¹ Very few medieval music treatises survive as autographs. One such is a manuscript copied by Prosdocimo de’ Beldemandis (Florence, Bibl. Laurenziana, Ashburnham 206), which includes three of his treatises: a fragment of the Tractatus practice cantus mensurabilis, the Brevis summula proportionum and Canon in quo docetur modus componendi et operandi tabulam quandam. I am grateful to Professor Jan Herlinger for bringing this to my attention. For a facsimile of the leaf with the colophon and a description of the manuscript, see his edition of Prosdocimo's Brevis summula proportionum quantum ad musicam pertinet (Lincoln, NE, 1987). Other autographs include the Introductorium (1442) of Johannes Keck and the Quatuor principalia of John of Tewkesbury (fl. 1351–92). On the Quatuor principalia attribution to John, see Luminita Florea Aluas, ‘Quatuor principalia: A Critical Edition and Translation, with Introduction and Commentary’, Ph.D. diss., Indiana University (1996), 5–29.

² For a description and history of the manuscript, see Dyer, Joseph, The Scientia artis musice: Teaching Music in the Late Thirteenth Century (Abingdon, 2018), 14–21Google Scholar.

³ Recent additions to the slim bibliography are Gardner, Julian, ‘The Cardinals’ Music: Musical Interests at the Papal Curia c. 1200–1304’, Early Music History, 35 (2015), 97–132CrossRefGoogle Scholar; and Stones, Alison, ‘Hélie Salomon, clerc de Saint-Astier et son traité musical’, Bulletin de la Société historique et archéologique du Périgord, 143 (2016), 165–76Google Scholar.

⁴ For a brief summary of the contents, see Dyer, The Scientia artis musice, xii–xvi.

⁵ I first became interested in the treatise because of this singularity; see ‘A Thirteenth-Century Choirmaster: The Scientia Artis Musicae of Elias Salomon’, The Musical Quarterly, 66 (1980), 83–111. On the author's name and his background, see Dyer, The Scientia artis musice, 1–13.

⁶ Rubrics 5.3, 7.21, 21.5, 22.12, 22.15.

⁷ Michael Walter, ‘Sunt preterea multa quae conferri magis quam scribi oportet: Zu Materalität im mittelalterlichen Gesangsunterricht’, in Schule und Schüler im Mittelalter: Beiträge zur europäischen Bildungsgeschichte des 9. bis 15. Jahrhunderts, ed. Martin Kintzinger et al. (Cologne, 1996), 111–43. Walther argues for ‘Mündlichkeit des Unterrichts’ in basic instruction (p. 122).

⁸ Both definitions are from The New Oxford American Dictionary; those of the Oxford English Dictionary are not dissimilar. In the Encyclopédie ‘Diagramme’ is defined as ‘a figure or construction of lines intended to explain or to demonstrate an assertion’, as quoted in Bender, John and Harriman, Michael, The Culture of Diagram (Stanford, CA, 2010), 7Google Scholar. The authors observe that this refers to the Greek use of diagramma in mathematical proofs. Hélie's preferred term is ‘figura’.

⁹ This is reproduced in van Waesberghe, Joseph Smits, Musikerziehung: Lehre und Theorie der Musik im Mittelalter, Musikgeschichte in Bildern 3/3 (Leipzig, 1969), 81Google Scholar (Abb. 29).

¹⁰ Einsiedeln, Stiftsbibliothek, Cod. 79 (522), p. 12; my thanks to P. Justinus Pagnamenta, OSB, for permission to reproduce this image.

¹¹ On images and medieval education, see Karl-August Wirth, ‘Von mittelalterlichen Bildern und Lehrfiguren im Dienste der Schule’, in Studien zum städtischen Bildungswesen des späten Mittelalters und der frühen Neuzeit, ed. Bernd Moeller et al. (Göttingen, 1983), 256–370.

¹² For colour reproductions, see Tilman Seebass, Musikdarstellung und Psalterillustration im früheren Mittelalter, 2 vols. (Bern, 1973), 2: 1–9.

¹³ De musica, ch. 37 (‘De similitudine virilis femineique chori ad autentos et plagas’); Thomas H.J. McCarthy, ed., De musica and Sententiae (Kalamazoo, MI, 2015), 28–9, 122–5 and lxxviii–lxxix. My thanks to Professor McCarthy for confirming this point. The earlier edition is that of Joseph Smits van Waesberghe, Corpus Scriptorum de Musica 2 ([Rome], 1951), 17–20 [hereafter CSM]; cf. Jacques de Liège, Speculum musice, ed. Roger Bragard, CSM 3/6 ([Rome], 1973), 171–5 (6.58). For a close analysis of Aribo's teaching, see Gabriela Ilnitchi, The Play of Meanings: Aribo's De musica and the Hermenuetics of Musical Thought (Lanham, MD, 2005).

¹⁴ It is the earliest surviving musical hand from southern France according to Stefano Mengozzi, The Renaissance Reform of Medieval Music Theory: Guido d'Arezzo between Myth and History (Cambridge, 2010), 63–72. Many ‘musical’ hands are depicted and discussed in Smits van Waesberghe, Musikerziehung: Lehre und Theorie der Musik im Mittelalter, 120–43. See also Anna Maria Busse Berger, Medieval Music and the Art of Memory (Berkeley, 2005), 81–95; and Susan Forscher Weiss, ‘The Singing Hand’, in Writing on Hands: Memory and Knowledge in Early Modern Europe, ed. Claire Richter Sherman and Peter M. Lukehart (Seattle, 2000), 35–45, 174–83.

¹⁵ ‘In manus autem articulis modulari sedulus assuescat …’; De musica cum tonario, ed. Joseph Smits van Waesberghe, CSM 1 (Rome, 1950), 49; Hucbald, Guido, and John on Music: Three Medieval Treatises, ed. Claude V. Palisca, trans. Warren Babb, Music Theory Translation Series 3 (New Haven, 1978), 103.

¹⁶ Diplomatic copies of two of the images (Figs. 4 and 5 of the present article) have been published in Matthias Hochadel, ‘Terminologische Konzepte im Traktat des Elias Salomonis’, in Quellen und Studien zur Musiktheorie des Mittelalters 3, ed. Michael Bernhard (Munich, 2001), 191–215, at 205 (singing lesson) and 210 (tonus).

¹⁷ Hans Schmid, Musica et Scolica Enchiriadis una cum aliquibus tractatulis adiunctis, Bayerische Akademie der Wissenschaften: Veröffentlichungen der Musikhistorischen Kommission 3 (Munich, 1981), 90–104; Musica enchiriadis and Scolica enchiriadis, trans. Raymond Erickson (New Haven, 1995), 53–63. A new edition is Roberto Pia, ‘Musica et Scolica enchiriadis: Introduzione, traduzione e commento’, Ph.D. diss., Pontifical Institute of Sacred Music, Rome (2016), http://lnx.pubblitesi.it/schede-sintetiche/musica/1219-roberto-pia-musica-et-scholica-enchiriadis.

¹⁸ Dyer, The Scientia artis musice, 156–65 (text) and 213–19 (commentary). The phrases in the bands of the semicircle are all borrowed from the text of rubric 30.

¹⁹ The reading of rubric 30.18 takes into account both possibilities: ‘parum sonas, nimis sonas’.

²⁰ Gregory the Great is identified by the inscription over his head, ‘Gregorius presul …’, a text prefaced to many graduals. The presence of Euclid (never mentioned in the treatise) is puzzling. Given that all the illustrations in the treatise, save one, are enclosed in circles, it may have to do with his prestige as a geometer.

²¹ Dyer, The Scientia artis musice, 40–1 (rubric 8.19). An anonymous reviewer pointed out a similarity between the colour of the ink (brown) used for the ‘slurs’ here and the faint lines joining the circles in the image with the enthroned bishop (Fig. 5). I think that it is reasonable to see the author's hand here and in the (rather poorly executed) corrections to the tonary.

²² For an example see Figure 8 below.

²³ Such medallions were a conventional feature of genealogical trees and trees of consanguinity.

²⁴ Similar roundels illustrate the muses and the harmony of the spheres in Franchino Gaffurio, Practica musicae (Milan, 1496). Apollo is seated at the top; the central axis is occupied by a three-headed serpent.

²⁵ ‘Quid est tonus in genere? Tonus in genere est figura septem litterarum et unius clavis, sex punctorum et octo tonorum et totius cantus tam artificialis quam naturalis continens naturam’ (rubric 10.3–4); Dyer, The Scientia artis musice, 42 and 186.

²⁶ Cf. ‘Seculorum species sunt species omnium octo tonorum’ (19.51).

²⁷ Michel Pastoureau, ed., L'arbre: Histoire naturelle et symbolique de l'arbre, du bois et du fruit au Moyen Âge (Paris, 1993).

²⁸ Olga Weijers, Le maniement du savoir: Pratiques intellectuelles à l’époque des premières universités (XIII^e–XIV^e siècles) (Turnhout, 1996), 203–27 (‘Mise en page des textes universitaires: les images et les diagrammes’); Wirth, ‘Von mittelalterlichen Bildern’, 296–300, Abb. 21–3 and 18–20, 23A–27 (divisio philosophie). On music in the divisiones, see Joseph Dyer, ‘The Place of Musica in Medieval Classifications of Knowledge’, Journal of Musicology, 24 (2007), 3–71.

²⁹ Liselotte Strauch and Walter Föhl, ‘Baum’, Reallexikon zur Deutschen Kunstgeschichte, vol. 2, cols. 63–90 (1938), www.rdklabor.de/w/?oldid=95640. The twelve branches of the tree of life, with the crucifix at its centre, depict the ‘fruits’ of Christ's redemptive sufferings. An exemplary depiction is that painted by Taddeo Gaddi on a wall of the refectory of Santa Croce in Florence (available on the internet).

³⁰ The choice of the word ‘consistory’ may reflect the author's experience in the Roman Curia. There is an image of a papal consistory, the pope surrounded by bishops (cardinals’ hats suspended in the air above) and councillors in Biblioteca Apostolica Vaticana, Vat. lat. 1389, fol. 3v; for a full-page colour reproduction see Vito Piergiovanni, ‘Il diritto Canonico: Il medioevo’, in Le università dell'Europa: Le scuole e i maestri, Il medioevo, ed. Gian Paolo Brizzi and Jacques Verger (Milan, 1994), fig. 30.

³¹ Johannes de Garlandia called the six principal consonances ‘genera generalissima omnium concordantiarum’; De mensurabili musica 9.12–13, ed. Erich Reimer, 2 vols., Beihefte zum Archiv für Musikwissenschaft 10–11 (Wiesbaden, 1972), 1: 69. Lambertus likewise used the expression to the plural: the six consonaces ‘quarum et prima genera sunt generalissima omnium concordantiarum’; The ‘Ars musica’ Attributed to Magister Lambertus/Aristoteles, ed. Christian Meyer, trans. Karen Desmond (Farnham, 2015), 38–9. Neither author seems to employ ‘most general genus’ in the usual philosophical sense. Evidence of philosophical method in music theory treatises is reviewed in Joseph Dyer, ‘Chant Theory and Philosophy in the Late Thirteenth Century’, in Cantus Planus: Papers Read at the Fourth Meeting – Pécs, Hungary, 3–8 September 1990), ed. László Dobszay (Budapest, 1992), 99–118.

³² Isagoge: Porphyre, texte grec, Translatio Boethii, trans. Alain de Libera and Alain-Philippe Segonds (Paris, 1998); Porphyry the Phoenician: Isagoge, trans. Edward W. Warren, Mediaeval Texts in Translation 16 (Toronto, 1975), 28–41. The Greek text with an Italian translation and Boethius's Latin version has been edited by Giuseppe Girgenti, Porfirio, Isagoge (Milan, 1995). Boethius's translation was previously edited as In Isagogen Porphyrii commenta, ed. Georg Schepps and Samuel Brandt, Corpus Scriptorum Ecclesiae Latinorum 48/1 (Vienna, 1906). The Isagoge has been translated with extensive commentary by Jonathan Barnes, Porphyry: Introduction (Oxford, 2003), 50–80 (genera) and 81–95 (species).

³³ On the modifications, especially the insertion of species as one of the five predicables, see Jean Wirth, L'image médiévale: Naissance et développements (VI^e–XV^e siècle) (Paris, 1989), 61–73.

³⁴ The attribution to the Peter who became pope has been called into question. Two Dominican friars, Petrus Alfonsi Hispanus and Petrus Ferrandi Hispanus, have been proposed as possible authors. See the three related articles on authorship by Angel d'Ors in Vivarium, 35 (1997), 21–71; 39 (2001), 209–54; and 41 (2003), 249–303; with the responses of Simon Tugwell, Vivarium, 37 (1999), 103–13, and Archivum Fratrum Praedicatorum, 76 (2006), 103–15.

³⁵ While ‘difference’ stands in the background of Hélie's explanation of tone as genus and the eight ecclesiastical tones as species, he does not avert to this category – only to genus and species.

³⁶ Isagoge 1.2–4; ed. De Libera-Segonds, 2; trans. Warren, 29; trans. Barnes, 3 and 54–65 (commentary). The Greek word for ‘family’ is γένος.

³⁷ Isagoge 10; De Libera-Segonds, 19; trans. Warren, 52; trans. Barnes, 15–16.

³⁸ Peter of Spain: Summaries of Logic, ed. Brian P. Copenhaver with Calvin Normore and Terence Parsons (Oxford, 2014), 130–1; see also Summulae logicales 2.2–9; ed. Joseph M. Bocheński (Turin, 1947), 15. Still useful is the introduction and translation of Francis P. Dineen, Peter of Spain: Language in Dispute, Amsterdam Studies in the Theory and History of Linguistic Science 39 (Amsterdam, 1990), 17–24.

³⁹ ‘Species subalterna est, quae cum sit species, potest esse genus; … sunt enim genera respectu inferiorum et species respectu superiorem’; Summulae logicales 2.10, ed. Bocheński, 16–17; ed. Copenhaver, 134. This chain of ‘hierarchically ordered series of genera and species’ is what defines the Tree of Porphyry; Desmond P. Henry, ‘The Predicables and Categories’, The Cambridge History of Later Medieval Philosophy: From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100–1600, ed. Norman Kretzmann et al. (Cambridge, 1982), 128–42, at 129. ‘Species’ presupposes ‘genus’ and vice versa.

⁴⁰ Isagoge 2.5, ed. de Libera-Segonds, 6; trans. Warren, 35–6.

⁴¹ Wirth, L'image médiévale, 63. Carl Linnaeus's classification system introduced greater specificity, making genus and species absolutes. A dog cannot be a dog from one point of view and a cat from another.

⁴² Eleonore Stump, Boethius's In Ciceronis Topica (Ithaca, NY, 1988), 246.

⁴³ ‘Haec tibi plana facit arbor porphyriana’; Summulae logicales 2.9–10; ed. Bocheński, 17–18. Boethius included merely a graphic depiction (‘cuius rei subiecta descriptio sub oculos ponat exemplum’) of the relationship of genus, species, etc.; Boethius, In Isagogen Porphryrii Commenta 3.4, ed. Schipps-Brandt, 209.

⁴⁴ Peter Schroeder Heister, ‘Arbor porphyriana’, in Enzyklopädie Philosophie und Wissenschaftstheorie, ed. Jürgen Mittlestrass, 2nd edn, 6 vols. (Stuttgart, 2005), 1: 192–3 (slightly truncated from the first edition). Useful for its general discussion of trees as demonstration models is Ian Hacking, ‘Trees of Logic, Trees of Porphry’, in Advancements of Learning: Essays in Honour of Paolo Rossi, ed. John L. Heilbron (Florence, 2007), 219–61, at 224–37 and 242–5 (‘The Canonical Tree of Porphyry about 1235: Peter of Spain’); also Annemieke R. Verboon, ‘The Medieval Tree of Porphyry: An Organic Structure of Logic’, in The Tree: Symbol, Allegory and Mnemonic Device in Medieval Art and Thought, ed. Pippa Salonius and Andrea Worm (Turnhout, 2014), 95–113, at 100–3.

⁴⁵ Umberto Eco called the whole concept of the philosophical tree into question; see Semiotics and the Philosophy of Language (Bloomington, 1984), 61–4 (‘a tree which is not a tree’).

⁴⁶ Johannes de Grocheio used feminine family relationships to characterise the principal intervals: ‘there is one first harmony, like a mother, which is called diapason by the ancients, and another, like a daughter, contained in it, called diapente, and a third proceeding from them, which is named diatesseron’ (‘est enim una prima armonia quasi mater, que dyapason ab antiquis dicta est; et alia quasi filia in ista contenta dyapente dicta; et tertia ab eis procedens que dyatesseron appellatur’); Johannes de Grocheio, Ars Musica, ed. and trans. Constant J. Mews et al. (Kalamazoo, 2011), 50–1 (3.3); Ernst Rohloff, ed., Die Quellen Handschriften zum Musiktraktat des Johannes de Grocheio (Leipzig, 1967), 116.

⁴⁷ In the medallions the plagals are not called cousins (nepotes) but socii (companions) of the authentics. On the meanings of this latter term, see Mariken Teeuwen, The Vocabulary of Intellectual Life in the Middle Ages, Études sur le Vocabulaire Intellectuel du Moyen Âge 10 (Turnhout, 2003), 135–6 (‘socius, collegiatus’).

⁴⁸ See the richly illustrated survey of Christiane Klapisch-Zuber, L'arbre des familles (Paris, 2003); eadem, ‘The Genesis of the Family Tree’, I Tatti Studies in the Italian Renaissance, 4 (1991), 105–29 (with 23 plates); eadem, L'ombre des ancêtres: Essai sur l'imaginaire médiévale de la parenté (Paris, 2000), though focusing mainly on the genealogical tree, has an excellent summary of the arbores iuris (pp. 36–9). See also Andrea Worm, ‘Arbor autem humanum genus significat: Trees of Genealogy and Sacred History in the Twelfth Century’, in The Tree, ed. Salonius and Worm, 35–67, at 44–54 (‘Trees of Consanguinity as Trees of Knowledge’). The large Babenberger triptych at Klosterneuburg near Vienna is a spectacular example.

⁴⁹ Max Conrat Cohn, Arbor iuris des früheren Mittelalters mit eigenartiger Komputation, Abhandlungen der Königlich-Preussischen Akademie der Wissenschaften: Philosophisch-Historische Klasse 41 (Berlin, 1909); Klapisch-Zuber, L'ombre des ancêtres, 36–9. Trees of consanguinity can be of daunting complexity; see A. Amanieu ‘Arbre généalogique’, Dictionnaire de droit canonique, 7 vols. (Paris, 1935–65), 1: 901–13 (actually concerning the tree of consanguinity).

⁵⁰ Salonius and Worm, eds., The Tree, 109–30. Trees of consanguinity are not considered in Anthony Melnikas, The Corpus of the Miniatures in the Manuscripts of Decretum Gratiani, 3 vols. (Rome, 1975).

⁵¹ Etymologiarum sive originum libri XX, 2 vols., ed. W.M. Lindsay (Oxford, 1911), lib. 9, cap. 6.23–7; ed. and trans. Marc Reydellet, Étymologies, livre 9 (Paris, 1984), 212–17. Isidore's triangular Stemma I (somewhat resembling a pine tree) prevailed as a standard form until the twelfth century. It is explained in Anna C. Esmeijer, Divina Quaternitas: A Preliminary Study in the Method and Application of Visual Exegesis (Amsterdam, 1978), 109–12. She also traces the gradual incorporation of vegetal details; see also Christiane Klapisch-Zuber, ‘De la nature végétale de l'arbre généalogiques’, in Le monde végétale: Médicine, botanique, symbolique, ed. Agostino Paravicini Bagliani (Florence, 2009), 433–46.

⁵² An early example is the Arbor consanguinitatis of Lambert of St Omer (Ghent, Rijksuniversiteit, MS 92, fol. 102v), reproduced in Susanne Wittekind, ‘Visualizing Salvation: The Role of Arboreal Imagery in the Speculum humanae salvationis (Kremsmünster, Library of the Convent, Cod. 243)’, in Salonius and Worm, eds., The Tree, 117–42, at 133 (Fig. 6.10) and 132–4 (‘arbores consanguinitatis et affinitatis’).

⁵³ Die Darstellung der Arbores Consanguinitatis und der Arbores Affinitatis (Tübingen, 1982), 14–15 and 79–85.

⁵⁴ This development is studied by Hermann Schadt, Christian Klapisch-Zuber and contributors to the collection of essays published as The Tree, ed. Salonius and Worm. The most familiar of medieval genealogical trees was the ‘Tree of Jesse’, which depicted the lineage of Jesus Christ. Inspired by the prophecy of Isaiah that ‘a virgin will come forth from the root of Jesse’ (Isa. 11:1), it was the most frequently depicted tree of the Middle Ages. Jesse, the father of David, is shown as a reclining figure from whom arise a variable number of ancestors up through Mary and culminating with the figure of Jesus.

⁵⁵ For a list with sources, see Dyer, The Scientia artis musice, Appendix 4 (pp. 256–9).

⁵⁶ Hélie was quite irritated that some people were credulous enough to think that F (and not E) was the proper rule of tone 4 (rubric 19.55).

⁵⁷ Dyer, The Scientia artis musice, 150–8 (rubric 28.7), 210–12.

⁵⁸ Rubric 10.13.

⁵⁹ In my edition of the treatise I have (reluctantly) rendered the verb as ‘plange’.

⁶⁰ Each clavis can have 1–3 associated hexachord syllables (puncti in Hélie's vocabulary).

⁶¹ Hugh of St Victor may have approved: ‘memoria enim semper gaudet et brevitate in spatio et paucitate in numero’; De tribus maximis circumstantiis gestorum, ed. William M. Green, ‘Hugo of St Victor: De tribus maximis circumstantiis gestorum’, Speculum, 18 (1943), 484–93, at 490.

⁶² Schadt, Die Darstellung der Arbores Consanguinitatis, 90–100, 154–64. In legal manuals this figure could represent Justinian in his role as lawgiver.

⁶³ For a bishop at the centre of a tree of consanguinity (c.1325) in a manuscript of the Decretals of Gregory IX, see Gerhard B. Ladner, ‘Medieval and Modern Understanding of Symbolism: A Comparison’, Speculum 54 (1979), 223–56, at 241–9, and Fig. 13; see also John B. Friedman, ‘Les images mnémotechniques dans les manuscrits de l’époque gothique’, in Jeux de mémoire: Aspects de la mnémotechnie médiévale, ed. Bruno Roy and Paul Zumthor (Montréal, 1985), 169–83, at 177 (BAV, Pal. lat. 629, fol. 5r; miniature from the Decretals of Gregory IX).

⁶⁴ Dyer, The Scientia artis musice, plates 4–6 and 8.

⁶⁵ There is a ‘colour coding’ of the cantors’ copes. The taller figure has a red cope, the shorter a blue one for tones 1–2 and 5–6. The colour scheme is reversed for tones 3–4 and 7–8.

⁶⁶ The present article was in its final form before the publication of Karen Desmond, Music and the moderni, 1300–1350: The ars nova in Theory and Practice (Cambridge, 2018), which includes a consideration of the Tree of Porphyry and mensural music theory (pp. 185–97).

⁶⁷ Quatuor principalia, Distinctio prima, chs. 23 and 24; ed. Florea Aluas, 405–7 and 409–11 (Latin); 669–72 and 673–5 (English).

⁶⁸ Petrus Picardus, Ars mottetorum compilata breviter, ed. F. Alberto Gallo, CSM 15 (Rome, 1971), 16 (1–2) and 23 (12); cf. ‘Haec omnia leviter patent in arbore qui sequitur’; p. 30 (apparatus criticus). Petrus claimed to be following the teachings of Franco of Cologne and Johannes: ‘dicta mea arti Magistri Franconis de Colonia necnon et arboris Magistri Johannis de Burgundia quantum potero conformabo’ (ed. Gallo, 16). Christian Berkhold, ‘Die “arbor” des Johannes de Burgundia’, in Cantus Planus: Papers Read at the Seventh Meeting – Sopron, Hungary, September 1995, 2 vols., ed. László Dobszay (Budapest, 1998), 2: 653–64. See also Michel Huglo, ‘Recherches sur la personne et l'oeuvre de Francon’, Acta Musicologica, 71 (1999), 1–18. Johannes is mentioned (‘positio tercia Iohannis videlicet de Burgundia ut ex ore ipsius audivimus’) in an introductory remark to Franco's Ars cantus mensurabilis in Paris, BNF, lat. 16663, fol. 76v (part of the Tractatus de musica of Jerome of Moravia).

⁶⁹ Liber de musica, ed. Frederick Hammond, CSM 27 ([Rome], 1977), 63–4; diplomatic sketches of the trees are printed on pp. 40, 42, 47, 55 and 57. The diagrams are reproduced in Smits van Waesberghe, Musikerziehung: Lehre und Theorie der Musik im Mittelalter, 172–5. (The semicircular illustration of four-voice polyphony from the Scientia artis musice is reproduced on the preceding page.) See also Busse Berger, Medieval Music and the Art of Memory, 106–10 (note 14 above).

⁷⁰ ‘Musica ars a nobis sub arboris figura visa est. Nam arbor musice magnitudo eius est. Rami consonantie eius sunt, flores species, mala proportiones’; De proportionibus 3. Prologue, ed. Oliver B. Ellsworth, Nova musica and De proportionibus, Greek and Latin Music Theory 9 (Lincoln, NE, 1993), 338. Ciconia may not in this brief statement have been describing only a ‘symbolic tree’, as Ellsworth believed. Ellsworth cited a similar passage in Marchetto (Lucidarium 1.2.4), in which the branches of the ‘tree of music’ are proportioned by numbers; ‘its flowers are the species of consonances, its fruits are the sweet harmonies produced by these consonances’; The Lucidarium, ed. and trans. Jan W. Herlinger (Chicago, 1985), 78–9. Marchetto's rhetorical flourish does not imply the depiction of an actual tree exemplifying these relationships.

⁷¹ De memoria et reminiscentia 1 (449b 31); David Bloch, trans., Aristotle on Memory and Recollection: Text, Translation, Interpretation, and Reception in Western Scholasticism, Philosophia Antiqua 110 (Leiden and Boston, 2007), 26–7.

⁷² De anima 3.7 (431a 14–17; The Complete Works of Aristotle: The Revised Oxford Translation, ed. Jonathan Barnes, 2 vols., Bollingen Series 71/1–2 (Princeton, 1984), 1: 685. See also Robert Polansky, Aristotle's De anima (Cambridge, 2007), 485–93, and the comments about phantasia (Vorstellung) in Michael Krewet, Die Theorie der Gefühle bei Aristoteles, Studien zu Literatur und Erkenntnis 2 (Heidelberg, 2011), 55–9, 323–39, 363–72, 510–12. David Bloch (Aristotle on Memory, pp. 64–71) has argued for the participation of a real physical image. On phantasia in a philosophical-musical context, see Dyer, Joseph, ‘Music, Passion, and Virtue in Two Quodlibetal Questions of the Philosopher Pierre d'Auvergne’, Philomusica on-line 15/2 (2016), 1–54Google Scholar, at 11–14.

⁷³ ‘Memory, even of intellectual objects, involves an image, and the image is an affection of the common sense. Thus memory belongs incidentally to the faculty of thought, [but] essentially it belongs to the primary faculty of sense perception’; De memoria 1 (450a 11–13; ed. Barnes 1: 715; trans. Bloch, 28–29). Distinguishing between the immateriality of ordinary sensation and that of phantasia cannot be addressed in the present limited context. For a balanced assessment, see Johansen, Thomas Kjeller, The Powers of Aristotle's Soul (Oxford, 2012), 199–234CrossRefGoogle Scholar.

⁷⁴ On Dreams 2 (460b 2–3; Barnes, 1: 732).

⁷⁵ De anima 3.2 (435b 23–25; Barnes, 1: 677).

⁷⁶ ‘Sunt igitur duae memoriae: una naturalis, altera artificiosa. Naturalis est ea, quae nostris animis insita est et simul cum cogitatione nata; artificiosa est ea, quam confirmat inductio quaedam et ratio praeceptionis’; Calboli, Gualtiero, Rhetorica ad C. Herennium (Bologna, 1969), 150Google Scholar. Calboli published an Italian translation, Retorica ad Erennio, with the same publisher in 1969. Quintilian dealt with memory in book 11.2 of Institutio oratoria, giving due attention to ‘artificial’ memory (11.2.17–26), though his preference is for the ‘natural’ approach, for which he provided guidelines (11.2.27–50); ed. and trans. Russell, Donald A., Institutio Oratoria: The Orator's Education, 5 vols. (Cambridge, MA, 2001), 5: 59–85Google Scholar. There is also an edition with Italian translation by Adriano Pennacini, trans. Maddalena Villozza, 2 vols. (Turin, 2001), 576–99. Both texts, along with Cicero's De oratore 2.350–360, are edited in Blum, Herwig, Die antike Mnemotechnik, Spudasmata: Studien zur Klassischen Philologie und ihren Grenzgebieten 15 (Hildesheim, 1969), 194–204Google Scholar. A recent English translation of De oratore is May, James M. and Wisse, Jakob, Cicero on the Ideal Orator (De oratore) (Oxford, 2001)Google Scholar.

⁷⁷ On the loci, see Rhetorica ad Herennium 16.29, ed. Calboli, p. 150; Friedman, ‘Les images mnémotechniques’, 172–3 and 175 (on the tree of consanguinity as an ‘arbre mnémonique’).

⁷⁸ ‘Ut eorum quae vult memorari quasdam similitudines assumat convenientes, nec tamen omnino consuetas, quia ea quae sunt inconsueta magis miramur, et sic in eis animus magis et vehementius detinetur’; II^a II^ae q 49 art 1 ad 2. Cf. also In ep. I ad Tim. 4.2. Thomas's discussions of images concern mainly devotional ones (statues and paintings of the Lord and the saints); see Wirth, Jean, ‘Structure et fonction de l'image chez Saint Thomas d'Aquin’, in L'Image: Fonctions et usages des images dans l'Occident médiévale, ed. Baschet, Jérôme and Schmitt, Jean-Claude, Cahiers du Léopard d'Or 5 (Paris, 1996), 39–57Google Scholar.

⁷⁹ ‘Praetera, etiam Tullius dicit quod in imaginibus, ut per eas memoremur indigemus duobus: scilicet studio et ut raras et inusitatas, quae quasi mirabiles sunt, imagines nobis constituimus’; De bono 2.2.21; ed. Heinrich Kühle et al., Opera omnia ad fidem codicum manuscriptorum edenda 28 (Münster in Westf., 1951), 248. This subsection of Albert's treatise (‘De partibus prudentiae’, art.1 and 2) recycles the teaching of ‘Tullius’ [Cicero], presumed author of the Rhetorica ad Herennium.

⁸⁰ Dyer, The Scientia artis musice, 184–5, 201–3.

⁸¹ Anselme Davril and Timothy M. Thibodeau, eds., Guillelmi Duranti Rationale divinorum officiorum, 4 vols. (Turnhout, 1995–2003), 1: 36 (my translation). Further on the topic see Esmeijer, Divina Quaternitas, 1–29 (‘pictura quasi scriptura’).

⁸² Pierre Riché, ‘Le rôle de la mémoire dans l'enseignement médiévale’, in Jeux de mémoire, 133–48, at 144–8; Yates, Frances, The Art of Memory (New York, 1966)Google Scholar. The seminal survey of the topic is Carruthers, Mary, The Book of Memory: A Study of Memory in Medieval Culture, 2nd edn (Cambridge, 2008)CrossRefGoogle Scholar. A brief overview is Jacques Verger, ‘I principi pedagogici: La scritture, l'oralità, il gesto’, in Le università dell'Europa, 44–69, at 48–52 (note 30 above); also Weijers, Olga, A Scholar's Paradise: Teaching and Debating in Medieval Paris (Turnhout, 2015), 79–93CrossRefGoogle Scholar (‘Reading texts: the basis of learning’).

⁸³ On the absence of musica from the university course of studies, see my ‘Speculative Musica and the Medieval University of Paris’, Music and Letters, 90 (2009), 177–204.

⁸⁴ Johannes de Burgundia is thought to have done this with his ‘trees’ (note 68 above).

⁸⁵ Only the Lover Sings: Art and Contemplation (San Francisco, 1990), 31 and 33; the essay was originally published in Baukunst und Werkform (Frankfurt am Main, November 1952).