"Allegory of Music", c.1522
Dosso Dossi
in the Horne Museum, Florence

Depictions of naked people are so common in Western visual art, that it is hard to realize how revolutionary they appeared in the Renaissance. Italian artists stripped their figures of the conventional characters - and the modish dress - given them in the high Middle Ages. Instead, they turned to the distant past, to the splendid animal vigour of its pagan gods, and emulated both the form and spirit of antique art. Nudity was glorified, to maximize the beauty and expressive power of the human form. Renaissance artists turned to the writings of the Roman architect Vitruvius, for a canon of bodily proportions that best represented the classical ideal. To understand the body accurately, Leonardo and Michelangelo dissected corpses, and so acquired more precise anatomical knowledge than any of the doctors. Artists took example from their work, and from drawings and prints circulated by the workshops of Mantegna, Raphael, Durer, and others. Dosso Dossi admired the great Venetian masters, coming in contact with Giovanni Bellini and Titian while employed by the d'Este family in Ferrara. Like them, Dossi provided frank displays of flesh for their patron, and his "Allegory of Music" is first and foremost an essay on the human form.


In Dossi's musical allegory, the male figure to the left strikes an anvil with a hammer, pausing mid-blow to confront a torch-bearing putto that appears from the clouds. Vigorous action is expressed by the contrapposto twists to the man's body, in the manner of a figure by Michelangelo or Raphael. Ultimately, the prototype comes from antique statuary (such as a fragment known as the Belvedere torso) that was widely copied and admired. Likewise, Dossi's females are types of a Venus, disrobing or standing nude. His seated woman adopts a very similar pose to that of a so-called 'Cleopatra' (left), issued as a print by Jacapo de'Barbari. Her torso, and the tilt of her head, follow Barbari's earlier engraving, though Dossi disposes her limbs more naturally than in the languid and rather awkward original. Dossi may have derived his standing nude, with her muscular back, from another Barbari print, "Victory and Glory", or even from Albrecht Durer's "Four Witches", engraved in 1497. None is an ideal beauty, and Dossi typically painted squat and sturdy bodies, with unduly thick limbs. The matronly nude, to the right of his painting, has pinched buttocks and a boneless, meaty arm, that conceals any grace to her outline. Still, the famous poet Ariosto, working alongside him at the court of Ferrara, counted Dossi among the greatest Renaissance artists. The figures have an earthy realism, and "Allegory of Music" is coherently structured. Moving from left to right, the variety in each person's pose decreases, from the action figure of the man on the left to the statuesque woman on the right margin of the canvas. In the same direction, their individual charms increase - from swarthy male to milk-skinned females, the first half clad, the next fully nude. Their identities seem enigmatic today, while a viola (or lira), lying discarded and half concealed on the ground, is the most immediate evidence of any musical story. Other clues - notes inscribed on tablets propping up the two females - are almost lost amidst the expanse of human flesh. But the narrative is united by a blast of wind, entering from the left. It bends the flame of the cherub's torch and billows the man's red robe in the air, while the woman's bodies seem swayed by its force. They cock their ears, as if the air carries strains of secret sounds, inaudible to us, and as mute as the musical instrument and notations below.

Air was known to conduct sound, but it was also life-giving breath, or pneuma, essential to spirits that animated the body. Renaissance doctors found confirmation in the writings of Galen, of the 2nd century, that contained pneumatic theories grounded in Stoic philosophy. Leonardo da Vinci wrote of spiritual motions, flowing through the limbs, to contract muscles and cause movement. The immortal part of man occupied his body as heavenly spirit, "as it were the air which causes the sound of the organ". Air, or pneuma, was the stuff of the soul and the cosmos, and the primal force of creation that breathed life into muddy chaos. God had created Adam this way, and in Sanskrit and Hebrew, as well as Greek and Latin, the words for 'soul' or 'spirit' are related to the words for 'breath'. The ancient Corpus Hermeticum described God's breath rotating the stars, and planets suspended in breath. Their heavenly influence could be drawn down to earth by aerial powers, since like attracted like. Marsilio Ficino would supplicate a planet with music especially attuned to it, since "the very matter of song, indeed, is altogether purer and more similar to the heavens than is the matter of medicine" (that is, more effective than potions made of herbs and minerals). Ficino, head of the Platonic Academy in Renaissance Florence, called it natural magic. In the Platonic and Pythagorean traditions, rightly-made music harmonized body and soul with proportionate measure. Number held sway over both macrocosm and microcosm: according to the ratios that move us in music, rays from the stars could be affective in hidden ways. Curative powers were attributed to music, with support from the Bible story of David, who calmed King Saul's madness by playing his harp. Music was no casual entertainment, no passing breeze of air or pneuma - it had spiritual substance. For Leonardo, sound - and even images -travelled in circles in the air, just as waves that result from a pebble thrown in a pond. Both sound and light acted with spiritual force on the senses, but Leonardo could not allow them independent bodies - aerial spirits would quickly disperse, and they could not speak or move, due to lack of physical substance. But Ficino, writing in 1489, gave music a life and soul of its own:

"For this too is air, hot or warm, still breathing and somehow living; like an animal, it is composed of certain parts and limbs of its own and not only possesses motion and displays passion but even carries meaning like a mind, so that it can be said to be a kind of airy and rational animal."

Illustration 3 : JUBAL,
from "The Mirror of Human Salvation", German, 1400-50.
Music manuscript

In Genesis, Jubal was the first musician, "the father of all such as handle the harp and the pipe". Here, he is shown penning a musical manuscript in primitive notation, on a strangely levitating table. Early notation, of the 9th century, consisted of simple signs above a written verse. They were called neumes (from pneuma, the Greek word for 'breath'), and indicated how to interpret the sounds and pitch direction of the text. For the first time, a melody could be read from the page, rather than passed on orally. As the system evolved, neumes were strung around a horizontal line, that established their pitch relative to the note F. The line was usually drawn in red. Another parallel line was added later, to indicate C, and was often coloured green or yellow. So the stave expanded, and neumes assumed a variety of shapes to clarify the rhythms and pitches of the song.

Jubal was a descendant of Cain, and lived before the Deluge, east of Eden in the land of Nod. He had a half-brother, Tubalcain, who was the first blacksmith and "an instructor of every artificer in brass and iron". In Dossi's "Allegory of Music", it may well be Tubalcain at the anvil. (The two women could be his sister and mother, otherwise the mothers of both brothers, as per Genesis 4:16-22.) Jubal, the primordial musician, is not included in the tableau; at best, he is represented in proxy by the viola, one of his inventions. In fact it was mostly Tubalcain, with hammers and anvil, that personified Music from the 14th century on. In depictions of the Liberal Arts, and books on music theory, he became identified with the blacksmith of another musical tale, of Greek rather than Hebrew provenance.

The legendary Pythagoras, in the 6th century BC, had heard ringing sounds emerging from a smithy. On investigation, he found different pitches arose when the blacksmith struck the anvil, according to which hammer he used. By weighing them, Pythagoras fixed music with immutable mathematical laws. Nicomachus knew the legend in the first century, and Boethius amplified his account in "De institutione musica", early in the 6th century. He gave the heaviest hammer the lowest note, while the fourth, fifth, and octave above it were sounded by lighter hammers, with progressive weights of 12, 9, 8, and 6 pounds. Boethius's treatise became the authority on music theory for much of the Middle Ages, so many others were to repeat his Pythagorean myth. Eventually, the classical legend and the Biblical account of the origins of music were conflated, and a further layer was added to the tale in the Renaissance. The humble smithy was exalted, to become the forge of the Roman god Vulcan. The blacksmith was transfigured from the legendary but mortal Tubalcain (or Jubal, or Pythagoras's smith), and became an immortal god. Vulcan was a popular deity in Ferrara, where Duke Alfonso I owned foundries where the finest artillery pieces were cast. For his official portraits by Titian, Alfonso posed proudly beside a cannon, a weapon of fire and metal. In nearby Mantua, where his sister Isabella d'Este held court, Andrea Mantegna had portrayed Vulcan in his "Parnassus", of 1497. The nude god (also in red cloak, with forge and anvil) was coupled with music-making Apollo, who played his lyre while the Muses danced. In Dossi's work, a puff-cheeked child blows a little extra musical inspiration in Vulcan's ear, and enlightens him with fire from the forge.

To Renaissance connoisseurs, the past divulged the fixed laws of the first music, and contemporary music was both a continuation and a culmination of ancient traditions. Boethius's book was put into print in 1491, while other ancient works on the subject - by Aristides Quintilianus and Ptolemy, for example - were becoming known. Dossi, as painter to the Duke of Ferrara, was familiar with music played at court, and acquainted with learned humanists who understood the finer points of theory. The key to his own Pythagoreanism can be found at the very centre of "Allegory of Music", where minute musical notes dance over the surface of the anvil. Here he makes his only attempt at the impossible, to mimic with paint a real sound occurring in the present moment. It is not the universal and undifferentiated music present in the gust of air above (if that indeed was his intent), nor the potential music of a finished compositions, in static notation below. It is raw sound, of actual notes leaping in the air. Dossi's novel, cartoon-like event is assiduously ignored by the living creatures around it. The nude figures avert their gazes to left and right, discretely away from the viewer, to disclose a subtle focus at the source of sound. Its precise nature can be guessed at by numbers written on the hammers: the one at the feet of Dossi's Vulcan should ring out the lowest note, since it is labelled XII. Another on his bench is numbered VIII, to sound a fifth above, so the one in the smith's hand would be a IX or a VI. According to Pythagoras, the note springing from the anvil is either a fourth, or an octave, above that made by the hammer on the ground.

Founders of music

Illustration 4 : THE NUMBERS OF MUSIC,
from "De Musica", Francinus Gaffurius, 1492.

Gaffurius was the choir master at Milan Cathedral when he penned several important works on music theory. To outline the principals of tuning, he illustrated the common legend of the forge, where different hammers rang out different notes on the anvil. Instead of showing Pythagoras as the interested bystander, the Biblical Jubal appears in the upper left of the woodcut. His brother Tubalcain is replaced by six blacksmiths, whose hammers are numbered according to weight. The four traditional hammers, of 6, 8, 9, and 12 pounds, are supplemented by two others - a four-pounder to give a higher note, and a bass hammer of sixteen pounds. They extend the range of pitches by a fifth upward and a fourth down, for a two octave range equivalent to the human voice. The same numbers are applied to bells, tumblers of water, pipes, and plucked strings, and Pythagoras demonstrates their use. Philolaus puts in an appearance, as the earliest known Greek author to write down the mathematical ratios of music.

The Greeks spaced notes at different pitches, by forming ratios between numbers to structure their music. The largest musical numbers, according to Pythagorean legend, apply to the heaviest hammer that gives the lowest note when struck on an anvil. Likewise, the larger the bell, the more water there is in a tumbler, and the longer the pipe, the lower the note produced. But greater weight applied to a string tightens it (like turning a guitar's tuning peg), and pitch is raised rather than lowered. The numbers shown on weights, at the bottom left of Gaffurius's drawing, would have a contrary effect to those indicated for other instruments. In addition, string pitch is measured according to the square root of the tension, so the overall range of the strings would be reduced, from the expected two octaves to one. The Greeks, in reality, measured lengths, plotted by Pythagoreans on single-stringed monochords. Their figures never represented weights attached to strings, let alone hammers applied to anvils. An anvil could be likened to a bell, and the hammer that strikes it to the bell's clapper. Then, contrary to ancient lore, the anvil is more likely than any hammer to determine pitch of the sound. Leonardo da Vinci was cautious, noting how an anvil was not suspended like a bell, to vibrate freely. Even so, he thought it could not produce different notes, any more than a single bell could, so the intervals recorded in legend must lie in the hammers. Leonardo went on to track the way the sound might travel, through walls and apertures, compared to paths taken by light, smell, and magnetism.

In modern terms, Pythagorean ratios represent relative wavelengths or, conversely, frequencies, while a Renaissance minstrel understood them as guides to the tuning and fingering of strings on his viol. The apocryphal story of the blacksmith had been received authority for fifteen centuries, until Vincenzo Galilei, father of the famous scientist, challenged the legend openly in the 1580s. He did what previous music theorists had blatantly neglected - he made experiments. By increasing a string's tension in the ratio 4:1, he raised its pitch an octave; he found two coins, one three times the weight of the other, whose sounds were an octave apart. As the octave was not always defined by the ratio 2:1 (or two hammers weighing twelve and six pounds) the Pythagorean legend was exposed as a nonsense. In 1627, Marin Mersenne formulated the first equations of pitch from experiments with simple strings, and he and Galileo (the son) laid out the basis for a science of sound. Previously, craftsmen had relied on empirical methods, rather than theorists, to produce sophisticated string, wind, and percussion instrument. Bells were some of the most difficult to tune, though sets of small bells, playing the notes of an octave, were made in the early 12th century. To shape each bell, modelling wax was measured out in Pythagorean ratios so that, after casting, the low bell was twice the weight of one an octave higher. The same arithmetic could not apply to larger bells, where diameter is doubled to drop the tone an octave, resulting in an eight-fold increase in weight. For mid-range bells, alterations in both diameter and weight are balanced to achieve changes of pitch. Carillons of two dozen beautifully tuned bells, ringing about four octaves, hung in belfries in Flanders by the middle of the 16th century.

Tamburo, or drumming machine

Leonardo da Vinci, c1498.

Leonardo was reputed to be an excellent musician, as a singer and lyre player. He sketched many novel instruments, notably a glissando flute that could slide from note to note. Other inventions were mechanical, altering the way an instrument was played, and some were entirely automated. His drum machine would beat out a tattoo when drawn behind a cart, or pushed like a wheelbarrow. A cogwheel on the axle drives two cylinders with pegs on their surfaces, that trip the levers of the drumsticks. A similar mechanism was used in the Low Countries to operate the hammers for playing bells, and is much like the device used in music boxes today. In all cases, the spacing of pegs determines the timing and type of each sound (whether drumbeat or pitched note). The same sounds will recur with each turn of the cylinder, which suits the repeating music of rounds. Leonardo noted the machine's potential to mimic vocal music, in the caption to another sketch:

"Here you make a wheel with pipes that serve as clappers for a musical round called a Canon, which is sung in four parts, each singer singing the whole round. And therefore I make here a wheel with four cogs so that each cog may take the part of a singer."

Rounds, such as "Row, row, row your boat" and "Kookaburra sits in the old gum tree" are still popular tunes today. When one singer reaches the end of the first line, another singer enters with the same tune. The first singer continues on with the second line at the same time, so the voices overlap, making harmonies from different parts of the same melody. Many voices can join in, staggering their entries the same way, and all can begin again when they reach the end of the song. Popular rounds are short tunes, typically eight bars long. They are simple forms of the perpetual canon, one of which faces us in Dossi's "Allegory of Music" (beneath the left hand of the central nude). Written in a circle, it works the same way as a simple round but is three times as long, equivalent to 24 bars in length. The tune begins at the top and travels clockwise, to end back at the top. One complete circuit contains a single melody; signs are placed at the compass points, to show where three other singers enter with the same tune. The circular format makes its musical form immediately apparent to the eye, indicating that all parts may begin again as soon they reach the end. The canon is nevertheless a simple one - all parts are at the same pitch or at an octave - and is even marred with compositional 'flaws', that make it sound a little pedantic. It is unlikely to be the work of any of the famous musicians, from France and Flanders, attracted to Ferrara by the patronage of the d'Este family. As the canon only appears in Dossi's picture, its unknown composer may well be Dossi's patron, even Alfonso I himself. Other rulers, notably Henry VIII and Pope Leo X, wrote their own canons, so why not Alfonso? The Duke sang, played instruments like others of his kinfolk, and performed on the viol at his wedding to Lucrezia Borgia, in 1502. By insisting on his own composition at the fore of a painting, a patron would add to his fame, and Dossi could but comply. Of course, circular notation is a little difficult to read - music is normally written on a horizontal stave - but it is decorative and expressive, as much as functional. A half dozen other canon circles are known up to Dossi's time, but a second canon shown in Dossi's "Allegory of Music" takes a different and unique shape.

On the stone slab shadowed by the standing nude (far right), is a stave of music bent in a triangle. It is the second Agnus Dei from Josquin Desprez's "Missa L'homme arme super voces musicales" (as identified by H Colin Slim, in the spring edition of the Journal of the American Musicological Society, 1990). Agnus Dei II is a mensuration canon for three voices where, as in the circular canon or a round, each voice sings the same melody. Here their entries are not staggered, but all start at the same time. They differ in their timing (or mensuration), so the slowest voice is accompanied by a second, sung at twice the speed, and a third at three times the speed. When the first part has come to the end of one side of the triangle, the other parts have completed the second and third sides, respectively, and the canon comes to an end. Like the circle canon, the graphic shape of the notation mirrors the form of the music perfectly. Josquin may have written his Agnus Dei in a triangle, although Dossi's painting provides us the only known example (and no other music of the time was triangular). When sung, the effect is eerily intellectual rather than expressive - the different rhythms (of two different duples and a triple) provide a slight tension, with a suggestion of syncopation in the middle. The outer parts are an octave apart, with the faster triplets in the treble. The middle voice is slowest and raised a fifth interval from the base, so the harmonies progress with remarkable smoothness. Agnus Dei II is a bravura exercise, set near the end of a long and difficult mass, and any singers performing it successfully could feel well pleased.

Josquin's proportional canon

Illustration 6 : "AGNUS DEI II", from 'Mass of the Armed Man', Josquin Desprez, 1502.

Josquin was the most famous musician of his generation, and the above extract comes from the first printed book devoted to the work of a single composer. The Agnus Dei is laid out normally, along horizontal staves, instead of a triangle as in Dossi's painting. It begins just before the word 'Agnes' at the top, where three time signatures are provided for the different parts. The C in the middle denotes the slowest part, the broken C below is for another at double the speed, and the topmost broken C with a 3 provides for the swiftest part. (They indicate one, two, and three beats to a bar, though bar lines were a later innovation.) Along the bottom line there are two signs, like reversed question-marks with double dots. They represent the points of Dossi's triangle: the slower parts, in single and duple time, reach these positions as the part in triple time finishes the entire piece. Following the notes are the words 'Triam in unum' - 'Three in one' - similar to a 'trinitas in un(um)' inscribed above the triangular canon in "Allegory of Music".
Pithy quotes were frequently attached to 'puzzle' canons, supplying clues to their manner of performance; the motto here indicates three voices, three time divisions, and so on, as well as making obvious reference to the Holy Trinity. The rest of Josquin's mass was equally thoughtful in construction. It was based on the melody of a popular tune, "Fear the armed man". About thirty other masses, by various composers, were written to the same melody, and Josquin himself employed it for a later mass. In this first version, the theme is quoted in the various voices, at different pitches, played backwards, and syncopated - a technique called imitation, of which Josquin was the acknowledged master. The mass has an overall structure as well, with each section beginning on progressively higher notes. Starting with a Kyrie on C, they climb the hexachord, the six notes in the Guidonian Hand. The mass ends with a third Agnus Dei on A - the Agnus Dei II, above, is one of the few sections to not participate in the overall scheme, nor use the Armed Man melody.

Josquin was one of the most important composers in Western history, shaping the future direction of music. He was born in Belgium, but little else is known of him personally, and his only signature is found carved into a wall of the choir stall in the Sistine Chapel. Despite a reputation for being temperamental, he was given a highly lucrative appointment at Ferrara in 1503, by Alfonso's father, Ercole I. The court had an exalted musical reputation throughout Italy, rivalled only by the Sforza's in Milan; in hiring Josquin, Ercole hoped "to place a crown upon this chapel of ours". To honour the Duke, Josquin had written a mass called "Hercules Dux Ferrariae". He constructed a theme by converting the vowel sounds in its title to notes - re, ut, re, ut, re, fa, mi, re. Each vowel was matched to one in a solmization syllable, those names given to notes of the hexachord by Guido d'Arezzo, in the 11th century. Josquin's technique was enduring, and J S Bach, for one, would later use a similar method to spell out his name in notes. Josquin left behind many lasting memories, and after he fled the plague in Ferrara, the music of his Agnus Dei II circulated in manuscript form. By the time Dossi included the piece in his "Allegory of Music", Josquin had been dead a year. The stone tablet on which it is painted reminds us of a gravestone, a memorial to one of the greatest composers to pass through Ferrara. It also resembles a composer's slate, the kind that Josquin was said to use.

Popular legends spoke of two ancient, stone pillars that survived the Deluge, with the secrets of all the arts inscribed on them in hieroglyphs. In the first telling of the tale (by Josephus in the first century), they were made of brick and stone, to preserve human knowledge against the twin catastrophes of flood and fire, warned of by Adam. By the 12th century, it was supposed one pillar held the key to music, and the story became entwined with the legends of Tubalcain and Pythagoras. In this form, it was included in books on music theory in the Renaissance, as well as in more general works. Around 1515, Dossi had painted two other women, holding stone tablets inscribed with geometric designs. One was Circe, who featured in Homer's Odyssey, the other may be Melissa from Ariosto's "Orlando Furioso". Both are sorceresses, involved in casting spells of transformation. Circe changed men to animals while the good fairy Melissa could change them back again. Dossi's musical tablets are also magical, in their own way, inscribed with notations that only initiates could decipher, and made doubly secret by being encrypted as puzzle canons. The sounds exemplified on the left of "Allegory of Music" - the orderly ratios of the forge and compositions improvised on the viola - could be encapsulated permanently in talismanic diagrams. The musician-cum-magician would make the music live again, by proper reading of the geometric markings.

It is possible to interpret Dossi's painting according to specific music theories of the time. The lower half, for example, can be divided according to ancient categories of music, found in "De Institutione Musica", by the Roman author Boethius. His highest order was musica mundana, or heavenly music, that regulated cosmic harmony at an exalted level. It gave musical proportions to celestial motion and the four elements - earth, water, air and fire - in "one body machine". The Christian symbol of the Trinity, Josquin's triangular mass, would suit musica mundana. The circle canon, to its left, may symbolize the lower manifestation of human music, or musica humana. It controlled the body and soul of man and aspired to the ideal, but was not as steadfast as musica mundana. The circle was an oft-used symbol for the microcosm of man, a reflection of the greater macrocosm of the heavenly spheres. Leonardo's "Vitruvian Man" (below) gave it a painterly form, as proportions of the human frame governed by both a circle and a square. Musica instrumentalis was the third and lowest form of music, being man's poor attempts to imitate the divine prototype. The viola provided the means; the sounds from the anvil gave a mathematical guide, that grounded music theory on a heavenly basis for two thousand years. It is impossible to be certain that Dossi had Boethius (or any other theorist) in mind, when painting "Allegory of Music", as the painting allows multiple interpretations. Any iconographic programme seems to have had little resonance in the work of other painters. Even individual symbols might not agree, so we find when John Bull penned his canon "Sphera Mundi", almost 100 years later, he used the more familiar circular stave to represent the macrocosm, rather than the unusual triangle of Dossi.

Canon of proportions

Illustration 7 : "VITRUVIAN MAN", Leonardo da Vinci, c1492.

For Leonardo da Vinci, painting was the supreme art form, best able to imitate all of nature and make visible the inventions of the mind. Its beauty came from the harmony of proportions, seen as surfaces and shapes, that could be recreated by painters in a lasting form. Nowhere was harmony more evident than in the human form, where relationships between the parts and the whole could be measured geometrically. The same could be said of musical chords, since geometrical intervals separated notes played simultaneously. But the proportional beauty of each harmony lasted but a short while, before another took its place, making music "a younger and lesser sister" to painting. All the harmonies in a painting were evident at once, to be appreciated at leisure, and they stirred the onlooker's soul to rapture.

Leonardo's remarks were part of a wider debate, on the relative status of the various arts. He was concerned, in the "Paragone" (or "Comparison") of about 1492, that painting be accepted alongside music, as one of the Liberal Arts. Musical intervals, established from antiquity, were compared to the relatively new geometry of perspective. Both space and pitch could be divided - so lights, shades, and distances receded from the eye in regular proportion, just as notes were spaced. Painting represented bodily things best, though music was allowed a special purpose for "figuration of the invisible". Only then did music approached the status of painting, though both fared better than poor poetry, which lacked the geometric beauty Leonardo required. He argued poetry was incapable of harmony, as if the parts of a song - soprano to bass - were sung one after the other, rather than together. Leon Battista Alberti held a different hierarchy, fifty years previously, and had ranked music first. Architecture came second, as a musical art of rhythms and harmonies, and Alberti recommended Pythagorean proportions be used for plans, elevations, and volumes.

Alberti found another harmonious use for geometry in the perspective method, described for the first time in his treatise "On Painting", of 1435-6. Perspective was a great innovation of the Renaissance, along with revival of the nude figure and the study of human proportions. The appearance of nature could be convincingly compressed into the two dimensions of a painting, using converging straight lines that mimicked the operations of the eye. Its inventor is said to have been Filippo Brunelleschi, designer of the new dome on Florence Cathedral. Alberti passed the method on to other artists, and Piero della Francesca, Leonardo, and Durer elaborated on the art. Of course, some mathematics was required, and Alberti began his treatise by discussing the basics of geometry - the point, the line, and the plane. These are generated one from the other, so that two points define the ends of a line, and a third point sets the plane in the form of a triangle. Josquin's music takes such a shape in Dossi's "Allegory of Music", in the only area of the painting to use perspective convincingly. The triangle of music is foreshortened, and the horizontals of the stone tablet seems to converge to a vanishing point above the anvil. Together, they provide the main evidence of a logical (albeit minimal) recession in depth, whereas forms elsewhere merely overlap. The circle canon represents another fundamental of geometry - the path traced by one point rotating round another, at a set distance in the same plane. The form suits the circular movement of the music, and is one of a vocabulary of simple shapes preferred by Renaissance artists.

Around 1510, Nicoletto Rosex had circulated an engraving of the legendary Greek painter, Apelles, gazing in rapt concentration on a board displaying diagrams of a circle, a triangle, a square, and an octahedron. More recently, the abstract painter Wassily Kandinsky thought the shapes were more than they appeared; in 1914 he decided the circle represented the spirituality of blue, while intellectual yellow was given to the triangle, and the square stood for red and matter. When musicians become interested in shapes, it is usually as a secondary, decorative adjunct to the necessary task of notation. Written music evolved, much as an alphabet for sound, as a practical way to ensure the permanence of musical repertoire. (In the 7th century, prior to the invention of notation, Isidore of Seville had remarked "unless sounds are remembered by man, they perish, for they cannot be written down".) A stable notational system had developed by the Renaissance, that became increasingly standardized as printed manuscripts became commonplace and musical literacy increased. Very rarely, scribes have been forced to encroach anew on the graphic domain, searching for visual ways to code music. Such was the case in the 1950s and 60s, when conventional notation was challenged by jazz improvisation and electronic instruments. Conversely, notation was borrowed for visual purposes when Dossi scattered notes on his anvil, to indicate the presence of sound. Other, more general similarities between art and music emerge, as analogous forms or theoretical descriptions. In "Le Institutioni Harmoniche" of 1558, Gioseffo Zarlino compared perspective lines to musical imitation, the compositional technique perfected by Josquin Desprez:

"Therefore, as the ingenious painter of perspective represents to the human eye such a variety of things and figures that it seems a true miracle, and this by means of the straight and oblique lines, the raw material of his art, which he leads together in different places...thus does the musician, who knows the nature of the materials mentioned and uses them in composing so as to represent to the ear such a number and variety of harmonies that it is marvellous to hear them; he intones one single part and draws from it (so to speak) one or more of other parts in imitation."

Illustration 8 : "BELLE, BONNE, SAGE", Baude Cordier, from the Chantilly Codex, c1400.

At the end of the 14th century, some composers arranged their music into recognizable shapes on the page. They followed an ancient literary practice, where the words of poetry or prose were written out in fanciful patterns. Baude Cordier relied on music and lyrics alone to shape a heart, and express the theme of his rondeau "Belle, Bonne, Sage". Cordier (whose very name comes from the French word for 'heart') offered the song to his lady, along with his heart. To reinforce the sentiment, the word 'heart' (in the second line) was replaced with its picture, drawn in red outline. The device is a rebus, common enough in children's books, and Leonardo da Vinci penned a page or two. He occasionally used musical notes on a stave, for their solfa syllables to be placed in words: Josquin reversed the process to construct a tune from Ercole's title.

Art from the heart

Cordier's heart is a treat, no more necessary to performance than Dossi's circle and triangle. But some notes are coloured red for technical reasons, to indicate complex changes in note values. Red might shorten each note by a third, or lengthen it by half, depending on the context. Coloration changed the rhythm of a written passage, and syncopation or triplets were common results. Timing was colour-coded, to accommodate the subtle refinements of some late 14th-century music. As musical tastes became simpler, and notation improved, the coding was abandoned. By 1502, Josquin's "Agnus Dei II" could indicate complex timings with black figures only, and Dossi's triangular version follows the imperative of its form. Not so Cordier's heart, where music takes shape from the lyrical theme. Still, the dependence of shape on content, whether that of music or words, is still intimate and rare.