Didactic images in a thirteenth-century French music theory treatise: the Scientia artis musice of Hélie Salomon

JOSEPH DYER

doi:10.1017/S0961137118000207

Didactic images in a thirteenth-century French music theory treatise: the Scientia artis musice of Hélie Salomon

Published online by Cambridge University Press: 09 April 2019

JOSEPH DYER

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JOSEPH DYER*: Affiliation:
Joseph.Dyer@umb.edu

Article contents

Abstract
Image and diagram
The images in the treatise
Singing in four voices
A ‘singing lesson’
Tonus and the ecclesiastical tones
Tonus and the Tree of Porphyry
Tonus and the tree of consanguinity
Other musical trees
Pedagogical value of images
Conclusion
Footnotes

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Abstract

The Scientia artis musice, a music theory treatise completed in the year 1274 by Hélie Salomon, a cleric from the village of St-Astier (Périgord/Dordogne), covers all the usual topics treated in such sources: letter names, hexachord syllables, the claves (letter + syllable(s)), the musical hand, mutation, staff notation, clef placement and chant genres. It includes an incomplete tonary with representative chant genres together with a commentary on the seculorum (differentiae) appropriate to various chant incipits. A lengthy instruction on the performance of parallel four-voice organum is also included. The Scientia is the only medieval theory treatise whose eight illustrations (called ‘figurae’) include human figures. These images relate directly to matters covered in the treatise and serve to make its main points more easily committed to memory. Of especial interest is the image of an enthroned bishop that serves as the focal point for a novel exposition of the tonal system of chant as (1) a set of logical relations modelled after the Tree of Porphyry and (2) a variant of the tree of consanguinity. Since the sole surviving copy of the treatise is the original, all these details must reflect the author's intention.

Information

Type: Research Article
Information: Plainsong & Medieval Music , Volume 28 , Issue 1 , April 2019, pp. 1 - 27
DOI: https://doi.org/10.1017/S0961137118000207 [Opens in a new window]
Copyright: Copyright © Cambridge University Press, 2019

The Scientia artis musice was completed (albeit with lacunae) in the spring of 1274, while its author, Hélie Salomon, a native of the village of Saint-Astier in Périgord, was serving in the papal Curia, then resident at Lyon for an important church council. The original manuscript of the treatise was presented to Pope Gregory X (1271–6) in that city, where it remained until the first decade of the seventeenth century, when it was purchased for the library then being assembled for Cardinal Federico Borromeo – the present Biblioteca Ambrosiana at Milan – where the manuscript now carries the shelf mark D 75 inf. It is the earliest (and virtually only) medieval music treatise to survive in the original manuscript, prepared under its author's personal supervision.Footnote ¹ This is proven both by an insertion a the bottom of folio 1, in which an unnamed parish priest (‘plebanus’) attests (rather tepidly) to its merits, and by the presence of the dedication inscription, inserted in available space at the bottom of folio 4v (Fig. 4). In offering his treatise to the pope, the author sought in return the award of a canonry in his home village of Saint-Astier. There would be no point to including either of these inserted items in a copy. There is, in fact, no evidence that the treatise was ever copied in the Middle Ages or Renaissance. The librarian of the Biblioteca Ambrosiana brought the existence of the Scientia artis musice to the attention of Abbot Martin Gerbert, who published it in the third volume of Scriptores ecclesiastici de musica sacra potissimum (1784).Footnote ² Gerbert omitted most of the tonary, and the shape of the images was misrepresented beyond recognition: all the circular images were converted into squares.

Hélie Salomon's terminology is frequently idiosyncratic – perhaps one reason why it has rarely been studied or referred to since its publication more than 230 years ago.Footnote ³ The author consistently uses ‘seculorum’ (instead of the more usual ‘differentia’) to denominate the cadential formulae of the psalm tones and ‘singing in four voices’ (rubric 30) instead of the more usual ‘organum’. For this reason the treatise might have escaped the attention of scholars researching psalmody or early polyphony using the resources of the Thesaurus Musicarum Latinarum database.

The Scientia artis musice is a decidedly practical manual, not a treatise devoted to speculative musica and mathematical proportion. Its thirty-one ‘rubrics’ (i.e., chapters, a name derived from legal terminology) cover the basic elements of medieval music theory: letter names, hexachord syllables, the claves as combinations of letter and syllable(s), the musical (‘Guidonian’) hand, mutation, staff notation, clef placement and chant genres.Footnote ⁴ Exceptional is the aforementioned rubric that offers instructions on how to sing chant in parallel four-voice organum.Footnote ⁵ Several times Hélie addresses his pupil directly as ‘tu minor’,Footnote ⁶ but one cannot imagine that the treatise was destined for a beginner or even a boy in his early teens, as ‘minor’ might suggest. The use of such direct address enhances the probability that the Scientia artis musice preserves a record of its author's viva voce teaching, cast in written form as a model to guide a cantor whose responsibility it was to instruct pueri in the singing of chant.Footnote ⁷ More than half of the treatise (rubrics 11–27) is taken up by an incomplete tonary with explanatory commentary. The comments virtually disappear after tone 4, perhaps an indication of haste in preparing the manuscript for presentation to the pope or because most of the essential matters had already been covered in the extensive comments to tones 1 and 2.

Image and diagram

I will refer to the illustrations in the treatise as ‘images’ for a reason. A distinction exists between an image and a diagram, the former having more layers of complexity than the latter. An image may be defined as ‘a physical likeness or representation of a person, animal, or thing’, while a diagram is ‘a simplified drawing showing the appearance, structure or workings of something; a schematic representation’.Footnote ⁸ An extraordinary exemplification of the centrality of images (as well as diagrams) is the publication in eleven volumes of 5,569 engravings in the Recueil des planches sur les Sciences, les Arts libéraux, et les Arts mécaniques (Paris, 1762–72). The thousands of images in these volumes formed a complement to the seventeen volumes of the Encyclopédie des Arts et des Métiers of Denis Diderot and Jean Le Rond d'Alembert (Paris, 1751–65). Most of the detailed images of the Recueil could not be fully understood independently of the narration provided by the text of the Encyclopédie. The operation of a windmill (Planches, vol. 4), for example, could never be understood without such a narrative (Fig. 1).

Fig. 1.

Windmill from Encyclopédie: Recueil des Planches, vol. 4.

Many medieval music theory treatises contain diagrams that illustrate mathematical proportion: the division of the gamut into species of fourths, fifths and octaves.Footnote ⁹ Absent a narration, they could almost be said to ‘speak for themselves’. On either side of the central vertical in Figure 2, a diagram from a manuscript of the Musica enchiriadis, the overarching diapason curves enclose smaller curves representing the fourth (diatesseron) and fifth (diapente) that make up the octave.Footnote ¹⁰ Diagrams of this type were linked to the division of the monochord; still others indicated points of mutation from one hexachord to another.

Fig. 2.

Interval diagram (Einsiedeln, Stiftsbibl., cod. 79 (522), p. 12). (colour online)

The images in the treatise

The images (figurae) of the Scientia artis musice belong to a different tradition, one that is represented in no other music treatise of the Middle Ages inasmuch as it is the only medieval theory treatise in which human images appear.Footnote ¹¹ They are not merely decorative features – as, for instance, Musica depicted as a female figure holding a monochord or the Davidic musicians depicted as jongleurs in the tonary BNF, lat. 1118.Footnote ¹² While Aribo's De musica describes the relationship between the authentic and the plagal tones as two dancing ‘choirs’ of men and women represented by overlapping circles, none of the extant manuscripts have human images corresponding to the narrative.Footnote ¹³ The eight images of the Scientia artis musice must have been part of the original conception, since two of them are surrounded by text. Oddly enough, only three are specifically referenced in the text: (1) the image with exercises in the grouping and separation of notes (Fig. 4), (2) the tonus image with an enthroned bishop (Fig. 5), and (3) the semicircular image that depicts the singing of four-voice parallel organum. The latter includes phrases from the text of rubric 30, which describes the technique in great detail.

Seven of the eight images in the treatise are enclosed within circles carefully drawn with a compass, the only formal exception being the semicircular image just mentioned that recapitulates the Scientia’s instructions about the singing of organum. Table 1 lists the images in the treatise; the four that are reproduced in the present article are indicated within square brackets.

Table 1.

Images in the Scientia artis musice.

The first image in the treatise is a musical (‘Guidonian’) hand enclosed within a circle and displayed in a slanted position, uniquely so among the numerous hands depicted in medieval theory treatises (Fig. 3). This is, moreover, the sole example of a musical hand that incorporates a human image – perhaps intended as a portrait of the author? A large index finger (also a unique feature) is poised to point to joints of the hand, on which the claves (a combination of pitch letter and sol-fa syllables) are inscribed.Footnote ¹⁴ The possible combinations are exhaustively catalogued in rubric 2 of the treatise and exemplified visually in the image of the hand. Once mastered, the hand served as an excellent, ever-present aide-mémoire, whose pedagogical value is evident from its popularity. (The images of the Scientia artis musice and the ‘art of memory’ will be discussed below.) Johannes Affligemensis (speaking only of the syllables) affirmed the superiority of the hand over the monochord for basic instruction in musical intervals.Footnote ¹⁵

Fig. 3.

‘Guidonian’ hand (Milan, Bibl. Ambrosiana, D 75 inf., fol. 3^v). (colour online)

Singing in four voices

The only image in the Scientia artis musice besides the hand that has drawn scholarly notice is the semicircular illustration related to rubric 30, which depicts four singers singing four-voice parallel organum. Martin Gerbert had it engraved as half of the frontispiece to the third volume of the Scriptores, in which the Scientia artis musice was published.Footnote ¹⁶ The style of organum described in the Scientia is identical to that found nearly four centuries earlier in the Musica enchiriadis tradition (more precisely in the Scolica enchiriadis), yet Hélie's exposition of the method is exclusively practical, unconcerned about the theory behind the simple and composite ‘symphonies’ of the Enchiriadis.Footnote ¹⁷ Strictly speaking, a visual representation would not have been essential, since Hélie's meticulous description of the practice in rubric 30 leaves nothing to be desired, but the striking image of the four singers (seated) summarises his instruction in a memorable way.Footnote ¹⁸ The singers in the image are arranged to illustrate graphically the intervals between the voices (5th–4th–5th), but Hélie advises that (for practical reasons) those who sing in octaves should stand next to each other.

The singers who sing in octaves are linked by bands that describe their relationships: ‘The third [voice] resounds with the first, because it models itself on the lowest’ and ‘the fourth gives forth melodies, the second voice mediating’ (‘Tertia cum prima resonat quod capit in ima [and] Dat modulos quarta mediante voce secunda’). Between the first and second singers, just below the inner band, is inserted the phrase ‘parum sonas nimis’, an injunction (also present in the text of rubric 30) that admonishes the singer to sing more loudly.Footnote ¹⁹ A band of text that begins next to the director (rector) must be read across the width of the illustration: ‘Custodiatis / diligenter / prima[m] voce[m]’. The phrase below reads: ‘pausatim / pausati[m] / exaltetis voces’. The first reiterates the responsibilities of the singers to coordinate their voice parts with the first (lowest) voice; the second is a general injunction to sing with full voice, but not stridently. Elsewhere in the rubric (30.23) Hélie condemns the kind of stentorian singing he has heard from the canons in Lyon. Between the third and fourth singers in the curve of the semicircle is the instruction: ‘Cu[m] fueritis gravatus / Resumatis cu[m] pot[erit] si e[st] p[er] p[rim]u[m] i[n] q[ua]rto / et ex necessitate fit aliqu[ando] faciendu[m]’. This sums up instructions in the text of rubric 30 about how the singers can recover from a breakdown in performance: the sonorities of the fifth and the fourth must be built up again from the lowest voice.

A ‘singing lesson’

The second image in the treatise (Fig. 4) elucidates what I have described in Table 1 as a ‘singing lesson’. On either side of the circle are the figures of Pope Gregory the Great (left, seated) and Euclid (standing right, wearing a doctor's cloak and biretta).Footnote ²⁰ Kneeling at the lower left is a figure representing the author of the treatise in the act of presenting his work to Pope Gregory I, reinterpreted for this purpose as the reigning pontiff, Gregory X. Hélie's petition for the award of a canonry at his birthplace, Saint-Astier, is at the bottom of the page.

Fig. 4.

A ‘singing lesson’ (Milan, Bibl. Ambrosiana, D 75 inf., fol. 4^v). (colour online)

Inside the circle are puncti (crudely notated), ascending on the left and descending on the right placed on freely drawn lines intended to represent musical staves. They have six pitches, accompanied by the appropriate sol-fa syllables (ut-la on the left, la-ut on the right). The only exception is the second stave from the top on the right, where the last two pitches and their syllables (re, ut) have been scraped away. Hélie draws attention to this omission (perhaps he erased the notes himself?), but he can offer no reason for their absence other than that they are no longer in use (‘nulla ratione caret, sed usus abolevit’).Footnote ²¹ Either Gerbert or the Milanese scribe who prepared a copy of the manuscript and its illustrations for him resupplied the deleted pitches and syllables. As described in the text of rubric 8, the pitches are first to be sung separately (separatim), as indicated by the short vertical lines (called tricte) that divide them, and then grouped (copulatim) by twos, threes, etc. These groupings are indicated by ‘slurs’, perhaps their first appearance in the history of music. The meaning of copulatim seems evident enough – legato – but the alternative mode of articulation, separatim (quasi pausatim) is not so obvious. What degree of separation is intended?

Tonus and the ecclesiastical tones

A set of four circular images of identical layout depict the paired authentic and plagal tones along with the seculorum proper to each tone (mode).Footnote ²² (See Table 1.) These are preceded and introduced by an image (Fig. 5) that elucidates an utterly unique theory of the structure of the tonal system of Gregorian chant and the relationships between authentic and plagal tones. This image, which occupies all of rubric 9, depicts an enthroned bishop flanked on either side by four vertically aligned medallions. The four medallions on the viewer's left represent the authentic tones (1, 3, 5, 7); the four on the viewer's right represent the related plagal tones (2, 4, 6, 8).Footnote ²³ The whole is bounded by five concentric rings drawn alternately in blue and red ink.Footnote ²⁴ Over the bishop's head is inscribed the phrase ‘Primus inventor / omnium tonorum’ – the line of text split by the top of his mitre. He must represent Pope Gregory the Great, since he wears the same vestments and mitre as the figure identified as this pope in the previous image (Fig. 4). Gregory's presence here would be consistent with the purpose of the image – to demonstrate the interrelationships among the tones, of which Gregory could be regarded as their legendary ‘inventor’.

Fig. 5.

Tonus and the eight tones (Milan, Bibl. Ambrosiana, D 75 inf., fol. 5^v). (colour online)

Rubric 10 supplies a discursive explanation of the teaching encoded in this complex image, which could never be understood without such an explanation (cf. the previous reference to the windmill). Hélie first poses the question: ‘What is tone as genus?’ He answers that ‘tone as genus is the image (figura) of seven letters and one clavis, six notes and the eight tones, embracing the nature of all chant, artificial as well as natural’.Footnote ²⁵ This statement is elaborated as follows:

Rubric 10.6–10

This passage establishes two sets of relationships between the authentic and the plagal tones. All eight tones are called equally species of ‘tonus in genere’ (tone considered as genus),Footnote ²⁶ but at the same time the four authentic tones are said to be genera in their own right with the four plagal tones as species under them (10.6–8). In addition, the authentic tones are called sons of tonus, while the plagal tones are said to be sons of the authentics and consequently grandsons of tonus. Both concepts (genus-species and familial relationships) are woven together in the author's explanation, which likewise involves a ‘tree’ (10.6) – two in fact – whose branches I will now attempt to disentangle.

The genus-species link and the ‘familial’ relationships involve two different kinds of ‘trees’: (1) the Tree of Porphyry, a diagram that exemplifies the descent (according to principles of logic) from the highest genus (substance) to the lowest species and (2) a tree of consanguinity that depicts familial (blood) relationships. Trees were familiar demonstration models in the Middle Ages.Footnote ²⁷ The philosophical divisio scientiarum, for example, displayed within roundels connected by straight or undulating lines the interrelationships among the domains of human knowledge.Footnote ²⁸ There were also trees of vices and virtues, the tree of life, genealogical trees and trees of saints of the religious orders, to mention only a few representative types.Footnote ²⁹ The term was often employed metaphorically: any resemblance to a natural tree with branches and foliage growing from the ground up might be slight or non-existent.

Tonus and the Tree of Porphyry

The title of rubric 9 (the tonus image) is spread across the top of folio 5v. It reads: ‘De consistorio tonorum ut in genere generalissimo et in specie et ordine eorumdem’ (‘Concerning the consistory of the tones as in most general genus and in species and their ordering’).Footnote ³⁰ The reference to species and especially the expression ‘most general genus’ points in the direction of two philosophical texts well known in the thirteenth century: the Isagoge of Porphyry and the Summulae logicales attributed to Peter of Spain (later Pope John XXI, d. 1277).Footnote ³¹ The Isagoge, an introduction to the Categories of Aristotle by the third-century neoplatonist philosopher Porphyry (ad 223/4–305), formed (in the Latin translation and commentary of Boethius) part of the logica vetus.Footnote ³² It amounted to an adaptation rather than an exact transmission of Aristotle's teaching in the Categories (and Topics).Footnote ³³ Students at a medieval university would have begun their studies in logic with the Isagoge, admired for its clarity and succinctness. A source contemporary with the Scientia artis musice that transmitted these ideas is the Summulae logicales.Footnote ³⁴ The first six of its dozen libri correspond to Aristotelian teaching; the final six, to more modern ‘scholastic’ logic. Since Hélie Salomon had had some university training, he would have been familiar with one or another (or both) of these texts. For instance, he occasionally initiates a discussion according to the format of the academic questio (‘queritur utrum’), but he never follows through according to the established protocols of the genre.

For Porphyry (and hence for the scholastics) the predicables that could be said of anything were: genus, species, difference, property and accident.Footnote ³⁵ Porphyry proposed three definitions of genus, two of which apply to the discussion of tonus in the Scientia artis musice: (1) genus as ‘the origin (ἀρχή) of anyone's birth’ and (2) genus as ‘that under which a species is ordered (ὑποτάσσεται)’.Footnote ³⁶ Later in the Isagoge, Porphyry lists differences between genus and species, the first of which is the fact that ‘the genus contains the species; the species do not contain the genera, for the genus is more extensive (πλεῖον) than the species’.Footnote ³⁷ Species, unlike genera, cannot be ‘predicated of several items’ indiscriminately. Species can be predicated only of items that differ in number; for example, the hundreds of millions of individuals on earth who all fall under the species ‘rational animal’.

The second chapter of the Summulae logicales (‘De praedicabilibus’) repeats the Porphyrian definition of genus and species, supplementing it by further definitions of each term. It offers three definitions of genus: (1) ‘a collection of many things (collectio multorum) somehow related to one another and to a single origin’, (2) ‘the beginning of any line of descent’ and (3) ‘[something] under which one puts a species’.Footnote ³⁸ The Summulae distinguishes between genus generalissimum (the term used by Hélie in the title of rubric 9), above which there can be no higher genus, and genus subalternum; making the distinction that ‘a subaltern species, while it is a species, can be a genus; … [subaltern species] are therefore genera with respect to what is below and species with respect to what is above’.Footnote ³⁹ The principle of ‘subalternation’ is of crucial importance for the understanding of Hélie Salomon's concept of the structure of the tonal system of medieval chant.

The Summulae replicates the teaching of Porphyry, who, after listing relationships of genus and species descending from the most general genus (substance), through body, animate body, animal, rational animal, to man and individual men (Socrates, Plato), concludes that ‘these intermediates have two relations: one with prior classes in which they are called species and the other with posterior classes in which they are called genera’.Footnote ⁴⁰ In other words, something can be a species from one point of view and a genus from another and vice versa.Footnote ⁴¹ Eleonore Stump summarised the principle in the following way: ‘except for the highest genera, all genera are subaltern genera – that is, they can all be described also as species; all species except lowest species are subaltern species – that is, they can all be described also as genera’.Footnote ⁴² After defining the levels of logical relationships, the Summulae logicales concludes with the remark that ‘the Tree of Porphyry makes this all clear to you’.Footnote ⁴³ About half of the 400 surviving medieval manuscripts of the Summulae include such a ‘tree’, but only a minority of them sport vegetal embellishment.Footnote ⁴⁴ Thus we can speak of ‘trees’ in the Scientia artis musice without requiring the presence of something the looks like a natural tree.

In Figure 5, tonus, symbolised by the enthroned bishop in the centre of the image, occupies the place of ‘most general genus’. The eight ecclesiastical tones are described as equal species of tonus, but this statement is immediately qualified. Under a different aspect the four authentic tones, species of tonus, can be construed as subaltern genera, of which the plagal tones are in turn species, one under each subaltern genus. Once this principle is understood, Hélie's theory is rendered clearer: the authentic tones are species of tonus, but they are concurrently subaltern genera with respect to the related plagals, which are species under them. This is exemplified in the diagram in Figure 6.

Fig. 6.

Genus/Species relationship of tonus and the eight tones.

Hélie confirms the genus–species relationship between authentic and plagal tones in rubric 14, defining it there with respect to tones 1 and 2, but the explanation can be applied to each of the other three authentic–plagal pairs.

Rubric 14.4–5

In rubric 19 the plagals are again called species of the authentics:

Rubric 19.50

Thus, to summarise: the authentics, species of tonus regarded as genus generalissimum, are under another aspect regarded as subaltern genera, each of which has a single species beneath it: its related plagal. The idea that each of the subaltern genera has but a single species makes for a somewhat stunted Tree of Porphyry, a point that does not diminish the coherence of Hélie's explanation.Footnote ⁴⁵ All this constitutes a curious, but from a logical standpoint reasonable, conceptualisation of the tonal system of medieval chant. It is not concerned with the historical development of the system, but rather with modelling a philosophically grounded explication of the inherited structure.

Tonus and the tree of consanguinity

In rubric 10.6–10 (quoted earlier) Hélie introduced a parallel filiation (even in the etymological sense). With respect to a second type of ‘tree’ the authentic tones are said to be sons of tonus, and the plagal tones his grandsons, thus making the authentics their fathers: ‘the aforesaid four sons are as genus and head of the other four grandsons’ (10.8). The four authentic tones are said to relate to tonus as to their father and among themselves as ‘brothers’. Rubric 10.9–10 calls attention to the faint lines on the bishop's right (viewer's left) that link the medallions vertically with each other as brothers and horizontally with the figure of the bishop, their ‘father/tonus’.Footnote ⁴⁶ The same feature is present in the medallions on the left (viewer's right) side of the bishop, where the plagal tones are called ‘sons’ of the authentics and grandsons of the aforementioned father [tonus]’.Footnote ⁴⁷ One must imagine the lines passing behind the figure of the bishop linking the parallel medallion on either side. At the end of rubric 10, Hélie confirms the relationships among the tones as a tree of relationships, here identified specifically an arbor matrimonii, or tree of consanguinity (arbor consanguinitatis) as it was more generally known, in which the central figure ‘in persona hominis’ is the progenitor:

Rubric 10.30

The mention of descendants hints that Hélie might have also had in mind a genealogical tree, which depicts individuals of a specific, often noble, family, thereby indicating lines of succession.Footnote ⁴⁸ (One still speaks of a ‘branch’ of a family.)

The medieval tree of consanguinity originated in the diagrams used in Roman law to display family relationships, direct and collateral, mainly for purposes of establishing inheritance and succession rights.Footnote ⁴⁹ Also called arbor iuris from the ninth century, it passed into standard legal manuals such as the Decretals of Gratian (causae xxxiii–xxxvi) and those of Gregory IX.Footnote ⁵⁰ In the Etymologiae, Isidore of Seville included a chapter entitled ‘De agnatis et cognatis’, to which he added three stemmata exemplifying the relationships.Footnote ⁵¹ Although Isidore referred to ‘ramusculi’, the depiction of an actual tree – trunk, branches and leaves – was not assumed, though the way was prepared for the eventual insertion of tree-like decoration or actual trees in later manuscripts. The ‘vegetalisation’ of such designs, displaying the shape of a tree with its branches, dates from the beginning of the ninth century (Fig. 7).Footnote ⁵²

Fig. 7.

Isidorean arbor consanguinitatis (Montpellier, École de médicine, ms. 53, fol.138). (colour online)

According to Hermann Schadt, 90 per cent of the arbores consanguinitatis in the canon law manuals lack vegetal decoration, as one might expect in practical manuals designed for functionality rather than ostentation.Footnote ⁵³ Most remained unadorned stemmata, not least of all due to the problems of adapting a physical tree, which ascends from a root, for a diagram that maps out descendants of a common ancestor.Footnote ⁵⁴ Some ‘trees’ of this type were triangular geometric shapes, sometimes superimposed on a human figure.

The medieval Christian tree of consanguinity, unlike its Roman predecessor, determined degrees of family relationships between which marriage was licit or illicit, not questions of inheritance; hence the suitability of the of the alternate name ‘arbor matrimonii’. The ‘trees’ served canon lawyers, for whom determining impediments to marriage (or seeking dispensations from marriage) were a stock-in-trade. It is not at all surprising that Hélie Salomon would have adapted the tree of consanguinity as a demonstration model. The nearly two dozen legal maxims quoted in the Scientia artis musice confirm that he was familiar with the workings of the legal profession.Footnote ⁵⁵

The inscription inside the top medallion (tone 1) on the viewer's left in Figure 5 is representative: ‘first tone / son of tonus / brother of the third [tone] / father of the second / .f.a.b.e.d’ (‘primus tonus / filius toni / frater tercii / pater secundi / .f.a.b.e.d’). Similarly, the tone-8 medallion (on the lower right) reads: ‘eighth tone / grandson of tonus / son of the seventh [tone] / companion of the sixth / .g.a.b.e.g’ (‘octavus tonus / nepos toni / filius septimi / socius sexti / .g.g.b.e.g’). The string of phrases and letters in each medallion (analysed in Table 2) delivers a maximum amount of information in a small space.

Table 2.

The Tonus medallions (Fig. 5).

The first four phrases in the medallions express the ‘family’ relationships already explained. The last letter of the following group of five letters is the final of the tone; the first is the ‘rule’ of the tone, identified elsewhere in the treatise as the third above the final in the authentics and the final itself in the plagals.Footnote ⁵⁶ The author recommends that this letter be used as a clef at the beginning of a piece in order to indicate the tone (mode).Footnote ⁵⁷

The function of the three middle letters (Table 2, col. 4) is more difficult to determine. They are described thus: ‘the remaining [letters] for a planctus ascending and descending, above as well as below’ (‘reliquas pro planctu ascendendo et descendendo, tam subtus se quam supra se’).Footnote ⁵⁸ ‘Planctus’ and the related verb ‘plangere’, though they appear twenty-nine times in the Scientia artis musice, are found in no other medieval theory treatise in a technical sense. Neither term is ever defined in the Scientia, and the basic meaning of plangere, ‘to beat or strike’ (also ‘to lament or bewail’), sheds little light on the intended meaning. Hélie is quite insistent that certain pitches can be ‘planged’, while others cannot under any circumstances be associated with ‘plangere’ or be subjected to whatever the word implies.Footnote ⁵⁹ The three pitches associated with plangere in the treatise (E/e, a, B/b) have a semitone above, necessarily so in the case of E/e and B/b, potentially so in the case of a, assuming the presence of ♭. This obvious commonality does not go very far in explaining why a special term would need to be employed to describe them. In the Gregorian repertoire, a is found most often with a whole tone above. Nor is it obvious why the pitches are listed each time in a different order (Table 2, col. 4).

The image of tonus flanked by medallions representing his ‘descendants’ is framed by five concentric circles drawn alternately in blue and red ink. Letters, roman numerals and hexachord syllables (puncti) are inserted at widely spaced intervals inside the rings. The letters A–G in the outermost ring run in a counter clockwise direction, beginning beneath the bishop's feet. The seven claves (i–vii) in the second ring begin opposite G (gama) on the lower left and also run counter clockwise. They stand in exact correspondence to the seven letters of the outer ring.

It appears that, of the sol-fa syllables, only ut, re and la are aligned with entries in the other rings. Whether or not this is intentional is difficult to establish. The syllable ‘la’ is aligned with clavis 7 and the letter F, a pitch which can be sung only to ‘fa’ or ‘do’ (soft hexachord), never to ‘la’.Footnote ⁶⁰ Placed in the innermost ring are the eight tones, not in numerical order (1–8) but each opposite the letter ‘on which each tone makes its letter’ (‘in qua littera quilibet tonorum facit litteram suam’), that is, opposite the pitch that corresponds to the ‘rule’ of the tone (and the preferred clef letter). The four rings along with the material enclosed within them demonstrate the power of a single image to impress upon the memory in a compact form the essential elements of a teaching.Footnote ⁶¹

While the figure of a bishop representing tonus as most general genus in a tree of Porphyry might pass with only a brief comment, a celibate bishop's role as ‘father’ of the four authentic tones and ‘grandfather’ of the plagal tones might seem more than a little awkward. It was not uncommon, however, for medieval trees of consanguinity to include a ‘presentation figure’ of authoritative standing, like an emperor or king.Footnote ⁶² In a genealogical tree that role would have been fulfilled by the ancestor regarded as the founder of the house. In the present context it seems fitting that Pope Gregory, whose identity (as we have seen) can be confirmed by the second image in the treatise (Fig. 4), should be enthroned in his role as inventor and fons et origo of the tonal system of the chant that bears his name.Footnote ⁶³ The authentic and plagal tones can be related to him as ‘descendants’.

Four of the circular images in the Scientia artis musice depict paired authentic and plagal tones with their respective seculorum.Footnote ⁶⁴ They are related to the tonus image just discussed, though the connection is never specifically brought out. Figure 8, which illustrates tones 3 (authentic) and 4 (plagal), may serve as a representative example. Here and in the other three parallel images the abstract medallions of the tonus illustration become ‘enfleshed’ as cantors – one tall, the other short – recognisable by their staffs of office. The taller in a blue cope represents the authentic tone; the shorter in a red-coloured cope, its related plagal – in other words, the son and grandson of tonus, respectively. The other three images of the tones are similar, even to the colour of the copes worn by the cantors.Footnote ⁶⁵ On either side of the two figures are the (crudely notated) seculorum of the psalm tones – the authentic (3) at the top and the related plagal (4) at the bottom. The clefs, puncti and lines intended to represent the staff were drawn by hand. Their roughness contrasts sharply with the perfect circles framing the Scientia’s images.

Fig. 8.

Tones 3 and 4 with seculorum (Milan, Bibl. Ambrosiana, D 75 inf., fol. 17^r). (colour online)

Other musical trees

Hélie Salomon was not the only music theorist to employ a tree as an illustrative model, but all of the other ‘musical’ trees demonstrate rhythmic relationships – not the structure of the tonal system as is Hélie's intent.Footnote ⁶⁶ There are two minutely detailed ‘trees’ of rhythmic values in the treatise known as Quatuor principalia.Footnote ⁶⁷ The Ars mottetorum of Petrus Picardus refers to two trees devised by a certain Johannes de Burgundia, but the intended diagrams were never entered in any of the three surviving manuscripts of the treatise.Footnote ⁶⁸ One of Johannes's trees would have illustrated the relationship among the long, breve and semibreve; the other, the relationship among ligatures on the basis of propriety, perfection, etc. Johannes Vetulus de Anagnia (14th century) employed six complex trees in his exposition of rhythmic values.Footnote ⁶⁹ The composer and theorist Johannes Ciconia supposed the entire ars musica could be represented in the image of a tree, of which the branches are the consonances. The flowers represent species (of fourths and fifths); the apples, proportions.Footnote ⁷⁰ It was not a concept that he developed further. Such trees illustrate (1) how many very short rhythmic values (minima) fit into a longer one (semibrevis), and (2) how many of both fit into a still longer value (brevis). They foreshadow the diagrams familiar from modern music theory books that illustrate for beginners the relationship of note values from the semibreve to the hemidemisemiquaver.

Pedagogical value of images

Though the saying that ‘a picture is worth a thousand words’ is of fairly recent coinage (the early twentieth century, in fact), the wisdom of that adage has long been appreciated. In De memoria et reminiscentia Aristotle affirmed that ‘it is not possible to think without an image’ (‘νοεῖν οὐκ ἐστιν ἄνευ φαντάσματος’).Footnote ⁷¹ He restated this in De anima: ‘to the thinking soul images serve as if they were contents of perception … hence the soul never thinks without an image’ (‘τῇ δὲ διανοητικῇ ψυχῇ τὰ φαντάσματα οἷον αἰσθήματα ὑπάρχει … διὸ οὐδέποτε νοεῖ ἂνευ φαντάσματός ἡ ψυχή’).Footnote ⁷² In De memoria he affirmed the principle that memory, ‘which relates to what is past’, cannot exist without an image.Footnote ⁷³ He did not mean, of course, that an ‘image’ (‘φάντασμα’) had to be exclusively a mental picture of some physical object; it could be closer to what we might think of as an idea, concept or mental construct of some sort preserved in the absence of a present stimulus or object of sensation. Persisting in memory, images could be recalled as required and used as the subject of further contemplation (to speak in philosophical terms). Once imprinted on the memory, an image recalled the content of the image in its physical absence. Aristotle observed as much in De insomniis: ‘even when the external object of perception has departed, the impressions it has made persist and are themselves objects of perception’.Footnote ⁷⁴ Since ‘the sense organ is capable of receiving the sensible object without its matter … even when the sensible objects are gone, the sensings and imaginings continue to exist in the sense-organs’.Footnote ⁷⁵

Book 3 of the anonymous Rhetorica ad Herennium, believed in the Middle Ages to be an authentic work of Cicero, promoted the use of images in the exercise of ‘artificial’ memory. Whilst natural memory might suffice for many tasks, more complex and demanding ones required mastery of specialised techniques.Footnote ⁷⁶ The Rhetorica ad Herennium recommended that ‘we ought to set up images of a kind that can adhere longest in the memory, and we shall do so if we establish images as striking as possible’. Important were not just the images themselves, which should be colourful and memorable, but also their background and arrangement.Footnote ⁷⁷ Not all of these aspects are germane to the images in the Scientia, but Rhetorica ad Herennium’s emphasis on the importance of images of a striking character most certainly is.

Thomas Aquinas, commenting on memory as part of the virtue of prudence, observed that ‘when a man wishes to remember a thing, he should adopt some suitable likenesses, not, however, ones too ordinary, because we are struck more by what is out of the ordinary (ea que sunt inconsueta), and thus in such things the mind is more and more intensely occupied’.Footnote ⁷⁸ Whatever is more strongly impressed on the mind and frequently recalled is less likely to be forgotten. Thomas's teacher, Albert the Great (c.1193–1280), in arguing for a by then traditional practice, expressed similar views: ‘in images, so that we might remember through them, we have need of two things, that is, study and that [they be] uncommon and unusual; which [images] as they are remarkable, we organize for ourselves’.Footnote ⁷⁹ Albert and Thomas were, of course, speaking of the ars memorativa that assigned arbitrary meaning to exceptional images, but the points about serious application (studium) and the value of images that were out of the ordinary possess a perennial validity. The figure of the bishop and the contents of the medallions in rubric 9 (Fig. 5) or that of the organum singers confirm this principle. It is safe to say that Hélie's teaching is rendered memorable by its presentation within the framework of multifaceted images.Footnote ⁸⁰

In chapter 3 of the first book of the Rationale Divinorum Officorum (‘De picturis et cortinis et ornamentis ecclesiae’), Guillaume Durand alluded to Gregory the Great's letter (Ep. 9.209) on the value and appropriateness of images of the saints that were venerated in churches. Durand affirmed that ‘a picture moves the spirit more than something written’ (‘pictura namque videtur movere animum quam scriptura’).Footnote ⁸¹ The image places something, a ‘res gesta’, vividly before the eyes, but a text merely recalls the same to the memory through the sense of hearing, ‘which moves the mind less’ (‘qui minus animum movet’). Though Durand is concerned exclusively with sacred images, the principle could easily be applied to those in the Scientia artis musice.

Conclusion

As I have tried to show, images were powerful tools for the acquisition and organisation of knowledge in the Middle Ages.Footnote ⁸² The Scientia artis musice, which has all the marks of being a record of its author's oral teaching, was not directed to learned university students and masters, but to cantors and young students who might profit from the instruction.Footnote ⁸³ It may be that the eight figurae in the manuscript once formed a component of Hélie Salomon's pedagogical endeavours. Larger versions of some of them might have been mounted on a wall for purposes of instruction, though we know nothing about Hélie's career as chant instructor.Footnote ⁸⁴ The contents of the Scientia artis musice strongly suggest, however, that he had a good many years of practical experience as a teacher.

The unusual character of the images in the Scientia artis musice – unique in the music theory literature of the Middle Ages – would have facilitated their retention in memory and thus recall the teaching they embodied. Unfortunately, they never had an opportunity to fulfil this promise, since the treatise disappeared into a cupboard in Lyon, not to be discovered until more than three centuries had passed.

At present, when the public is bombarded with a surfeit of images, their impact is far less than it once was. More than sixty-five years ago, the philosopher Joseph Pieper went so far as to say that ‘man's ability to see is in decline’ because ‘the average person of our time loses the ability to see because there is too much to see!’ (italics original).Footnote ⁸⁵ He said this at a time when relatively few people had television sets in their homes – much less Internet connections and an endless series of apps. Advertisers have long appreciated the power of images and that an image must be simple and intelligible at first glance, for it will soon be shoved aside by another one. Understanding complex images like those in the Scientia artis musice requires more of the viewer – medieval or modern – than can be satisfied by a casual glance. Hélie Salomon, more than any other music theorist of the Middle Ages, appreciated this fact and in his teaching. In the Scientia artis musice he attributed to the image a significant pedagogical role. As Aristotle maintained (and as our author would have agreed), ‘it is not possible to think without an image’ – even about medieval chant theory!

Footnotes

A previous version of this study was presented at the 2016 Cantus Planus meeting in Dublin.

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), 14–21.

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), 97–132; and Stones, Alison, ‘Hélie Salomon, clerc de Saint-Astier et son traité musical’, Bulletin de la Société historique et archéologique du Périgord, 143 (2016), 165–76.

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), 7. 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), 81 (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), 1–54, 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), 199–234.

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), 150. 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: 59–85. 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), 194–204. A recent English translation of De oratore is May, James M. and Wisse, Jakob, Cicero on the Ideal Orator (De oratore) (Oxford, 2001).

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), 39–57.

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). The seminal survey of the topic is Carruthers, Mary, The Book of Memory: A Study of Memory in Medieval Culture, 2nd edn (Cambridge, 2008). 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), 79–93 (‘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).