All the evidence we have decrees that music permeated every walk of fifteenth-century life, from popular and aristocratic entertainment to religious and civic ritual. The range of types involved must have been formidable — vernacular music reflecting the activities and preoccupations of the common people, including also music for popular religious worship and popular drama; the ‘official’ music of the Church, especially the unaccompanied plainchant melodies supposedly hallowed by the pen of Pope Gregory the Great, and passed down through subsequent generations; music for all manner of festive occasions, ranging from the most functional of fanfares to the specially commissioned major work; music for the fifteenth-century nobleman, often designed less to help him while away the hours than to demonstrate the splendour of his establishment, the refinement of his taste and the personal piety with which he lavished resources on his chapel. Music was sung or performed on instruments, executed by individuals or groups, played by ear, improvised or read from notation; as a branch of the quadrivium, it even became a cerebral pursuit, in which sound might give way entirely to philosophical and mathematical speculation.
Yet translating such an overview into tangible repertories which can be explored and characterised can be a problematic, even an impossible, task. This is not merely a matter of the loss of sources. First, it is clear that then, as now, the bulk of the material, as ephemeral as the situations which prompted it, was not considered worth preserving. Doubtless, in its widest sense, musical entertainment probably took in not only singers and instrumentalists, but ‘oral poets and tellers of tales (often to a musical accompaniment), fools, jugglers, acrobats and dancers; actors, mimes and mimics; conjurors, puppeteers and exhibitors of performing animals’. Second, a wide range of music had little or no written tradition; that of the common people is an obvious but by no means the only case. Third, and more subtly, much music depended so overwhelmingly on the individualism of the performer and the moment of performance that it was unnecessary to write it out. Indeed, to have done so would have lent false authority to a single version of something which was by nature semiimprovised, and was thus created anew on each occasion. Clearly, one would expect this to have been true in the cases of dance music and the singing of narrative poetry. In practice, however, it is likely to have applied to the entire range of activities which lay within the province of this kind of professional performer, the minstrel.
In practice, the minstrel’s position was not specially enviable. For the most part, pay and social status were low, though it appears that certain categories were more highly regarded than others — trumpeters tended to be near the top of the hierarchy, for example, presumably because they made a vital contribution to more formal occasions. That said, and ephemeral as minstrel music essentially was, we should not assume that it or those who performed it could never achieve any distinction. Indeed, whether residents or itinerants who were just expected to attend on ceremonial occasions, those minstrels who were fortunate enough to acquire court employment might achieve considerable personal reputation. Thus, in a familiar passage from Le champion des dames (c. 1440), Martin le Franc refers to a pair of blind performers at the Burgundian court whose gifts were such that Guillaume Dufay (1397?—1474) and Gilles Binchois (c. 1400—60), two of the most eminent composers of the day, were said to have been struck with shame and envy. Again, itinerants with court connections could command superior wages as they travelled the circuit around civic festivities and the homes of likely patrons; there was always the possibility of generous additional gifts both for them and for their colleagues who remained at court throughout the year.
Though of some historical interest, it is potentially misleading and possibly just poetic licence that Martin le Franc should have chosen to compare minstrels with the two best-known Franco-Flemish composers of the day. In practice, the minstrel and the ‘clerk’ musician (one who was trained to read and, in some cases, to write music) occupied quite different places in fifteenth-century musical life — and, indeed, quite different social strata. Specifically, the clerk musician had little to do with the ephemeral world of the minstrel, but sang music which, for the most part, was composed in the sense of actually being written out. In general, he was one of a team of singers, and therefore unlikely to come under the spotlight as an individual performer. Furthermore, although he might happen to sing and write secular songs, his official duties were usually those of a chaplain; hence he belonged to a cathedral or other such establishment, or to a court chapel.
No doubt much well-crafted entertainment flowed from the activities of the high-class minstrel; however, it was the clerk musician whose repertory was such that it had to be written down. Yet, in attempting to enter his world, we must realise that music was rarely copied for its own sake; there was normally a very particular reason for doing so. This was not necessarily, as one might assume, because it had the status of art in the sense that a given piece was regarded as an object of aesthetic contemplation — though, as we shall see later, this was a concept not entirely alien to the fifteenth century. Rather, it was far more likely to be its function which demanded its preservation. As the Catholic liturgy had developed and, over the centuries, spread across much of Europe, so it had become virtually inseparable from the plainchant to which it was sung. Consequently, texts and their associated music gained an almost scriptural authority, and were therefore necessarily copied throughout the considerable sphere of influence of the Roman Church. In practice, therefore, much of this repertory became remarkably international, despite numerous local melodic variants and more extensive variations deriving from regional liturgical uses. This plainchant was, of course, the essential written-out repertory of the clerk musician.
The varying degrees to which liturgy might be overlaid by music and ritual action remind us that plainchant was not merely functional, but in a crucial sense decorative, too. So, for example, while prayers and readings tended merely to be intoned (i.e. sung mainly on a single note but with a short recurring melodic formula at the beginning and end of each phrase), other parts of the text were sung in a less austere and more distinctively melodic manner. It is also clear that the grander liturgical occasions were reflected in a more highly decorated melodic style: hence, on the greatest feast days, specially florid chants were sung in order to signal and celebrate the solemnity of the occasion.
This general principle, that level of adornment reflects importance of occasion, provides a significant clue as to why sacred texts came to be set to polyphony, that is, music in independent vocal parts, the repertory which we most readily associate with the clerk musician. Simply, polyphony was a possible further layer of decoration which might be plain, even austere, or quite the opposite. Thus, at the most basic level, the polyphonic setting of a given text might be little more than simple harmonisation of its normal plainsong; indeed, large numbers of such settings survive in fifteenth-century sources, in particular of texts from the Office and the Proper of the Mass. At the other end of the spectrum, a piece of polyphony might draw on all the ingenuity at its composer’s disposal and, of course, require considerable reading and technical skills on the part of the performers.
Here, of course, we are talking about the highest endeavours of the clerk musician, which presents a convenient opportunity to examine some of the more conspicuous features of his compositional activities. What is particularly striking about the most ambitious music of the earlier part of the fifteenth century is that it seems to have been normal practice to begin with the construction of a ground plan which then served as the framework upon which the composer hung the text and built the details of the polyphony. So, for example, in the isorhythmic motet, a genre which largely originated in the fourteenth and continued in use until the mid-fifteenth century, the composer’s musical starting-point was a piece of plainchant, upon which he imposed a repeating rhythmic pattern, and which he placed in a foundation voice called the tenor. Above and possibly below this tenor, he successively added further vocal parts, which might also involve a degree of rhythmic predetermination; also, different sections might constitute melodic variants of each other (isomelism), and succeeding repeats of the underlying plainchant might be presented in progressively shorter note-values (half-length, third-length, etc.), giving an impression of gathering momentum. Very commonly, as a further layer of complexity, some of these melodic lines carried different texts, either on the same subject, or with one commenting on the other. Such additional elaboration was a matter of choice and local tradition; however, it was a conspicuous and universal feature of the genre that a complex edifice should have been built by successively superimposing further independent melodic lines over an initial foundation voice part. By contrast, most later music was created more as a series of events spaced in time.
During the 1430s and 1440s, the traditionally rather learned and esoteric isorhythmic motet was eclipsed as most prestigious genre by the so-called cyclic Mass, grouped settings of texts from the Ordinary of the Mass (generally the Kyrie, Gloria, Credo, Sanctus and Agnus Dei). At first, one of the most common compositional procedures here was to start by arranging a given segment of plainsong (usually extracted from the Office) over a preordained plan which was more or less reproduced across the five movements. As with the isorhythmic motet, the remaining vocal parts were then composed upon this foundation.
Such music was, of course, heavily dependent on compositional decisions made at the beginning of the creative process; certainly, by the time a piece of chant had been selected for an isorhythmic motet and the chosen rhythmic pattern applied to it, the overall structure and much of the musical detail had been largely predetermined. That creative process therefore became one of progressive elaboration of what might be quite a rigorous architectural scheme; indeed, within some traditions, it was even acceptable for the underlying musical structure to run counter to that of the words. It was, for example, commonplace in the English Mass repertory for the tripartite Kyrie text to be divided across two musical sections simply because a ground plan of two roughly equal segments had become a conventional part of the tradition.
That said, from early in the century, there had also run, in parallel, a tradition of smaller-scale settings, commonly of extra-liturgical votive texts, where the form of the words seemed to drive that of the music rather than vice versa. Presumably, these must have begun as a more modest part of the clerk musician’s trade. However, by the mid-century, the predominant trend was for this more text-oriented approach to be adopted also into more prestigious genres and, by the late Masses of Dufay and other similar works from the 1450s onwards, it had become normal for the form of the words to determine the shape of the musical foundation.
The smaller-scale music also tended to be composed rather differently, with simpler vocal parts conceived together rather than as successively superimposed layers. Indeed, as the fifteenth century continued, the trend ran steadily towards this new simultaneously composed style, even in increasingly complex polyphony. Certainly, by the end of the century, the layered manner of composition was rapidly becoming obsolete in favour of a style in which a given piece was divided into sub-sections, each of which was built from a short, pithy musical idea which was passed around the voices in imitation. With this came a distinct move towards the ‘series of events spaced in time’ mentioned above, the potential for varying tension from one moment to the next, and therefore the possibility of more obvious expressiveness. Even in the early part of the century, it is instructive to compare the rather inscrutable world of the isorhythmic motet and the early Mass cycle with the more communicative manner of smaller-scale music of the time. Though many composers remained equivocal over ‘expressing the sense of the words’, there was an unmistakable general move towards a more deliberately eloquent type of text-setting, especially in the last third of the fifteenth century. Perhaps the most notable products of this trend were the later motets of Josquin Desprez (c. 1440—1521), in which the composer not only shows an impressive ability to match musical type to text, but also cultivates a clarity of word declamation which was taken as the ideal for sixteenth-century sacred polyphony.
By now, it will be clear that complex polyphonic sacred music was far from essential to the liturgy — indeed, most people would never have heard anything other than chant or the most basic polyphony unless they had contact with a large church or cathedral or with the court of a prince or other nobleman. Rather, the driving force leading to the establishment of a group of clerk musicians competent to sing complex polyphony and the provision of music for such a group was only likely to come from ecclesiastical, royal or other kind of aristocratic patronage; indeed, the quality of a person’s household chapel was an important indication of his status. Accordingly, some noblemen went to considerable lengths to attract high-quality musicians to their courts. Thus, among the best employed by Philip the Good of Burgundy were Binchois and the Englishman Robert Morton (c. 1430—after 1472); while his son retained an excellent chapel first as count of Charolais and then as duke of Burgundy, with Antoine Busnois (c. 1430—92) as his most distinguished resident composer. Remarkable, too, were the Sforza court in Milan during the 1470s, which boasted not only Josquin, but also significant lesser figures like Gaspar van Weerbeke (c. 1440—1518), Johannes Martini (c. 1440—97 or 1498), Loyset Compere (c. 1445—1518) and Alexander Agricola (c. 1446—1506); and the d’Este court in Ferrara which at various times employed Josquin, Martini and Jacob Obrecht (c. 1450—1505). During times when the Papacy was not under political pressure and the pope was interested in music, the papal chapel also attracted important musicians, most of them Franco-Flemish. Dufay, Jean Pullois (d. 1478) and Josquin each spent several years in the papal chapel. In England, the best composers were traditionally drawn to the Chapel Royal or to the chapel of some royal personage close to the monarch.
In the circumstances, one would expect many of the clerk musician’s most impressive pieces to have been written for important state, even internationally significant, occasions. So, for example, Dufay’s isorhythmic motets Supremum est mortalibus bonum and Nuper rosarum flores celebrated respectively King Sigismund’s entry into Rome in May 1433 and the dedication of Florence cathedral in 1436, while his Mass Ave regina celorum was probably composed for the dedication of Cambrai cathedral in 1472. The texts of the motets were often distinctly topical, even polemical on occasions, and celebratory work might involve more or less transparent compliments to the parties involved. Josquin, for instance, based his Mass Hercule Dux Ferrarie on a musically encrypted version of the name Ercole d’Este. It is also clear, however, that an appreciable amount of sacred music was written to provide repertory for the various choral foundations which, though endowed by noble or ecclesiastical patrons, remained largely independent of the courts. These establishments were a particularly common feature in England, and usually — as, for example, with Oxford and Cambridge colleges founded at the time — had educational extensions. Although nowadays regarded as primarily educational institutions, the original foundations of such colleges and some schools (Eton College, for example) were often more concerned that sacred polyphonic music should be performed, commonly votive antiphons in honour of the Virgin Mary.
Though polyphonic sacred music remained the exception rather than the norm during the fifteenth century, and almost exclusively the province of the nobility and of the richest churches and foundations, its use clearly underwent an exponential increase. Thus the needs of different religious and secular establishments for repertory must have provided increasing stimulus to a market in music. In some cases, it may have been possible to meet this demand locally: so, for example, the two largest English manuscripts of mainly fifteenth-century music, the Old Hall Manuscript and the Eton Choirbook, contain works by what may be rather narrow circles of composers. Often, however, establishments must have looked further afield to supplement local repertory, and here it seems likely that transmission involved a variety of processes.
Doubtless, music was often passed on through various types of direct contact. So, for example, a group of five English Mass settings appear in a Burgundian manuscript dating from about the time of the marriage of Charles the Bold and Margaret of York in 1468. Whether or not actual copies of these works arrived with Margaret of York’s entourage is hardly the point: the fact is that cultural contact between the English and Burgundian courts was such that music could flow from the former to the latter, and there must have been countless similar circumstances in which cultural artefacts could be transmitted. In some cases, direct contact might even be between composers. It seems likely, for example, that Ockeghem, first chaplain to the French king and foremost composer at that court, passed on music, presumably including some of his own, to Cambrai cathedral when he twice visited Dufay in the early 1460s.
Precise details of how and why music was transmitted from place to place is all too rarely available. As to the mechanics of the process, it is likely that music was passed around in so-called fascicle manuscripts, individual or small connected groups of unbound gatherings containing one or two substantial works or a handful of smaller pieces. These fascicles were then either bound into larger volumes, or their contents copied into larger collections. There is also evidence, particularly in the Low Countries and from the last years of the century, of manuscript workshops;22 these seem to have fulfilled commissions, either using repertory specified by whoever was responsible for the commission, or else drawing on whatever stock of appropriate music was available.
Products of this type were often presentation manuscripts which, perhaps in most cases, were not intended for normal use. As one might expect, those that were copied for the singers frequently had a well-defined purpose: so, for example, a given source might contain music for the Mass or for the Office. Surprisingly, there are also manuscripts which contain seemingly random musical collections; one explanation, which is obvious but not without its problems, is that these were repositories of repertory from which performing manuscripts could be compiled.
Whatever the problems involved in answering specific questions of transmission, there is no doubt that music did travel; indeed, many styles became international within a remarkably short space of time. It is significant, for example, how widely distributed is the spiky, rather dissonant, style which seems to have originated in late fourteenth-century France; the smoother style which grew out of it just after the turn of the century also seems to have taken over quickly across most of Catholic Europe. For a while after that, perhaps rather surprisingly, the most critical stylistic developments in fifteenth-century sacred music were initiated in England. Indeed, the English manner (the so-called contenance angloise) was described as the fons et origo of a new and highly favoured type of music, its best-known proponent being John Dunstable. However, while his works and those by other English composers of his and the following generation were widely copied and imitated by continental musicians from the 1430s until around the middle of the century, the rather discursive feel of the style eventually fell out of favour. Subsequently, it was the Franco-Flemish composers of the later part of the century who tightened it up, in particular curtailing its long flowing lines in order to make the words more audible. The resulting so-called Franco-Flemish style became the new norm, as with earlier styles rapidly spreading throughout Catholic Europe.
Of all the genres available to the late medieval clerk musician, the courtly secular song is the one which perhaps comes closest to the objet d’art whose beauty is to be contemplated for its own sake rather than in terms of some external function. Subject matter was highly stylised — even esoteric, as with some unusual work from the court of the Avignon popes, which combined highly arcane texts with self-conscious musical ingenuity. In general, however, the trend during the fifteenth century was towards something rather less mannered, with texts more straightforwardly reliant on the language and symbols of the courtly love tradition. As convention decreed, text and music were connected according to the long established tradition of the formes fixes, with the rondeau becoming the most favoured type. What emerged — and, indeed, dominated courtly secular song for most of the rest of the century — was the elegant and subtle manner of what is still called the Burgundian song, though in practice the term is used more in a generic than a literal sense, since many of its proponents had little or no association with the Burgundian court.
Attention should be drawn here to the existence of several specially beautiful presentation manuscripts of the song repertory, of which one of the most remarkable was that known as the Chansonnier cordiforme, because of its heart shape, and the fact that, when open, it appears as two hearts joined. It has to be said, however, that taste for such conceits, indeed for the rituals of courtly love in general, declined steadily towards the end of the fifteenth century. Accordingly, the Burgundian song gave way to a new, less rigidly structured type which eventually developed into the tuneful and dance-like French chanson and Itahan frottola of the early sixteenth century.
In general, non-courtly vernacular song of the period was rarely written out in such a way that it has survived the passage of time. Though traces survive from across Europe, the most familiar repertory to have been preserved in any quantity is the English carol, a verse and refrain genre whose precise function remains something of a mystery. From the early part of the century, subject matter varies from the devotional (Ther is no rose of swych vertu) to the political and patriotic (Owre Kynge went forth, otherwise known as the Agincourt Song), and this variety remains until the demise of the genre in the early sixteenth century. Range of musical style is also surprisingly wide — despite a general tendency towards a tuneful, semi-popular manner, there are also a number of far more refined and sophisticated pieces, especially among the more austere devotional carols of the later years of the century.
Fundamentally, the clerk musician was a servant whose employment prospects lay most obviously at court or in the Church. However, he was unlikely to be employed simply as a musician, even though it was his musical abilities which had first attracted his patron’s attention. So, for example, a cathedral musician of some standing was likely to hold a number of benefices in addition to his ‘official’ post. As was pointed out earlier, even clerk musicians at court were normally chaplains; they, too, might hold such benefices as their employer could, by his influence, acquire for them.
Servants or not, some clerk musicians seem to have led remarkably varied lives and even achieved notable social status — here it is instructive to consider the career of Dufay, quite the best documented of any composer before 1500, and one which, though probably more diverse than many, cannot have been entirely untypical. Born in the late 1390s, he received musical and presumably a more general education at Cambrai cathedral, an institution with which he retained links throughout his life, even though he disappears from its records for some time after 1414. His whereabouts over the next few years are uncertain, though he may have been a member of Pierre d’Ailly’s household at the Council of Constance (1414—18), certainly had associations with the Malatesta of Rimini and Pesaro in the early 1420s and seems likely to have lived in Laon in the mid-1420s. By 1427, he was in the entourage of Cardinal Louis Aleman, then papal legate at Bologna, and he probably became a priest early the following year. Although documentation for these early years is very thin, it does not appear that Dufay’s activities were purely musical, despite the significant reputation which he was acquiring as a composer of both sacred and secular work. It is also clear that, whatever remuneration he received from a succession of influential patrons during these years, he, like most other church musicians of any consequence, also relied to some extent on benefices.
Dufay spent most of the period 1428—37 as a papal singer, with a short interlude at the court of Savoy, apparently because, for a variety of political and financial reasons, the papal choir had to be considerably run down in 1433. One may judge something of his standing at the time by the important commissions he received; for much of the period, too, he appears in documents as master of the papal chapel, though it is unclear what this meant in practice. His activities cannot have been exclusively musical, however; it is clear, for example, that he had achieved a degree in canon law by 1436 at the latest.
For all his reputation, a composer like Dufay was far from immune to political events. Thus, following the deposition of Pope Eugenius IV by the antiPope Felix V in 1438, he found himself forced to choose between the generous patronage of Cambrai cathedral, beholden to Duke Philip the Good of Burgundy and supporter of Eugenius, and the less predictable sponsorship of the new anti-pope who, as Duke Amadeus VIII of Savoy, had employed him in 1433. Calculating that Cambrai was the safer alternative, he returned there in 1439 to a position whose initial nature is unclear for lack of documentation. However, he soon became master of the cathedral’s petits vicaires, held various administrative posts and was responsible for a thorough overhaul of the cathedral’s music books, both of polyphony and plainchant. He also seems to have had close connections with the Burgundian court, being described variously in accounts as cappellanus, cantor and even familiaris to the duke.
One might have expected Dufay, widely regarded as the greatest living com poser, but now in his forties, to have settled down quietly in Cambrai for the rest of his life. However, for reasons which are unclear, he seems to have spent most of the 1450s elsewhere, perhaps associated with the Savoyard court. By 1458, however, he had returned again to Cambrai, where he remained until his death. Despite his advanced age, it is clear that he was still composing during these last years, and that he maintained a wide range of contacts, among them Charles the Bold of Burgundy. His social standing was evidently such that he was entrusted with entertaining Pierre de Ranchicourt, bishop of Arras, when he visited Cambrai in 1472 to dedicate the cathedral.
No doubt other clerk musicians led more or less colourful lives — though Binchois was perhaps exceptional in spending some time as a soldier, possibly in the service of William de la Pole, earl of Suffolk, as part of the English force occupying northern France. John Dunstable was regarded as remarkable not only as a composer, but also as a mathematician and astronomer; in addition, he was for a while granted rights over certain lands in northern France, and was accorded the title armiger, suggesting a status which few musicians could have expected to achieve. None the less, a number of features stand out as commonplace. First, the careers of many composers were international, in some cases involving much travel; it was particularly common, for instance, for Franco-Flemish musicians to spend at least part of their careers in Italy. Second, an ambitious and able composer might cultivate the patronage of a wide range of ecclesiastical and secular authorities. Certainly, he would want the relative financial security of benefices, which might be acquired through the good offices of either of these; and in consequence he would very probably be in some grade of holy orders. Third, as we have seen, his employment was not necessarily limited to musical duties.
The topic of musical education has been left until a late stage in this survey because it opens up broader questions as to what music was, not merely in the conventional sense of organised sounds, but also within the wider sphere of philosophical thought. True, the initial training of the clerk musician was straightforward in nature. A boy who showed promise would be taught, perhaps from quite a tender age, under the auspices of a cathedral, college or other institution set up specifically to perform sacred music. Here he learnt the chant repertory and, depending on the institution, he might also learn to sing, read and improvise polyphony to whatever level of sophistication was required. Though evidence is far from clear, continued education of more gifted individuals is likely to have been by a process akin to apprenticeship.
Presumably traditions which made little or no use of the written note relied still more on such apprenticeship. We have evidence, too, that both nobility and courtiers might aspire to musical skills as a sign of social accomplishment, acquired probably under the individual tutelage of a resident minstrel or clerk musician; though few are likely to have gone to the lengths of Charles the Bold of Burgundy who is said to have written songs and a motet, possibly under the guidance of Dufay.
It is not surprising, then, that many treatises should have survived which deal with a range of practical aspects of music: notation, and the composition and improvisation of counterpoint, for example. However, there also survives a considerable number of more abstract and academic treatises, reminding us that musical education was not concerned entirely with practice. Perceived at its highest level, music was a component of the quadrivium, the basis of all medieval and Renaissance university learning. Its study stretched from the philosophical musica mundi (the harmony of the universe) and musica humana (the harmony of the ideally attuned human being) down to the audible musica instrumentalis. The last mentioned was, in turn, divided into higher and lower levels — respectively the abstract musica speculativa, which was essentially a mathematical account of musical theory, and musica practica, music as composed and performed.
The basis for academic study of music and the ultimate source for most of the speculative treatises was Boethius’ treatise De institutione musica, a largely mathematical document whose tone, widely echoed by later pedagogues, is captured in his notably dogmatic conclusion to Book I:
there are three classes of those who are engaged in the musical art. The first class consists of those who perform on instruments, the second of those who compose songs, and the third of those who judge instrumental performance and song. But those of the class which is dependent upon instruments and who spend their entire effort there ... are excluded from comprehension of musical knowledge ... None of them makes use of reason; rather, they are totally lacking in thought. The second class of those practising music is that of the poets, a class led to song not so much by thought and reason as by a certain natural instinct. For this reason this class, too, is separated from music. The third class is that which acquires an ability for judging, so that it can carefully weigh rhythms and melodies and the composition as whole. This class, since it is totally grounded in reason and thought, will rightly be esteemed as musical. That person is a musician who exhibits the faculty of forming judgements according to speculation or reason relative and appropriate to music concerning modes and rhythms, the genera of songs, consonances ... as well as concerning the songs of the poets.
It may be no coincidence that Boethius chose to divide his musicians into three types; one is reminded, for instance, of the division Plato made in his Republic, much as one would not wish to take the parallel any further. Certainly Boethius draws much of his authority from classical philosophers, notably Plato and the neoplatonic movements, Aristotle, Ptolemy and, inevitably, the followers of Pythagoras. Yet for all his mathematical rationalism, we find that number in music (as indeed elsewhere) could never be separated from moral associations, and this feature of his thinking is clearly implicit in that of his later medieval and early Renaissance disciples. As with the other elements of the quadrivium, one of the most central concepts is ratio, since mathematics, geometry, astronomy and music represent proportion respectively in number, on a surface, in space and in sound. Of the different types of ratio which exist, the multiple (2:1, 3:1, etc.), being the simplest, attains the highest form of perfection, with more complex relationships being correspondingly less perfect. This carried an obvious acoustical significance, since multiple and other simple ratios relate to the most perfect consonances. However, the moral connotations of simple proportion were such that they did not merely relate to the superiority of consonance over dissonance; simple proportion meant consonance in all its perceived manifestations, and was therefore seen to partake of the harmonious perfection of God’s creation.
Neither, in practice, were such considerations an entirely academic matter. Certainly, it does not take any great leap of faith to imagine that even the modestly regarded musica practica might raise itself within the broader intellectual framework if it could in some way emulate this perfection; indeed, one might positively expect the most ambitious music to do so as a sign of its aspirations. It is not surprising, therefore, that the use of proportions is fairly commonplace, if far from universal, in such works — for example, the lengths of subsections in isorhythmic motets were very often cast in one or other of the ratios 3:2:1 or 6:4:3. Yet practice was far more complex than might be anticipated. In particular, it appears that such proportions as were used did not necessarily preserve the simplicity which the Boethian view would suggest was morally ideal. Indeed, it is obvious that composers were often interested far less in simple proportions than in significant numbers, chosen for either their arithmetical elegance or their symbolic meaning. As one might expect from a mathematician, Dunstable’s music is especially rich in the use of both proportion and numbers with arithmetical or symbolic significance; indeed, in some cases, his usage looks to have been notably arcane, taking in Greek gematria, amongst a wealth of ingenious mathematical devices.
Here, of course, we encounter a highly esoteric art in which layers of decoration were contained within a superstructure which was not random, but which added further dimensions of symbolic meaning of which God was no doubt aware, but listeners and singers alike were oblivious. it represents medieval musica practica at its most uncompromisingly erudite, one might say in its most occult, form. Significantly, we have also moved into an area about which both Boethius and the medieval musical theorists were largely silent — one which must surely have been considered a more advanced level of study than the quadrivium. Ultimately, though, it belongs to a manner of thinking which did not accord with changes of taste which were taking place in the fifteenth century. True, a few composers, most of them English, cultivated proportion and significant numbers until as late as the 1520s; however, only patchy evidence has so far been found for such techniques in continental music after the isorhythmic motet fell out of favour. Yet again, we see that crucial move away from the characteristically medieval ‘edifice with decorative overlay’. The more pragmatic style which we have seen to take its place, and the trend towards the ‘series of events spaced in time’, had altogether different connotations, looking forward, ultimately, to that greater preoccupation with text which is associated with Renaissance values.