"Jupiter, Mercury & Virtue", 1523-4
Dosso Dossi

It was once said that the goddesses of Virtue and Fortune had a bad quarrel. In her distress, Virtue sought the aid of Jupiter, chief of all the gods. But Mercury intervened, and told her to wait: the gods were busy, he said, making cucumbers blossom and painting the wings on butterflies. In the 1520s, Dosso Dossi set the scene to canvas, in "Jupiter, Mercury and Virtue". Gesticulating on the right, Virtue is personified as a fubsy figure bedecked in flowers. A nude man, at the centre of the canvas, enjoins her to silence. He is none other than Mercury, with caduceus in hand and wings on his helmet and heels. Moving right to left, the story culminates with a bearded man working at an easel. He may be Dosso Dossi himself, though we cannot be certain of the likeness. He has taken the guise of the god Jupiter, head of the Roman pantheon, with a stylised lightning bolt at his feet. On a canvas, he paints multicoloured wings on butterflies. They seem to come alive under his brush, and fly free of the picture surface. Jupiter's supernatural artistry is a metaphor for all creation, in the world of nature as well as art.

"Jupiter, Mercury and Virtue" serves as an allegory on the art of painting itself. Jupiter works on his painting-within-a-painting, with palette, mahlstick and brush; Dossi had used the same tools to complete the picture in its entirety. His human effort is god-like, and the painter's craft is ennobled by its unique, mythological setting. A few years earlier, Dossi had linked another creative enterprise to the gods, in his "Allegory of Music". The two pictures are often compared, though they were probably not intended as companion pieces (they have different dimensions, after all), Yet there is a certain symmetry to Dossi's treatment of painting and music, as subjects for exalted allegories, befitting the highest human endeavour. Each picture contains three figures, of legendary or ambiguous status, sufficient to convey its story in discrete stages. Their poses and gestures decrease in vigour as the stories progress: the "Allegory of Music" traces the evolution of music from left to right, while the legend of "Jupiter, Mercury and Virtue" unfolds in the opposite direction, right to left. Each tale begins or ends with a simple act that summarizes the creative impulse involved. Vigorous blows from Pythagoras's legendary hammers set the tone for music, whether raw notes dancing on an anvil or the sophisticated notation of Josquin Desprez. Painting's tale culminates in an equally potent act, at the canvas where a god quietly paints butterflies into being.

The story of Pythagoras was well known, how he inadvertently heard the melodious sounds coming from a smithy, and so unravelled the secrets of music, the universe, and everything. For two millennia, his mathematical truths were passed down in Greek, Latin and Arabic. Less popular was the legend of painting cucumbers and butterflies, and people in Dossi's day thought it originated in Roman times, from the pen of the Greek satirist Lucian. But the charming tale was apparently an invention of Leon Battista Alberti, the famed Quattrocento architect and art theorist. Occasionally, traces of the story have re-emerged, as in a 19th century manual on artists' pigments, called "Chromatography". There, the colours of newly discovered aniline dyes were rapturously described. The purple prose, at first, seems worthy of its author, George Field. He would elsewhere call on chemistry, as much as poetry, to justify an Analogical Philosophy that united colour with music. But Field had died before aniline dyes were invented, when the paint manufacturers, Winsor and Newton, reissued the book. The passage that follows is a later inclusion by their editor: in a curious parallel, he replaced Alberti's Jupiter with an industrial chemist, as creator of the butterfly-coloured world we live in today:

"Previous to the year 1856 the colouring matters derived from coal-tar were practically unknown. Until then, that black evil-smelling substance was looked upon as almost worthless; but gradually the unsightly grub emerged into a beautiful butterfly, clothed first in mauve and next in magenta. After its long winter of neglect, there sprung from coal-tar the most vivid and varied hues, like flowers from the earth at spring. At a touch of the fairy wand of science, the waste land became a garden of tropic tints, and colour succeeded colour, until the whole gamut had been gone through... Mr. W. Perkin...created a new and important branch of chemical industry - the manufacture of coal-tar colours. The violet mauve led the way, followed by the red magenta, the blue azuline, the yellow phosphine, the green emeraldine, the orange aurine, by purple, and brown, and black. Such were the hues, with many intermediate tints and shades, which one reaction brought forth. The world rubbed its eyes with astonishment; and truly it seemed almost as wonderful to produce the colours of the rainbow from a lump of coal, as to extract sunshine from cucumbers."

from "Field's Chromatography" (1835),
revised by Thomas Salter, 1869.

Dossi was just as proud of the colours he used, tilting Jupiter's palette forward so we can see them. The viscous oil paints cling to the palette's surface, where they are mixed into shades and tints, as required. A variety of reds, from dark to bright, is ranged along the front edge, with separate dollops of other colours - possibly yellow, blue, and green - in the shadow behind. Each pigment was finely ground in oil, which coated every particle in a thin film. The oil disallowed chemical reactions between pigments, when mixed, so different colours could be freely blended. The method was imported from the Netherlands, early in the Renaissance, and eliminated much of the need for every colour to be separately prepared and applied. Unlike traditional egg tempera, oils were slow to dry, and a painter could return to his palette the next day and expect to find the colours fresh. The painting, too, would remain wet for some time, permitting further manipulation. Colours could be mixed directly on its surface, using scumbling, glazing, and impasto techniques. The canvas ground itself (yet another innovation) allowed for quick and subtle touches, as the brush interacted with the tooth of the cloth.

Frescoes on plaster demanded a stricter technique, which lent itself to flat and decorative effects. Elaborate examples lined the walls of Palazzo Schifanoia, the summer palace of the dukes of Ferrara, with intricate allegories representing the months and signs of the zodiac. But Dossi had more recent examples before him. Spectacular oil paintings, by Giovanni Bellini and Titian, were housed in the Alabaster Chamber of the castle at Ferrara. Duke Alfonso commissioned Dossi to add to their number, and the artist learned much from the Venetian masters. Their seamless blend of colour, with light and shade, rendered the natural world convincingly, and made a myth seem plausible. Dossi aimed for a similar effect, with "Jupiter, Mercury and Virtue", and surrounded the Olympian gods with woodland, overlooked by an Italian hill-town. Perhaps he had fallen under the spell of another Venetian, of Giorgione, with his subtle allegories and wildly poetic landscapes. While some artists excelled in geometric perspective, others in idealized human anatomy, Dossi would earn a reputation as a foremost landscape painter of his day. In this enterprise, there were no canons of proportions to guide him, no recently unearthed antique statues to study, only the model of Nature herself.

In his own way, Dossi had tackled the challenge, voiced by Pauwels Franck, of how to represent motion in time and space. He would combine events into a single tableau, even where they were described sequentially in the original fable. By a subtle patchwork of small actions, Dossi suggested a larger story. In "Jupiter, Mercury and Virtue", for example, the three main protagonists act simultaneously. The triple combination is mirrored at Jupiter's canvas, where three butterflies share in the process of creation. The insect under Jupiter's brush nears completion; the one to the right seems to rest on the picture's surface, whilst the uppermost butterfly is the most lively and three-dimensional. Life emerges in successive phases that are intimately linked, like frames from a film or a cartoon. In his "Allegory of Music", Dossi had used similar techniques to subdivide his theme. The history of music, from primal sound to the High Renaissance, was telescoped into a single scenario. A blow of hammer to anvil (the musical equivalent to Jupiter's painting) set creativity in train. The action is merely implied, though its after-effect is visible as a resonance of tiny notes from the anvil. The cause was evidently a rebounding hammer in Tubalcain's hand, poised to strike again. Musical sounds coalesced into a circle or triangle, as notated staves prescribing the formal progressions in time and pitch. Of course, nothing really changes in the static painting. If the music were heard, we might sense a kind of movement in the flow of melody through time. The Aristotelian "Problemata", printed for the first time in 1498, had puzzled over our response to music:

"Why is sound the only sensation which excites the feelings? Even melody without words has feeling. But this is not the case for colour, or smell, or taste. Is it because they have none of the motion which sound excites in us?...Now these motions stimulate action, and this action is the sign of feeling."

In the treatment of Parkinson's disease today, therapists find patients can control their tremors more easily, when their movements are accompanied by music. Music helps Alzheimer sufferers, too; many are able to faithfully recall lyrics and melodies of songs, though they may have little recollection of other aspects of their lives. The ancient Greeks also considered music to effect the character and the soul, and they were aware of its mimetic qualities - as it moved, so it moved the listener. A battle hymn would inspire the tramping feet of an army, and a chant could invoke the presence of a god during religious rites. Wonderful powers were attributed to legendary performers, who could shift stones, charm animals, settle disputes, and cure illness with their music. Unique styles of music emerged from different Greek colonies, and the proportions of the Dorian mode found favour with Plato. He considered it necessary for a sound education, in harmony with a well-regulated state, and central to the structure of the cosmos. Music affected us in two ways, according to the "Problemata", by it rhythm, and by alteration in pitch. Since music was first used to accompany poetry, its rhythms were coordinated to the meter of verse. Theorists measured pitch distances between notes as mathematical ratios, with the aid of a one-stringed monochord. The actions in music, of both rhythm and pitch, followed the sequence of changes in a melody.
Notes sounded together did not count, as it was held that no movement occurred between them. The reverse was true for the other senses, implying that two colours, for instance, would create some kind of action when seen side by side. Aristotle had touched on the profound effect of juxtaposed colours, how purple wool in embroidery or weaving appeared differently against white or black thread. He also suggested the different colours might be ordered like notes, according to musical ratios. But the combination of musical tones, stacked together in a vertical chord, was a much later development. Harmony, as a relationship between simultaneous notes, was to become a chief beauty of Renaissance music. By the 19th century, Hermann von Helmholtz was able to supply a scientific rationale for harmony, and give a contemporary slant to issues raised by the "Problemata". In his seminal tome of 1863, "On the Sensation of Tone as a Physiological Basis for a Theory of Music", Helmholtz concluded music was more pliant than other art forms. Many kinds of movement - "graceful rapidity, grave procession, quiet advance, wild leaping" - could be expressed in notes. For Helmholtz, music was not bound by slavish imitation of nature; it evoked mental states, similar to those involved with movement of the voice and the body, and with thinking and feeling.

Helmholtz compared music to colour, in "A Handbook of Physiological Optics", of 1866. After a careful analysis of parallel wavelengths, of both sound and light, he found little reason to equate them. Instead, he searched the broader culture, for analogies to support his findings in the laboratory. The best paintings, according to Helmholtz, were indebted to the fundamental colours of vision. He detected the Young-Helmholtz primaries, of red, green, and blue-indigo, in masterpieces of Venetian painting. The artists had hit upon a truth of physics and physiology, in their quest for aesthetic equilibrium and colour harmony. They replicated colours of light as best they could, in pigments of paint. When combined two at a time, the primaries of light would produce secondary colours of greenish blue, purple, and yellow. We know them today as cyan, magenta, and yellow (or CMYK when black is included), and they form the basis of colour printing. These are complementaries to the primaries of light, and Helmholtz located their wavelengths with precision. He duly discovered evidence for artistic use of the secondaries, in paintings by Paolo Veronese. But recent cleaning of Veronese's "Wedding at Cana", of 1563, revealed that purple is no more present than red. Nor should Titian or Giovanni Bellini be accused of having neglecting yellow, in favour of a blue-green. The imitation of nature, rather than adherence to a theory, seemed to guide them among the many tints and shades.

Illustration 3 : "THE WEDDING FEAST AT CANA" (detail),
Paolo Veronese, 1562-3.

The ostensible subject of Veronese's vast masterpiece is the occasion of Christ's first miracle. He may have turned water into wine, but the painting is dominated, front and centre, by a group of musicians. Tradition holds that the figure in white, bowing a viola da gamba, is Veronese himself. Behind him, fellow painters Tintoretto and Jacopo Bassano play on viola and flute. Opposite, the man in red is Titian, underpinning their melody with his double-bass. If music be a metaphor, then Titian is the founder of the Venetian school of painting, Veronese its lead practitioner (with Tintoretto as a close rival), while Bassano is the rustic of the group. There are 130 other people at the feast, but none seems to speak; the picture was hung in the dining-room of a Benedictine monastery, where silence was strictly observed.

It seems a little outmoded, now, to take any Venetian master as a final authority on colour. At the time Helmholtz wrote, however, Veronese was considered the greatest coloriste by Thomas Couture, a prominent French history painter and teacher. Charles Blanc, standard-bearer for the Beaux Arts aesthetic, agreed that the colours of Veronese enchant the eye; only Eugene Delacroix could give colour more poetic and moral force, to "tune his lyre (as it were) to the tone of his thoughts". Helmholtz, despite all the harmonies he saw, could find no connection to harmonies he heard. He specifically denied any physical link between the three colour primaries, and the triad of notes in a chord. In the end, he settled for an analogy of music, not with colour, but with movement in three dimensions. A musical phrase could be translated in pitch, and remain recognizable, much the way a body could be moved from place to place. Like different bodies navigating the one space, various musical voices could coexist, as long as they obeyed rules to avoid the collisions of discord. Music represented a motive force, the power behind action, while painting could only show the result of the action, or the circumstances in which it occurred.

To form the canon by Bartolomé Ramos, four voices take up the same tune independently. Their entries are staggered, so singers will be at different points in the song at any one moment. The four vocal strands will braid together, in four-part harmony, before the first singer reaches the end. In the centre of the diagram, we are told something of the modes employed, and the sweet harmonies to expect from a proper performance. For that purpose, Ramos modified Pythagorean music, stating that, "although it is useful and pleasing to theorists, it is laborious and difficult for singers". In "Musica Practica" of 1482, he had tempered some major and minor thirds by ratios of 5 : 4 and 6 : 5, much to the ire of traditionalists. Ramos probably learnt the method from Arab theorists, in his native Andalusia, and it lent subtlety to his melodies and part-singing. The same ratios were rediscovered, in an antique Greek work by Ptolemy, and eventually incorporated into Western speculative music. Gioseffo Zarlino legitimised the new practice in "Le Institutioni Harmoniche", of 1558, where the numbers formed a basis for the tuning system known as just intonation.
A single stave, containing notation for the canon, was bent into a circle, echoing the shape of the earth and the heavenly spheres circling above. Ramos had embellished music with cosmic analogies in "Musica Practica", relating its strings and modes to the planets. According to an inscription below the notes of this canon, he showed the universe and music together in harmony. As the heavens turn, so the music flows. It begins at the top, where the East Wind sets the music in motion with a blast from his conch. Progressing clockwise, the melody gains impetus at each successive compass point, where the Four Winds blow. Their breaths are those of the singers, and indicate where each vocalist should enter the song. Before the melody comes full circle, four voices will be sounding together. Each singer may begin the melody again, after completing one turn, just as the sun will rise each day after circling the earth. For the work attributed to Ramos, here, as well as the score at the centre of Dossi's "Allegory of Music", circular notation stressed the analogy between canon and cosmos.

At the time Dossi was working on his allegories of music and painting, the Flemish composer Adrian Willaert was resident at the court in Ferarra. Willaert was expert in writing canons (though the amateurish circular version that Dossi painted was not up to his standard, apparently). He was also adept at handling the new style of music Ramos introduced, and proved it with a setting for a verse by Horace: it began (in Latin), "What cannot be accomplished through drinking?" Four voices set off in the standard Pythagorean style, and each part included a B flat. Gradually, extra flats were introduced, one at a time, but only in the tenor part. Half way through the piece, the tenor had six flats, so the intervals with all the other singers had changed. The effect was not quite like a modern modulation, between successive keys, but more like a shift in the soundscape: the stern relationships of Pythagoras had given way to the mellow harmonies of just intonation. By tiny movements, of distances adjusted between notes in each chord, a cumulative change swept through the piece. Willaert would move on in 1527, to found a famous school of music at St Mark's in Venice. Zarlino became one of his most avid pupils, and called his master "the new Pythagoras who corrected numerous errors".

Traditional ideas persisted, while techniques changed. Pythagoreans still maintained that planets made their own music as they orbited the earth, and musicians shaped canons into circles, to draw a metaphor down from heaven. Theirs were grand ideas, that connected qualities of music with the movements of the stars, somehow. There were two kinds of simple motion in the cosmos, wrote Aristotle in "On the Heavens" - motion in a straight line, and circular motion. The former was proper to the four elements, with earth and water sinking downwards, and air and fire rising vertically, to form a layered envelope round the earth. But what of circular motion? and for what simple body would rotation be natural? Aristotle decided there must be a fifth element, the aether, different and separate from all the bodies about us on this earth. It lay beyond the moon, the stuff of the heavens, and moved eternally in a perfect circle. It never altered or increased, it was neither heavy nor light, and could not be created or destroyed. There was something divine about the aether, since the stars had never been known to alter their course.

It was commonly believed the earth sat still, at the centre of the universe, while the planets and stars circled around it. The sun itself took a place among the planets, in deference to the earth. Many schematic diagrams survive from the medieval period, showing the accepted arrangement. In this example, the world is wrapped in the four elements - earth, water, air, fire - shown as rings of white, green, yellow, and red. Beyond them, the planets (from the moon to Saturn) occupy seven zones of pale blue. A darker blue strip contains the fixed stars, all those that maintain their relative positions while the night sky rotates. Next, within red-brown borders, seven titular gods personify the planets, and twelve signs represent the zodiac. The major constellations follow, then a dark blue band showing phases of the moon. The remainder of the disk has subdivisions, both astronomical and astrological, with 360 degrees of the circle marked on the outer rim. Back on earth, an astronomer appears, mapping the sky in degrees with his astrolabe. His job was to fix each star, even as it changed position.
Cyclic changes evolved from the movements of heavenly bodies, and the Four Seasons preside over the flow of time, from the corners of the page. (I presume spring and summer are the figures at the top, clad in green and red respectively, with autumn and winter in blue and pale robes below.) Other manuscripts might surmount the cosmographical scheme with angels and saints, some would supply four giants to support the universe on their shoulders. The Four Winds surrounding the canon of Ramos (Illustration 3, above) serve much the same purpose, to represent his music as a microcosmic version of the heavens. The winds blew the sky and planets around the earth, according to Hildegard of Bingen, a 12th century visionary. Wind was a symbol of the soul for Hildegard, and the sweetest wind was the voice of the Lamb of God. It resonated in bejewelled pipes, set in the crowns of virgins. Christ was the perfect song, a balance of music and lyrics, of divinity and humanity. Hildegard wrote the heavenly music down, as best she could, and even gave a speaking part to Satan (that cause of discord), to heckle the celestial choir.

The wind plays a pivotal role in Dossi's "Allegory of Music". It blows from the mouth of a babe, and similar children blast air on the canon of Ramos, above. The wind is both inspiration and cause of the music. It billows the red cloak of Dossi's blacksmith high in the air, adding drama and an impression of movement to the otherwise dark and silent space. In "Jupiter, Mercury, and Virtue" the situation is somewhat reversed. In the landscape beyond there blows a gale, which bends the trees and ruffles the robes of Mercury and Virtue. But painting is protected from the elements: the air round Jupiter is stilled, as if Mercury not only silenced Virtue but has quietened the very atmosphere itself. Only the wings of butterflies stir the air, as they flutter from the canvas. One is reminded of a modern metaphor, used to explain chaos theory, how the flap of a butterfly's wing in Brazil causes a tornado on the other side of the world. Perhaps Jupiter has unleashed havoc into the wider world, by creating life. Such a dark idea was not far from the Renaissance imagination. Many witches were burnt, for consorting with the Prince of the Powers of Air. As Satan's devotees, they flew through the sky in the company of goats and demons. Only the sound of consecrated church bells could bring them tumbling to the ground. After centuries of torture, witches became caricatured crones on broomsticks, and their escapades have turned into a jolly game of quidditch, with Harry Potter at Hogwarts.

Humans have always coveted the power of flight: around 400 BC, Aristophanes wrote a satirical play on the subject, of a clever Athenian who usurped the kingdom of the birds. Pisthetaerus, the hero of "The Birds", bribed others to join him in Cloud-Cuckooland, by handing out free wings at the gate. (He gained ascendancy over the gods, who could already fly, with promises of a home-cooked meal.) Winging through the air was the best way to get around, and it is no accident that Franck would draw wings on a globe, to represent Nature's supreme mastery of movement (Illustration 2). A fascination with aerial transport has continued well into the era of powered flight, and a skirr of wings accompanied the "Creation of the Birds", painted by Remedios Varo in 1957. The subject of her picture was uncannily similar to that of Dossi's "Jupiter, Mercury and Virtue". Life-giving primary colours emerged from an alchemical furnace, onto the palette of an owl-like artist. Under the combined influences of starlight and music, live birds flew off the painted page. Birds or butterflies, Varo and Dossi told the essentially the same tale; though separated by more than four centuries, their imaginations took a similar flight path. The Mexican magic realist, and the court painter of Ferrara, both fantasized about an artist's ability to create life itself.

UROBOROS is the name given a snake, or dragon, grasping its tail in its mouth. As used by the 3rd century alchemist, Zosimus, it becomes the reconciliation of opposites, an endless path, and the symbol of infinity.

Flight was not the only inspiring mode of travel in Dossi's day; in 1522, the remnants of Ferdinand Magellan's fleet limped back into Seville harbour, having circled the globe for the first time. Even as they had first sailed west, following the sun, Nicolaus Copernicus was already tracking another great journey - that of the earth itself. He would eventually fix the sun at the centre of the cosmos, in "De revolutionibus orbium caelestium" of 1543. The planetary orbits were rearranged around it, in circles, since "this form is the most perfect one", and "all objects strive to be bounded in this way". In the bowels of the earth, other cyclic changes were transforming the elements. Metals were gestated there in a sequence (according to a manuscript attributed to Albertus Magnus), with "each one of them easily going from one to the next like in a circle". Alchemists could replicate the natural process in their laboratories; gold might readily be fabricated from silver, since they lay side by side on the circle. The process was best synchronized to movements of the stars, and every stage marked by a colour change inside the alchemist's flask. The circle found its place in music, too, within a notation system for "Ars Nova", devised by Philippe de Vitry in 1322. At the beginning of the stave, a full circle indicated perfect (triple) time, while imperfect (duple) time was represented by a semicircle. (The latter is still used, as the symbol C, for a duple time signature of either 4/4 or 2/4.) When the whole stave was bent into a circle, as for the canon of Ramos, above, it allowed the melody to repeat. A remark made by Copernicus, of the solar system and its endless cycles of days and seasons, equally applied to the canon - "It is the circle alone that can bring back again that which has already taken place".

Illustration 6 : THE PERFECT CIRCLE.

(left) THE WHEEL OF FIDELITY,
woodcut from "The Triumph of Fortune",
by Sigismondo Fanti, 1527
(designs attributed to Dosso Dossi).

Sigismondo Fanti of Ferrara wrote "Triompho di fortuna", an early book on fortune telling. Dossi, it is believed, supplied some original designs for woodcut illustrations. On the left of Plate 34 (below), the author is represented as astronomer and mathematician, measuring a globe. Dosso Dossi is shown to the right, displaying his wares. His likeness is possibly based on a self-portrait, and the facial features are not unlike to those of Jupiter, in "Jupiter, Mercury and Virtue". (Each wears a shovel-shaped beard, but so did Duke Alfonso.) They frame two central disks, which are divided into more or less equal segments. Dice patterns, Roman numerals, and Arabic numbers run clockwise round the disks, in ascending (if irregular) order. Elsewhere in Fanti's book, other distinguished persons flank similar disks. Several musicians from Ferrara are among them, and conventional heads of the Winds occupy the bottom corners in some woodcuts. Here they blow on the lower disk, to circulate the numbers, and spin the wheel of fortune as they might turn the music of a canon.

Gioseffo Zarlino adapted the segmented disk (right), to tabulate musical ratios that Ramos de Pareja had introduced to the West. He knew another musical circle, from Ptolemy's "Harmonics" of the 2nd century AD, where notes were distributed around the zodiac. On Zarlino's disk, numbers run counter-clockwise round the edge and increase unevenly in size. Successive numbers create ratios with one another, to form the musical intervals named in each intervening segment. Starting at the top left, the numbers 1 and 2 form the diapason, or octave, with a ratio of 2:1. The sequence ends at the top right, with two semiditono, between 25, 30, and 36. They are minor thirds, a semitone less than two tones, and both their ratios can be reduced to 6:5. All the numbers (and ratios) have factors of prime numbers, up to 5, and Zarlino introduced the minor tone of 10:9, alongside the Pythagorean major tone of 9:8. The old semitone of 256:243 was replaced with one of 16:15, plus the minor semitone of 25:24.

In the 19th century, Helmholtz praised the system of just intonation, and credited Zarlino with re-introducing the correct, natural scale. "Le Institutioni Harmoniche" had presented the new music, with the help of diagrams. Most were in the old style - notes placed in a square grid, or a scale laid out in a strait line with semicircular loops connecting its notes. The latter kind of illustration came from antique manuscripts of Boethius, and was still standard practice among 16th century theorists. Zarlino's circular disk was most unusual, and, like Fanti's wheels of fortune, it was idealized. Its regular symmetry belied the fact that a couple of numbers were missing, most intervals were repeated, and the evenly-spaced segments could not indicate the relative sizes of ratios described. To the left, I have adjusted Zarlino's proportions, according to interval sizes in cents, and roughly located them along a modern C scale. A more rigorous version of the musical disk, applied to one continuous octave, would come from René Descartes in 1618, to be published in 1650. The first colour disk was printed around 1630, for Robert Fludd, but it too was idealized. Like Zarlino, Fludd divided the circle evenly, and he gave equal segments to each of seven colours. A more precise colour disk appeared in Isaac Newton's "Opticks", of 1704, where colours were sized proportionately. Descartes' musical diagram served as a prototype, and Newton retained spacings according to musical ratios, labelling divisions between colours by the names of notes.

Additional musical tunings arose for practical reasons, and Francinus Gaffurius would note, in 1496, how organists tampered with the perfect fifth interval. So that their instruments would be tuneful in several different modes, they raised or lowered the pitches of selected notes by tiny amounts. The result was a meantone temperament, a procedure outlined by Pietro Aron, in "Thoscanello de la musica" of 1523. Aron also described music, for the first time, as a progression of vertical harmonies, of chords rather than of linear melodies. As musical performance evolved, theorists developed the mathematical techniques to accommodate the changes. The art of painting had undergone a similar transformation in 1436, when Alberti gave the first account of linear perspective in "De pictura". The aim of the artist, he wrote, was to convincingly represent space in three dimensions, "but first of all I desire that he know geometry". He detailed the perspective method, of vanishing point and picture plane, that he had acquired from the Florentine architect, Filippo Brunelleschi. Alberti then directed painters to their ultimate aim - to tell the stories of the classical gods. Dosso Dossi was to oblige, almost a century later, by relating Alberti's own fable in "Jupiter, Mercury and Virtue".

Colouring was considered a third part of painting (along with outlines and composition), but it resisted any mathematical approach. Alberti acknowledged the philosophers, who commonly isolated seven colours in a sequence from black to white, and pondered the qualities that caused them. But, speaking "as a painter", he reduced the true colours to four, the number of the elements. Red was for fire, blue of the air, green for water, and earth was ashen grey. While the colours might describe the elements as they appear in nature, they were inadequate for artists. Leonardo da Vinci modified them by substituting yellow for the grey of earth: rightly, he hesitated to include green since it could be mixed from blue and yellow, though he suspected blue might be a kind of mix as well. In Dossi's "Jupiter, Mercury and Virtue", the palette seems to hold similar colours - as best I can tell from reproductions. They had appeared at least once before, coincidently, to symbolize the elements in 3rd century writings by Theon of Smyrna. Otherwise, elemental colours varied considerably, the red-yellow-green-white array in the Catalan atlas (Illustration 4, above) being but one example.

Mario Equicola was a renowned scholar, who wrote the programme for paintings by Titian, Bellini, and Dossi, which lined the Alabaster Chamber in Ferrara. In 1525, he observed "the meanings of colours are somewhat different among the Italians, the Spanish, and the French". Confusion increased with "The Meaning of Colours", by the poet Fulvio Morato, who ascribed divine and magical attributes to fourteen different hues. Published in 1535, when Fulvio was temporarily exiled from Ferrara, the small volume was popular and influential. But it was no guide to studio practice: one must go back a hundred years and more, to Cennino Cennini's "Craftsman's Handbook", to find a manual useful to painters. Then, colours were pigments of paint, defined by their manufacture and method of application. Like Alberti, Cennini made a bow to the tradition of seven colours, but his were all 'natural'. Four of them were found as minerals - black, red, yellow and green - while the other three needed some artificial processing - lime white, blues, and a yellow. Time and again, we are told a pigment was made by alchemy. If you want the recipe, go ask the friars; otherwise, save yourself the trouble and buy them ready-made from the apothecary.

Theophilus Presbyter had written down the pigment recipes of friars, early in the 12th century. His instructions, in "On Divers Arts", are so clear we might follow them today. By grinding up the naturally occurring crystals of cinnabar, the rich red of vermilion was made. Alternatively - but do not try this at home - mercury and sulphur could be heated in a sealed retort, to form the crystal artificially. This was alchemy at its best: a natural substance could be made and unmade, by man in a laboratory. Leonardo da Vinci praised the alchemists, "whose function cannot be exercised by nature herself", and cited glass making as among their skills. Nevertheless, he despised "alchemists, the would-be creators of gold and silver", and thought most were charlatans (despite claims to the contrary in the modern pot-boiler, "The Da Vinci Code"). Alchemy had a spiritual dimension as well, and texts full of arcane symbolism were printed in the Renaissance. They promised transcendence, enlightenment, even immortality, if certain procedures were followed. Alchemy was presided over by Hermes Trismegistus, the god Mercury, and its eventual goal was production of the Philosopher's Stone, typified in the Red King. They correspond uncannily to the characters at the very centre of "Jupiter, Mercury and Virtue".

The mysterious, occult forces of alchemy seemed natural to the Renaissance, as real as the astrological effect of the stars. An erudite audience could discover alchemical signs, if they chose, in Dossi's allegory. The figure on the right might be taken as Sulphur, her fiery spirit counterbalanced by Mercury. Together, they commonly made cinnabar; but in exalted and philosophical forms, Mercury and Sulphur were the basis for all matter. Alchemy uncovered their secret workings in nature and led, ultimately, to the Red King. At his slightest touch, power over life unfolded, as effortlessly as Jupiter conjured butterflies from a canvas. The Great Work of alchemy was an esoteric calling, practised secretively by an elite. Dossi's practitioners (if indeed they be so) are suitably aloof, atop a rise in the ground. They seem enclosed in a bubble of air, bordered on the left by the arc of a rainbow. It falls from the sky behind Jupiter's canvas, as if it were the source of the living colours that he uses. The bow itself is strangely drained of its colours, a supernatural apparition in an otherwise natural landscape. It defines a sacred precinct, according to ancient convention. In Mesopotamian texts, the domes and doorways of temples and palaces were likened to the bow of heaven. Romans continued to house the gods under a rainbow (see below): methods for painting it were standardized, and later described by Theophilus in his medieval manual of the arts. Dossi bypassed the tradition, overlooking nature's finest display to focus instead on the colours of an artist's palette.