aeterno et incommutabili deo?’ (From where else, however, should we believe that the soul is offered what is eternal and immutable, if not from the one eternal and immutable God?)

18 De ordine, ed. Green, William MacAllen, Corpus Christianorum, Series Latina 29, pars II, 2 (Turnhout, 1970), II, ix, 26–48Google Scholar . For different interpretations of the structure of De ordine, see Marrou, Saint Augustine, 185; Dyroff, Adolf, ‘Über Form und Begriffsgehalt der augustinischen Schrift De ordine’, Aurelius Augustinus, Festschrift der Görres-Gesellschaft zum 1500. Todestage des Heiligen Augustinus, ed. Grabmann, Martin and Mausbach, Joseph (Köln, 1930), 15–62Google Scholar , in partic. 34–43; and Rief, Josef, Der Ordobegriff des jungen Augustinus (Paderborn, 1962), 17–18Google Scholar .

19 De ordine II, xi, 33: ‘Sed neque in pulchris rebus, quod nos color inlicit, neque in aurium suauitate, cum pulsa corda quasi liquide sonat atque pure, rationabile illud dicere solemus. Restat ergo, ut in istorum sensuum uoluptate id ad rationem pertinere fateamur, ubi quaedam dimensio est atque modulatio.’

20 De musica I, ii, 2.

21 De musica I, i 1.

22 De musica VI, xii, 35.

23 Some of those passages were brought together in my article, ‘Sinnlichkeit und Vernunft in Augustins De musica’, Wissenschaft und Weisheit 57/2 (1994), 189–200Google Scholar . At that time, however, I did not yet see how this element would fit into Augustine's theory of rhythm or pedagogical conception.

24 Of course, it is not difficult to imagine rather complicated rhythmic constellations that can principally be reduced to equality. See Jeserich, Philipp, Musica naturalis: Tradition und Kontinuität spekulativ-metaphysischer Musiktheorie in der Poetik des französischen Spätmittelalters (Stuttgart, 2008), 139–140Google Scholar . But that is not the point. The problem is the fact that the aesthetical inclination to complexity and alteration cannot be explained by equality or number. Yet it seems to be the very divergence from equality that is an essential part of aesthetical pleasure.

25 Riethmüller, Albrecht, ‘Stationen des Begriffs Musik’, Ideen zu einer Geschichte der Musiktheorie, Geschichte der Musiktheorie 1, ed. Zaminer, Frieder (Darmstadt, 1985), 59–95Google Scholar , in partic. p. 87.

26 On inconsistencies in Augustine's ‘aesthetics’, see O'Connell, Art, pp. 17–18.

27 ‘Nihil enim est horum sensibilium, quod nobis non aequalitate aut similitudine placeat’ (De musica VI, xiii, 38).

28 De libero arbitrio, ed. Brachtendorf, Johannes, Augustinus: Opera, Werke 9 (Paderborn, 2006), II, xvi, 41Google Scholar : ‘Ut, quidquid te delectat in corpore et per corporeos inlicit sensus, videas esse numerosum.’

29 For this reason, the frequently quoted interpretation by Beierwaltes, Werner seems to misrepresent Augustine's ‘aesthetics’: ‘Aequalitas Numerosa. Zu Augustins Begriff des Schönen’, Wissenschaft und Weisheit, 38 (1975), 140–157Google Scholar . Also, Beierwaltes does not take into account that there are contradictions within Augustine's theory and that his theory might have been developed or changed in the course of time.

30 The constancy of this ontological view has been demonstrated by Horn, Wolfgang, ‘Augustins Philosophie der Zahlen’, Revue des Études Augustiniennes, 40 (1994), 389–415CrossRefGoogle Scholar .

31 As far as I know, statements that seem to be in contradiction to the number ontology such as the one from De ordine have never been collected and interpreted.

32 De musica VI, xiii, 38. In the early fourteenth century, Nicholas Triveth made the same claim: that any sensual pleasure results from ratios within the sensual matter such as colour, odour and taste. See Quodlibet XI, q. 19: ‘Utrum corpora caelesta per suum motum causent aliquam harmoniam’, ed. Lord, Mary L., ‘Virgil's Eclogues, Nicholas Trevet, and the Harmony of the Spheres’, Mediaeval Studies, 54 (1992), 267–273 (269–70)CrossRefGoogle Scholar .

33 De musica I, iv, 5.

34 De musica VI, iii, 4 and VI, viii, 20.

35 Phaidon, 74a–b.

36 De musica I, iii, 4: ‘Ut, si quis suavissime canens et pulchre saltans velit eo ipso lascivire, cum res severitatem desiderat, non bene utique numerosa modulatione utitur.’ (For example, if someone likes to be exuberant by singing sweetly and dancing beautifully while the occasion demands gravity, he [or she] absolutely does not use numerical measurement in the right way.)

37 De musica I, ii, 3: ‘Ergo scientiam modulandi iam probabile est esse scientiam bene movendi, ita ut motus per se ipse appetatur atque ob hoc per se ipse delectet.’ (Thus, the science of measurement is likely the science of right motion, provided that the motion is desired for its own sake and therefore pleases through itself.)

38 De musica I, iv, 5–6.

39 De ordine II, xi, 31: ‘Nam illud nos mouere maxime debet, quod ipse homo a ueteribus sapientibus ita definitus est: homo est animal rationale mortale. hic genere posito, quod animal dictum est, uidemus additas duas differentias, quibus credo admonendus erat homo, et quo sibi redeundum esset et unde fugiendum.’

40 Cf. De musica I, vi, 11–12.

41 Literature on the Augustinian dialogues can be found in Fuhrer, Therese, Augustinus (Darmstadt, 2004), 186Google Scholar .

42 De musica I, vi, 11.

43 De musica I, vi, 11: ‘Mirum, si hoc effeceris.’

44 Ibid.: ‘Nam ille venditor solidi cum isto comparandus non videtur, non enim accepto plausu aut qualibet sibi largita pecunia scientiam, si quam forte habet, qua populum delectavit, amittit, sed onustior nummo et laude hominum laetior cum eadem disciplina incolumi atque integra domum discedit. Stultus autem esset, si commoda illa contemneret, quae non adeptus multo esset ignobilior atque pauperior, adeptus autem nihilo esset indoctior.’

45 De musica I, vi, 12: ‘Quando igitur mihi vel persuaseris vel ostenderis quemlibet histrionum non ideo illam, si quam habet facultatem, vel assecutum esse vel exhibere, ut populo placeat propter quaestum aut famam, concedam posse quemquam et musicae habere scientiam et esse histrionem.’

46 De musica I, iv, 5: ‘Nam magni viri, etsi musicam nesciunt, aut congruere plebi volunt, quae non multum a pecoribus distat et cuius ingens est numerus, quod modestissime ac prudentissime faciunt (sed de hoc nunc disserendi locus non est), aut post magnas curas relaxandi ac reparandi animi gratia moderatissime ab iis aliquid voluptatis assumitur. Quam interdum sic capere modestissimum est, ab ea vero capi vel interdum turpe atque indecorum est.’ (It is not as you think. For either great men, even though they have no knowledge about music, wanted to please the crowd that does not differ very much from cattle and that is extremely numerous. (They did so very prudently and reasonably, though; but here is not the place to go into this.) Or they very moderately use some enjoyment in order to relax after serious worries and to recover mentally. It is very prudent to employ music occasionally in this way; however, to be swept away by music, even only occasionally, is ugly and shameful.)

47 De musica VI, xiii, 37ff.

48 De musica VI, xiv, 44: ‘Quid ergo facile est? An amare colores et voces et placentas et rosas et corpora leniter mollia?’

49 Augustine, Confessions, X, xxxii translated and edited by Outler, Albert C. (Philadelphia, 1955), 370Google Scholar .

50 Still one of the best surveys on this tradition is Münxelhaus, Barbara, Pythagoras musicus. Zur Rezeption der pythagoreischen Musiktheorie als quadrivialer Wissenschaft im lateinischen Mittelalter (Bonn, 1976)Google Scholar .

51 Commentarius in Posteriorum Analyticorum Libros, ed. Rossi, Pietro, Corpus Philosophorum Medii Aevi. Testi e studi 2 (Florence, 1981), I, 12, p. 194, 134Google Scholar .

52 In the Pythagorean tradition, arithmetics included qualitative elements of evaluation (cf. Marrou, Saint Augustine [1958], 259) that were still common in the Middle Ages.

53 Cf. Speculum musicae, ed. Roger Bragard, Corpus Scriptorum de Musica 3 (s.l., 1955–1973), II, ix, 7, p. 28, and IV, xxvii, 12–13, p. 67.

54 Speculum musicae IV, xxviii, 12, p. 73. For a more detailed account of Jacques's argument, see Hentschel, Frank, Sinnlichkeit und Vernunft in der mittelalterlichen Musiktheorie. Strategien der Konsonanzwertung und der Gegenstand der musica sonora um 1300, Beihefte zum Archiv für Musikwissenschaft 47 (Stuttgart, 2000), 44–65Google Scholar .

55 Jacques called this the order of generation and matter: ‘via generationis et materiae’ (Speculum musicae II, ix, 5, p. 28).

56 Speculum musicae IV, xxvii, 27, p. 70: ‘Sicut autem proportiones multiplices superparticularibus sunt perfectiores, sic superparticulares superpartientibus.’ (Just as proportiones multiplices are more perfect than proportiones superparticulares so proportiones superparticulares are more perfect than proportiones superpartientes.)

57 Speculum musicae IV, xxvii, 28, p. 70: ‘Non inconvenienter igitur videtur posse taxari perfectionis ordo inter consonantias ex ipsarum proportionibus, cum proportio ad causam ipsarum formalem reducatur.’

58 Speculum musicae II, iv, 9, p. 17: ‘Consonantia … dicitur de mixtione sonorum omnium distinctorum aequalium vel inaequalium, sive illorum mixtio dulciter et concorditer auditui se faciat, sive non, dum tamen ad certam reducibilis sit proportionem in numeris.’

59 The most recent and comprehensive account of Boethius's De institutione musica and its philosophical background is Heilmann, Anja, Boethius' Musiktheorie und das Quadrivium. Eine Einführung in den neuplatonischen Hintergrund von ‘De institutione musica’, Hypomnemata 171 (Göttingen, 2007)Google Scholar .

60 De institutione musica, ed. Friedlein, Gottfried (Leipzig, 1867; reprint, Frankfort, 1966), I, 8, p. 195Google Scholar , 6–8: ‘Consonantia est acuti soni gravisque mixtura suaviter uniformiterque auribus accidens.’Ibid., IV, 1, p. 302, 2–4: ‘Consonae quidem sunt, quae simul pulsae suavem permixtumque inter se coniungunt sonum.’ For a terminological discussion of the word suavis in the Middle Ages, see Carruthers, Mary, ‘Sweetness’, in Speculum 81/4 (2006), 999–1013CrossRefGoogle Scholar .

61 See, for instance, the order Boethius develops in De institutione musica I, 5–7.

62 Cf. especially Speculum musicae II, iiii–vi, pp. 16–23.

63 Of course, an argument that only works with the other concept on consonance might be found. In this case, the apparent inconsistency could not be solved. I have not, however, come across any such passage.

64 De institutione musica II, 1.

65 Speculum musicae IV, xxvii, 5, p. 66.

66 De institutione musica I, 7.

67 The concept of scientia media is well explained by Carlos A. Ribeiro do Nascimento, ‘Le statut épistémologique des ‘sciences intermédiaires’ selon s. d’Aquin', Thomas, in La Science de la nature: théorie et pratique, Cahiers d'études médiévales 2 (Montreal and Paris, 1974), 33–95Google Scholar . With respect to music, see Haas, Max, ‘Musik zwischen Mathematik und Physik: Zur Bedeutung der Notation in der Notitia artis musicae des Johannes de Muris (1321)’, in Festschrift für Arno Volk (Cologne, 1974), 31–46Google Scholar ; and Hirtler, Eva, ‘Die musica im Übergang von der scientia mathematica zur scientia naturalis’, in Musik – und die Geschichte der Philosophie und Naturwissenschaften im Mittelalter. Fragen zur Wechselwirkung von musica und philosophia im Mittelalter, ed. Hentschel, Frank (Leiden, Boston and Cologne, 1998), 19–37Google Scholar .

68 Evidence for this is provided in my book, Sinnlichkeit und Vernunft, 137–46.

69 Speculum musicae II, ix, 7, p. 28: ‘Tenebimus autem ibi ordinem Nicomachi.’

70 Ideological vestiges can still be detected in Jacques's theory. He exclusively uses the numerical ratios of Pythagorean tuning as ratios that constitute consonantiae, while he cannot explain why other numerical ratios do not make up consonantiae. In order to eliminate that problem, he introduces the concept of modulatio harmonica, which means that only some numerical ratios produce a sound mixture if applied to sound. On modulatio harmonica, see Hentschel, Sinnlichkeit und Vernunft, 51–7.

71 Speculum musicae IV, xxxii, 1, p. 93: ‘Perfecta concordia est sonorum distinctorum sibi permixtorum unitorumque veniens ad aurem dulcis et uniformis iucundaque melodia.’

72 Speculum musicae IV, xlvi, 15, p. 115: ‘Sufficiat autem superficialiter de hac loqui materia et de dictis quas poterimus assignare rationes. Oportet enim, secundum quod permittit subiecta materia, procedere proportionalitate. Non enim rationes sufficerent mathematico quae sufficiunt rhetorico. Proximum enim est mathematicum persuadentem acceptare et rhetoricum demonstrationes expetere. Haec autem materia non videtur pure mathematica.’ (Suffices it to talk just superficially about this matter and to determine the reasons of what has been stated. For it is necessary to proceed with commensurability according to what is permitted by the subject matter because the reasons that suffice for the rhetorician would not suffice for the mathematician. It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs. This matter, however, does not seem to be purely mathematical.) The sentence that I have placed in italics is a quotation from Aristotle's Nicomachean Ethics (1094b25) and it becomes intelligible only if its context is taken into account. In the translation by Ross, W.D. and Urmson, J.O. it reads: ‘for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits: it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs’ (Nicomachean Ethics, The Complete Works of Aristotle, Revised Oxford Translation, ed. Barnes, Jonathan (Princeton, 1984), vol. 2, 1730)Google Scholar . The idea of something being ‘evidently equally foolish’, as Ross and Urmson translate it, had in the original text been condensed elliptically to one single word: ‘paraplésion’. In Robert Grosseteste's Latin translation, this word is literally translated with ‘proximum’.

73 Speculum musicae IV, xli, 1, p. 106: ‘Concordiarum et discordiarum in vocibus et quare hae meliores, illae minus causas assignare facile mihi non est. Usus enim et ars docuit quod sapit omnis homo maxime in practicis. Ego autem musicis artificialibus instrumentis usus non sum, quorum tamen usus, una cum arte musicae, non modicum praebet experimentum ad securius et verius iudicandum communiter de consonantiis quae maioris concordiae sunt et quae minoris, et similiter de discordiis. Sed practici musici, solum usum habentes, etsi de his bene iudicent et prompte, causas tamen assignare nesciunt, nisi per artem invenitur.’ (The strange turn to the singular in the end of the quotation would need to be checked in the manuscript.)

74 This means neither that the senses are the cause for consonance (concordia) nor that they are able to give an explanation for the sensation which would still be the intellect's task. Cf. Speculm musicae I, xxix, pp. 86–90 and IV, xxxi, 8–9, p. 93 where Jacques refers to Aristotle's well-known differentiation between ‘quia’ and ‘propter quid’, that is, the ‘fact’ and the ‘reason why’ (cf. Aristotle, Analytica Posteriora I, xiii, 78a21sqq.; Posterior Analytics, trans. Barnes, Jonathan, The Complete Works of Aristotle. The Revised Oxford Translation, ed. idem, (Princeton, 1984), vol. 1, 127)Google Scholar . The senses recognise the fact of consonance (concordia) while the intellect would have to find the reasons for this sensation.

75 See Hentschel, Frank, ‘Der Streit um die Ars nova – nur ein Scherz?’, Archiv für Musikwissenschaft, 58 (2001), 110–130CrossRefGoogle Scholar .

76 Speculum musicae II, vi, 13–14, p. 22: ‘Ad iudicandum tamen et discernendum inter concordantias quae bona et quae melior, multum facit auditus, et maxime si est bene dispositus et in musicae scientia sufficienter instructus. Febricitans non bene iudicat de saporibus, et canis neque in consonantiis quantumcumque bonis, neque in cantibus delectatur propter cerebri paucitatem et capitis debilitatem qui ad discernendum odores melius est dispositus.’ (With regard to judgement and distinction of consonances, [i.e. the question] which one is good and which one is better, the sense of hearing is important, especially if it is in good form and sufficiently informed by speculative music theory. Anybody who is feverish does not judge well about taste, and a dog does not enjoy consonances however good they are, nor does it enjoy music because of the poorness of its brain and the weakness of its head that is better conditioned for distinguishing odours.) The punctuation has been slightly modified as against Bragard's edition.

77 Speculum musicae IV, viii, 3–5, p. 16; IV, xxvii, 31, p. 71; VI, lxxiv, 1–11, pp. 214–16.

78 Speculum musicae VI, lxxiv, 9, p. 216: ‘Sicut enim non omnium ora eodem capiuntur cibo, ita profecto non omnium aures eodem soni modo oblectantur.’

79 Anonymous IV, ed. Reckow, Fritz, Der Musiktraktat des Anonymus 4, vols. 1–2, Beihefte zum Archiv für Musikwissenschaft 4–5 (Wiesbaden, 1967), vol. 1, p. 82Google Scholar , 6.

80 Johannes de Garlandia, De mensurabili musica, ed. Reimer, Erich, Beihefte zum Archiv für Musikwissenschaft 10 (Wiesbaden, 1972), X, p. 74, 22Google Scholar ; Franco de Colonia, Ars cantus mensurabilis, ed. Gilbert Reaney and André Gilles, Corpus Scriptorum de Musica 18 (s.l., 1974), XI, p. 73, 31; Quatuor principalia, ed. de Coussemaker, C.-E., Scriptores de musica medii aevi, vols. 1–4 (Paris, 1864–76, reprinted Hildesheim, 1963), IV, ii, xx, vol. 4, p. 281Google Scholar .

81 Important terms are ornatus, purpurare and variare. See Anonymus cod. s. Emmerami (quem ed. Sowa), ed. Jeremy Yudkin (Bloomington and Indianapolis, 1990), I, 1, p. 96, 38–40; I, 1, p. 108, 39–41; I, 2, p. 170, 36–40, II, p. 206, 22–38; II, p. 208, 30–31; II, p. 222, 15–17; V, 1, p. 272, 15–19; VI, p. 282, 5–6.

82 Tractatus de musica, ed. Cserba, Simon M., Freiburger Studien zur Musikwissenschaft 2. Reihe, 2. Heft (Regensburg, 1935), pp. 176, 15–179, 21Google Scholar .

83 Speculum musicae II, x, 26–7, p. 32: ‘Moderni autem cantores nomen consonantiae non sic <arctant>, non sic restringunt. De pluribus sonis tam aequalibus quam inaequalibus, de ipsorum mixtionibus tam suavibus auditui quam non, ipsum verificant, et non omnino sine ratione, si vera sunt quae diximus. Cum enim musica paulative sit augmentata, quid mirum si consonantiae nomen sit dilatatum? In principio enim, cum sola musica simplici et modesta uterentur homines, consonantiis quattuor et quattuor chordis utebantur. Nunc autem, ampliata multum musica in chordis, in instrumentis, in modis, in consonantiis et cantibus, quid mirum si consonantiae nomen ad plures sonos et mixtiones quam tunc sit extensum?’

84 Speculum musicae IV, xi, 7, p. 22: ‘Hoc autem, etsi pro tempore ipsius Guidonis verum erat, non tamen pro moderno tempore.’

85 Johannes Boen, Musica, ed. Frobenius, Wolf, Johannes Boens Musica und seine Konsonanzlehre, Freiburger Schriften zur Musikwissenschaft 2 (Stuttgart, 1971), II, p. 45, 25–26Google Scholar : ‘Secundum diversitatem temporis et regionum multa nova et inaudita poterunt suboriri, sicut forte pronuntiatio commatis et trium semitoniorum minorum ac multorum similium, que, licet hactenus non audita sunt, forte tractu temporis per nova instrumenta et vocum habilitates posterius audientur, sicut nec ante Pitagoram fuit tanta subtilitas in cantu, quanta hodiernis temporibus est in usu, nec talem nos, qualem Anglici, Gallici vel Lumbardi in cantu facimus fracturam.’ (According to the diversity of time and place, much that is new and unheard might develop, such as perhaps the articulation of the comma and of three or more equal semitones which, though they have not been heard so far, may in time be heard with the help of new instruments or future vocal abilities, just as during the time of Pythagoras there was not such subtlety in singing as is the case nowadays. Also, we [the Alemanni] do not use such a rhythmical complexity as the Anglici, Gallici or the Lombardi.)

86 Assunto, Rosario, Die Theorie des Schönen (Cologne, 1963; 2nd edn, Cologne, 1987), 92Google Scholar . The book was again reprinted in 1996.

87 ‘Micrologus Guidonis de disciplina artis musicae in deutscher Übersetzung von Raymund Schlecht’, in Monatshefte für Musik-Geschichte 5/10 (1873), 135–177Google Scholar (152) (cf. Gerbert, Martin, Scriptores ecclesiastici de musica sacra potissimum, vols. 1–3 (St Blasien, 1784, reprinted Hildesheim etc., 1963), vol. 2, 14Google Scholar ).

88 Guidonis Aretini Micrologus, ed. Joseph Smits van Waesberghe, Corpus Scriptorum de Musica 4 (s l., 1955), XIV, 18–19, p. 161.

89 Cf. Schrade's, Leo review, in Musical Quarterly, 43 (1957), 115Google Scholar . A preliminary stemma of the text tradition has been established by Meyer, Christian, ‘La tradition du Micrologus’, Revue musicologique, 83 (1997), 5–31CrossRefGoogle Scholar . It does not, however, shed new light on the passage discussed here.

90 Micrologus, XV, 40, p. 172: ‘Qui cantum faciunt, rationabiliter discretas ac diversas neumas componant.’ An English translation is available in Babb, Warren, Hucbald, Guido, and John on Music (New Haven, 1978)Google Scholar .

91 Micrologus, XV, 41–3, p. 172: ‘Rationabilis vero discretio est, si ita fit neumarum et distinctionum moderata varietas, ut tamen neumae neumis et distinctiones distinctionibus quadam semper similitudine sibi consonanter respondeant, id est sit similitudo dissimilis, more praedulcis Ambrosii.’

92 Micrologus, XV, 19, p. 167: ‘quia in omnibus se haec ars in vocum dispositione rationabili varietate permutat’.

93 Micrologus, XV, 20, p. 167: ‘Quam rationabilitatem etsi saepe non comprehendamus, rationabile tamen creditur id quo mens, in qua est ratio, delectatur.’

94 Here, my interpretation clearly diverges from Karlheinz Schlager's more traditional reading: ‘Ars cantandi – ars componendi. Texte und Kommentare zum Vortrag und zur Fügung des mittelalterlichen Chorals‘, in Die Lehre vom einstimmigen liturgischen Gesang, ed. Ertelt, Thomas and Zaminer, Frieder, Geschichte der Musiktheorie 4 (Darmstadt, 2000), 217–292 (233)Google Scholar .

95 Epistola, 14, p. 82 (mind/soul); VIII, 24–5, p. 127 (mind/intellect); XIV, 5, p. 159 (character/mentality); XVII, 39, p. 194 (character/mentality).

96 Micrologus, XV, 22–5, p. 168.

97 Micrologus, XV, 27–9, p. 169.

98 Micrologus, XV, 50–1, p. 174.

99 Micrologus, XV, 61, p. 177.

100 Micrologus, XV, 21, p. 167: ‘Sed haec et huiusmodi melius colloquendo quam vix scribendo monstrantur.’

101 For date and authorship of the treatise see Hentschel, Sinnlichkeit und Vernunft, 268–70.

102 Compendium de musica, ed. van Waesberghe, Joseph Smits, Vetter, Eddie and Visser, Erik, Divitiae artis musicae A.9 (Buren, 1988), III, iv, 7–8, pp. 120–121Google Scholar : ‘Hic ergo rationis ordo est et naturae. Usus vero peramplius lasciviam perpendens simplicibus iam satur mixturis gaudet etiam ad sui opus, superpartientes sonos praedictis immiscens, nec rationis aut naturae tenet ordinem, sed, ut ita dicam, in modum textoris lanas simul commiscens et fila texendo, gratiosum aspectui panni profert artificium, simplici texturae panno praeeligibile. Sed et pictor naturales colores artificio transferens, innumera coloris genera placabilia simplicibus commiscet. Sed et Epicureus cocus aromatum varietate et, ut ita dicam, quadam alienatione saporum quamplurimos gutturi retinuit dulcissimos. Itaque nimirum sonorum mixturis auris gaudet, ut oculus colorum vel guttur saporum. Expedit tamen ut omnia rato sibi respondeant ordine.’ (Cf. Jacques de Liège, Speculum musicae IV, i, 4, p. 5). Following the manuscript Brussels, Bibliothèque Royale Albert 1er, 10162–6, fol. 54v, the word naturae has been added to the expression: ‘nec rationis aut naturae tenet’. Also ‘oculos’ has been replaced by ‘oculus’; a facsimile of the manuscript can be found in the edition.