A Shade of a Color Mixes a Color With Reconstructive Arts

7

Colour By NUMBERS

The Harmonious Palette in Early Modern Painting

EILEEN REEVES

H IDDEN AMID THE STANDARD TALES of rollicking adulterers and vigorous cheats of Celio Malaspina's 2 Hundred Novellas , published in 1609, is the story of a boorish Venetian pigment grinder and his tireless tormentors, a petty dealer in brass and a die cutter connected with the mint. There is neither philandering nor fleecing here: the pigment grinder has nothing but a modest shop of "different sorts of colors, chalks and minerals," an crumbling mother, an excess of superstition, and a clear deficit of common sense. Much of this story has to practise with the pigment grinder's efforts to avoid the die cutter, as he is convinced that the latter, a gifted sketch artist, is not but interested in collecting an unpaid debt, simply has too been ordered to depict the twelve most insane men in the city. The contumely dealer counsels the pigment grinder that in the interest of fugitive such portraiture, he should have himself shaved and even mutilated by the local barber, with the upshot that the dupe is initially unrecognizable even to his own female parent. Startled, finally, by the dice cutter'south unexpected appearance in his shop and panicked by the emergent cartoon, the pigment grinder plasters his whole caput with printer'south ink, grimaces to disguise himself further, and bellows, "At present merely try to sketch me!" (Malaspina 1609, 1:143–45v). 1

At stake in this story, conspicuously, is the social and professional identity of the paint grinder, a figure so misguided in his affections that he asks his antagonist the brass merchant to be "similar a male parent" to him, so abject in his quotidian activities, and so prone to "rushing barefoot in the rain from home to the shop, filthy, his hands, face up, and smock smeared with colors," that he might easily be taken as a madman. The nigh disconcerting episode of the entire story—the contumely merchant's proffer that the barber "engrave" the paint grinder as he likes—is the prelude to the first of several disfigurements (Malaspina 1609, 2:144r–v). That the die cutter is a man whose business is to make money and whose special talent is the ability to sketch bright portraits in chiaroscuro further suggests an asymmetrical segmentation of artistic labor, skilled disegno and crafty design being the province of the coiner, and color, for what little information technology is worth, the business concern of the impoverished pigment grinder. Given Malaspina's friendship with the prominent sculptor Leone Leoni, this aspect of the story might also exist read as a narrative variant on the more ritualized contestations of the artful merits of canvass painting and the low relief carving characteristic of coins and medals; rather than being judged by polished end products and presented by eloquent defenders, each art is reduced to the materials needed for its initial stages, and defined by the inarticulate remarks and comic gestures in which the protagonists specialize (on Malaspina, run into Ghirlanda 1960). And competing notions of naturalness are clearly a focus here as well, for while the primitive lifestyle, earthy products, and gullibility of the pigment grinder make him the embodiment of a naturale or simpleton, the crafty die cutter is renowned for his ritratti naturali or "life-like portraits" of the declared madmen of Venice.

Merely it is the opening incident in this serial of ruses that is most revelatory, equally it captures something of my business organization in this chapter, the vexed relationship of color and number in the early modern period, surely amid the nearly problematic efforts to mathematize nature. Having encouraged the pigment grinder to close up shop and to hide at abode in order to avoid the prowling coiner, the brass merchant decides to complicate his victim'southward life by altering the chalked numbers on the various wooden shutters covering the windows of the bottega . Perplexed and then maddened past the mismatch between shutter and window, the pigment grinder proves incapable of fitting the appropriate cover to each aperture, and he struggles with the task from the moment nearby church bells ring x o'clock at night until they sound the Angelus at dawn (Malaspina 1609, one:143v–144). Evidently unable to distinguish the openings on the basis of size, position, and shape, he relies on the arbitrary index provided by numbers.

It is not that the ruse provides the occasion for theft—in that location is footling enough in the paint grinder's store, and nothing that interests the amused onlookers—but rather that the episode itself exposes a crucial business of early modern natural philosophers and artists, the shifting and ofttimes unintuitive means in which numbers were continued with colors. In the spectacle of the pigment grinder'southward rage, the numbers with which he has structured his surround announced meaningless and arbitrary to all observers, and, whatsoever their original logic, are of unrecoverable significance to the victim himself. The numbers, in short, are talismanic, and useful only insofar as they serve to lucifer what are for the pigment grinder otherwise unrecognizable architectural elements. They embody the twin tendencies of a human defined by both credulity and superstition.

Malaspina'due south anecdote can be read, as I will argue here, as a vernacular response to the celebrated classical story through which number came to be linked commencement to audio and subsequently to color. Like Malaspina's novella, this tale, otherwise radically different in tenor and in import, emerges in the workplace. In the version told by Boethius in late Artifact in his Fundamentals of Music (1989) and repeated past endless followers, the study of harmony emerged when the aboriginal philosopher Pythagoras was inspired by the single consonance emitted past five hammers pounding molten metal in a forge. Later initial investigations of the thing, Pythagoras judged one of those implements inharmonious and set it aside; weighing the other four, he constitute that they differed in a ratio of 12:9:8:half-dozen. The various relationships between any pair of these weights, he noted, could thus be transcribed by the beginning iv natural numbers.

Such intervals, Pythagoras further argued, could also be translated to those betwixt tones on a monochord. When a string is divided in half and plucked, the diapason that sounds is ane octave higher in pitch than that emitted past the open up string. The diapente, produced when 2 of three equally divided sections are played, is one-5th higher than the open string; the diatessaron, emerging when three of four sections of the cord are struck, is 1-fourth higher. In the Pythagorean view, 9:8 or the interval betwixt the quaternary and the fifth, a whole tone, was itself anomalous, though the basis of harmony.

These aforementioned relations, Pythagoras added, held true for weights suspended on cords. Thus the divergence between a string begetting twelve pounds and ane bearing vi pounds would be an octave or diapason; between twelve and eight pounds a fifth or diapente; between eight and half-dozen pounds a fourth or diatessaron. The experimentation extended, later writers added, to containers filled with 12, 9, 8, and half dozen units of water, to pipes of 12, 9, 8, and half dozen units of length, and to bells of 12, 9, 8, and 6 units of volume, and the same consonances ever emerged (Boethius 1989). 2

These proportions—2:i, 3:2, four:three, and 9:8—are those that matter in this chapter: they were associated, though in somewhat unstable mode, with the range of hues running from white to blackness, especially in early on formulations of colour theory. 3 Once removed from their original musical context, they functioned as terms designating proportions of low-cal to nighttime, or white to black; entirely remote from painterly practice, they underwent further modifications when fitted to spatial presentations of the spectrum. Until the emergence of the clear stardom between main and secondary colors, and the simple combinations they offered, the proportions Pythagoras discovered in the forge formed the footing for many philosophical accounts of color.

"MORE COLORS THAN But BLACK AND WHITE"

Color is clearly a disastrous business for the paint grinder of Ii Hundred Novellas , whose workplace, literally structured by meaningless numbers, yields him very fiddling in the way of turn a profit. Apart from the conventional Venetian carta azzurra on which the die caster sketches his incriminating chiaroscuro portraits, other than the deep black of the printer's ink with which the pigment grinder covers himself, and the disappearing whites of his eyes as he takes on this disguise, no hues are mentioned in the story (Malaspina 1609, 1:144, 145). There is the strong suggestion, moreover, in the equivalence of "filth" with the various colors smeared on his hands, face, and smock, of an impoverished, grimy, and monochromatic globe. This environment is the parodic legacy of the early modern efforts to connect color with the Pythagorean ratios.

To summarize the problem with which natural philosophers of the sixteenth and seventeenth centuries were confronted, in On Sense and Sensible Objects Aristotle had sought to explain the origin of the "intermediate" or mixed colors yellow, cherry-red, purple, green, and blue by arguing that they arose through diverse admixtures of white and black, or of light and darkness. four This notion, well-nigh wholly incomprehensible to modern readers, would detect its virtually persuasive case in the reddish glow of nighttime clouds struck by sunlight, and allusions to this issue occur regularly in sixteenth-century discussions of color. Aristotle had further argued that merely "exactly numerical" ratios of white and black would yield attractive hues. While he preferred the hypothesis that all combinations involved an intermingling of white and black then thorough as to transform those hues, he acknowledged that other thinkers had imagined either a mixing of fine but essentially unaltered blackness and white particles, or a layering of the two substances. Significantly, these less probable alternatives were distinguished by their kinship with painting, while that favored past Aristotle could but be explained by analogy with musical ratios. 5

It is thus possible to believe that there are more colors than only white and blackness, and that their number is due to the proportion of their components; for these may be grouped in the ratio of three to two, or 3 to four, or in other numerical ratios, or they may exist in no expressible ratio, merely in an incommensurable relation of excess and defect, then that these colors are determined like musical intervals. For on this view the colors that depend on uncomplicated ratios, like the concords in music, are regarded as the most attractive, due east.g., purple and red and a few others like them—few for the same reason that the concords are few—while the other colors are those that have no numerical ratios. (Aristotle 1957, 233)

The Bolognese medico and philosopher Mainetto Mainetti offered one of the most influential commentaries on this Aristotelian text in 1555, tacitly discarding Aristotle's own lodge—white, yellow, red, violet, green, blue, blackness—then as to privilege the Pythagorean ratios. He began with the ascertainment that in the Aristotelian Problemata the color greenish was singled out for its restorative qualities, precisely because it was between the extreme points of white and black, the excesses of which disturbed the viewer'due south optics. "Two colors are between white and green," Mainetti wrote in accounting for dark-green's attractive nature, "yellow is beyond white and blueish before light-green. They arise in rational proportions, equally if a diapason and a diapente. Yellow is indeed in diapason, that is, ii to ane, since 2 units of calorie-free or effulgence and one of bawdy darkness generate yellow. Blue is rather in diapente, which is two to three, since blue is born of three units of effulgence, and ii of opacity" (Mainetti 1555, fourscore). Mainetti added that matters were similar for majestic and scarlet, already identified by Aristotle in On Sense and Sensible Objects as especially pleasing to viewers. As an intermediate hue between greenish and black, red could exist compared to the diapason, because it was composed of two units of opacity and 1 of brightness; regal, having 3 parts opacity to two of light, was like the diapente.

Returning to the argument afterward in his commentary, Mainetti further compared yellowish to the diapason and brown to the diapente. Here, however, the crucial ratios involved white and blackness, rather than light and nighttime: yellow contained two measures of white to 1 of black; brownish, three of black to ii of white (152). In both accounts, though, the diapason and diapente were associated with specific ratios; the diatessaron, judged comparatively pleasing, had no place in this organisation.

Mainetti's formulation appears to take been adopted in a somewhat condensed version by the Florentine physician Guido Guidi, who likewise identified dark-green as equally equanimous of clarity and opacity, blueish as embodying the ratio 3:two, red equally two:1, and royal as 2:3. Avoiding the terms "diapente" and "diapason," Guidi (1626) merely noted that "where certain proportions are maintained in admixtures, the colors volition be pleasing, as in the harmony of voices, but where such ratios are non preserved, they will be unappealing" (162). Likely written in the 1560s but unpublished for decades, this sort of word would prove durable. Its most striking feature is its distance from artistic practice: though he was the maternal grandson of Domenico Ghirlandaio, and associated with the Mannerist painter Francesco de' Rossi ("il Salviati"), in this instance Guidi deferred to the traditional and exclusively theoretical caption of color. six

Others who followed Mainetti'southward atomic number 82 sometimes sought to mute his overt reliance on musical intervals, and chose just to refer to the mathematical ratios of the Pythagorean traditions. Thus, for example, in a give-and-take of 1581, the Fribourg humanist Sébastien Werro presented black and white equally the sole elementary colors, and ruddy, rather than Mainetti's greenish, as the production of equal proportions of these two hues. Pinkish had a 3:two ratio of white to black; blue, conversely, a 3:2 ratio of black to white. Saffron had a 2:i ratio of white to black, while blood-red had the same ratio of blackness to white. The ratio of black to white in greenish was 5:4—effectively, the ditone or major third—only Werro did not draw on terms borrowed from the discourse of harmony. Yellow and brownish, finally, involved ratios of two:1, white to crimson and red to white, respectively, which meant that their proportions of white to black were 6:5 and v:6, that of the semi-ditone or minor third. This musical interval besides went unnamed in Werro'due south account (1581, 124–26).

AS PAINTERS DO

Such discussions, whatever proportions they involved, differed entirely from the actual practices of early modern painters. While artists relied on a variety of substances to obtain green and purple pigments, techniques for blending a saffron-based lake and azurite, or mashed iris petals and Naples yellow, or orpiment and indigo, or saffron and indigo, or for layering a red lake over azurite had been known for well more than than a century (Ball 2001; Salazaro 1877, 23–24, 25–26; Merrifield 1849, two:420–25, 584–87, 610–xi; Hall 1992, 15–xvi, 32). 7 Dyers in Mainetti's solar day could combine indigo and giallo santo , a yellow lake, to obtain greenish (Ruscelli 1557, 105v–106). To judge from early mod colored woodcuts, by the mid-sixteenth century several different shades of orange were produced through combinations of cherry lead or vermillion with ochre or pb-tin xanthous (Dackerman 2003, 57, 169, 206, 236, 274, 276, 277). This is not to say that such recipes were always reliable: the ambiguity of color terms, the imprecision of measurements and techniques, the variability caused past locale and season, and the trend of numerous substances to deteriorate over time, or in contact with other substances, guaranteed unpredictable results. Just the increasing incidence of concoctions favoring mixtures of blueish and yellow, or of ruddy and blue, or of red and yellowish, even or rather specially in the case of fake combinations, suggests a growing familiarity with knowledge that would soon be codified every bit a system of primary and secondary colors. 8

Nosotros might regard the monochrome globe of Malaspina'south pigment grinder every bit a symptom of the confused account of color offered past natural philosophers in this period. All the chalk, minerals, and pigments on his face up, hands, and smock seem reduced to a single "filthy" hue; the protagonist and his enemy the die cutter both produce, in rather different ways, faces rendered only in black and white; a quick chiaroscuro sketch on carta azzurra is identified as an extraordinarily lifelike portrait, as if its absent and abnormal colors were of no groovy importance. These narrative details signal that the elegantly calibrated admixtures of blackness and white, or light and night, would outcome solely in various shades of gray; but it is the human relationship of such discussions to the brass vendor'due south initial play a trick on that merits special consideration.

If we compare, for example, Mainetti'southward explanation of colour with Werro's subsequent elaboration, we can encounter that both systems can be read every bit linear spectrums running from light to dark, only that the transition from the original ratios to whole numbers produces peculiar features. Thus while Mainetti's spectrum progresses from white through yellow, blue, green, imperial, red, and black, were we to transcribe the harmonic ratios of light to dark as integers on a 100-betoken scale, the organization would propose something other than a compatible passage from i hue to the next. In such a configuration, white, of course would be rendered as 100, yellowish as 66, blue as 60, green equally l, purple as xl, red as 33, and black as 0. Werro's slightly more elaborate version yields a unlike chromatic ordering and more pronounced clustering; reduced to the same calibration and restricted to integers, information technology runs from white (100) to saffron (66) to pinkish (60) to yellow (54) to blood-red (50) to dark-brown (45) to green (44) to bluish (xl) to scarlet (33) and finally to black (0).

Information technology is difficult to detect a more apposite image of these reductions of color to number than that evoked by the contumely vendor's first play a joke on, where the paint grinder's difficulties in closing his store involved his inability to recognize, without the aid offered by numbers, the shutter designed for each discontinuity. Just as Werro's spectrum associates individual colors with specific numerical values distributed in nonuniform fashion and in a manner that correlates only weakly with hue, so the various windows of the shop, identified past a unique number and sometimes poorly differentiated in size, shape, and position, frame the pigments and display them as disjunct elements in a seemingly arbitrary sequence.

The revelation of the strange role numbers play for the paint grinder comes from the brass merchant, who in addition to altering "a two to a six, and a 6 to a four, and then forth," discreetly marks each shutter "at the pes with a sign known to himself," a signature of sorts, in gild somewhen to shut the place up (Malaspina 1609, ane:143v). While the episode implies more than the trickster's skepticism concerning the connection of number with colour than a systematic effort to explain the phenomena in other terms, his professional identity is telling. In Malaspina's coy phrase, this ruffian "plied his merchandise by selling diverse contumely objects in the remainder-makers' street" (1609, 1:143). His obvious propensity for deception, Malaspina'due south own first-class credentials equally an inveterate forger, and the widespread practice of tampering with mercantile measures suggest that these wares were fraudulent weights, rather than the legitimate metal components of balances and steelyards; as Francis Salary had observed in 1601, "this fault of using imitation weights and measures is grown so intolerable and common that if you would build churches, you shall not need for battlements and bells other things than fake weights of pb and brass." 9 The more firsthand bespeak may be, however, the brass merchant'due south implicit familiarity with metrology. 2 details from his final flim-flam—his perforation of the pail within which the pigment grinder twice pours wine purchased past volume, only to have information technology twice trickle away, unnoticed, as he carries it through the streets, and the clarification of the dupe's rage as "unmeasured"—ostend the expected opposition between ane who perceives weight, and one who does non (1609, ane:145r–v).

It was within the context of experiments with measures and weights that the increasingly elaborate substructure of Pythagorean proportions became most vulnerable to criticism. Skeptics included the Venetian mathematician and natural philosopher Giovanni Battista Benedetti, who explained consonance and racket in 1585 non by the ratios and the string lengths of the monochord, merely by the rates of the strings' vibration, the more pleasing sounds existence the issue of notes concurring with frequency, and the less amusing ones the product of interrupted or infrequent concurrences. Writing in 1589, Vincenzo Galilei turned to the story of the suspended weights, showing that the ratio needed to be iv:ane, not 2:ane, to produce an octave or diapason; 9:4, not 3:2, for a fifth or diapente; 16:nine, non 4:3, for a 4th or diatessaron. This adjustment of the proportions betwixt weights was not but the observation that the numbers needed to be squared, but more important, part of a sustained polemic confronting the prominent composer and music theorist Gioseffo Zarlino'south overreliance on Pythagorean ratios to explicate all natural phenomena (come across Drake 1999; Palisca 2006, 150–51; Peterson, 2011, 170–71; Heller-Roazen 2011, 67–68; Mancosu 2006, 598–604). 10

Both Zarlino'south enthusiastic elaboration of Pythagorean ratios and the sort of empirical cognition advocated by Benedetti and Galilei had renewed interest in the association of color with number. Given the cultural prominence of Venetian painting, the presence of a well-established textile manufacture in that metropolis, and the strong interest in colour perception amidst early modernistic natural philosophers and physicians nearby at the Academy of Padua, it is not surprising that the setting for these discussions was Venice. 11 Educated in philosophy at Padua before entering a career as a diplomat and a cleric, Filippo Mocenigo addressed the question of color in his Universal Institutions for the Perfection of Man of 1581 (on Mocenigo, see Bonora 2011). Such give-and-take occurred not in his examination of vision, however, where colour is hardly mentioned, but rather equally an bagginess to his presentation of sound and voice.

Mocenigo was strongly influenced by the piece of work of Zarlino. Given that the two men were both associated with the Venetian Academy, and that Zarlino had dedicated another work to Mocenigo's cousin, the Doge of Venice, this date is not surprising; the fact that Universal Institutions for the Perfection of Man emerged from the printing at the moment of Galilei'due south quickening conflict with Zarlino can only take increased interest in the matter. 12 Of particular relevance here is Zarlino's revision of the Pythagorean system, which made the first six, rather than iv, integers the basis of harmony. In addition to the diapason, diapente, and diatessaron, therefore, musicians might draw upon the more modern consonances of the ditone—5:4 or the major tertiary—and the semi-ditone—half-dozen:5 or the pocket-sized 3rd. xiii Every bit for the tone or 9:8, Zarlino had interpreted the story of Pythagoras and the hammers to mean that this basic unit enjoyed an intermediate status of something neither concordant nor discordant (Zarlino 1558, 61). 14

Mocenigo (1581) drew on these innovations to depict the spectrum in systematic fashion. "The outermost colors, which in their common relationship recall the diapason, are white and black," he began. "The three intermediate ones, which are in fact simple, but bordered by white and blackness, are red, which is closer to black than to white, yellow or gold, which is nearer to white, and hyacinth." This last color, a bright violet blue, he stated, was "therefore the midpoint, such that with respect to black, it can be compared to the diapente, and with respect to white, the diatessaron. With respect to red, information technology is like the semi-ditone, and with respect to yellow, the ditone. In the aforementioned manner, yellowish with respect to red resembles the diapente, while cherry with respect to black is like the ditone" (305).

Dissimilar Mainetti and successors such as Werro, Mocenigo used the harmonic proportions to articulate the spatial relationships of these colors to each other, rather than to bespeak notional measures of dark and lite, or blackness and white, in the presumed compositions. The layout of Mocenigo'south system of main colors tin readily be mapped onto Zarlino's discussion of the version of the diatonic scale he favored (Zarlino 1558, 120–22). fifteen

Figure 1. Gioseffo Zarlino, Istitutioni Harmoniche (Venice: 1558), 122.

A small difference lies in the distance in this theoretical configuration between yellow and white, shown hither every bit a major semitone, a unit Zarlino (1558) had laboriously described as a harmonious fraction of the diapente (121–22). Mocenigo (1581) had proposed instead that there would "besides exist the proportion of a [whole] tone, which is neither consonant nor anomalous," between these hues. He had farther stipulated that the proportions betwixt crimson and white, and between black and yellow would be dissonant (305).

In the most of import contrast to Mainetti and other Aristotelian predecessors, Mocenigo (1581) insisted on the proximity of his system to actual artistic practices, privileging offset the primary nature of 3 colors: "Information technology is clear that painters can make neither red, nor hyacinth, nor yellow—any more than they tin make white or black—from mixtures, unless a new concoction [that is, alteration by heat] is involved. However, all other hues can be produced from the admixture of whatever of these simple colors" (305). The schematic ordering of these secondary colors that followed would have impressed at least some of Mocenigo's initial audience less with its inaccuracy than with its credible distance from the model of On Sense and Sensible Objects , and with its resemblance to lower genres such as the painter's transmission and the book of secrets. "Blue arises from hyacinth and white," Mocenigo explained, "light-green from yellow to which some black has been added; cherry from blueish and black; brownish from black and white; ash-grayness from white to which some blackness has been added" (ibid.). xvi

Now PRINTED FOR THE FIRST TIME

Guido Antonio Scarmiglioni and Anselm de Boodt, two writers educated at the medical school of Padua in the tardily 1580s and eventual residents of Vienna and Prague, respectively, also offered modified versions of Mocenigo'southward system. 17 Scarmiglioni's Two Books on Colour appeared but in 1601. Its incoherent subtitle, At present Printed for the Beginning Time , and its preface both portray it as a text composed years earlier, and its numerous references to other works include nix published later 1590. Like de Boodt'south eventual publication of 1609, it offered all-encompassing reference to the practice of painters and dyers: Scarmiglioni gestured several times to various combinations of blue and yellow and of blue and ruby used to produce green and majestic. Unlike the more pragmatic guide provided past de Boodt'due south Natural History of Gems and Precious Stones , nevertheless, Two Books on Color also drew upon the flexible resources of the musical argument.

In reviewing the notion that painters were unable to make the 5 so-called primaries "through mixtures, unless heating were involved," and that "by mingling these hues they easily obtain others," Scarmiglioni (1601, 112) objected first of all to the exclusion of dark-green from this first rank of colors. The fact that i might observe, "every bit a quotidian feel," painters concocting this color from admixtures of xanthous and blue did not persuade Scarmiglioni of its secondary status, merely did justify its fundamental place, equidistant from the 2 hues of which it was composed, in his assortment of 7 primaries (120, 170). Matters were evidently more complicated for royal, whose confection he knew to involve "a small amount of red added to blue," for he located it between green and blue (117, 119, 169). Orangish seems to have figured only briefly, every bit a substance produced when minium was moistened with water; it had no condition every bit a dissever hue (120). Though Scarmiglioni adopted the terms of Zarlino's harmonic intervals, comparing the relationship of white to black to the diapason, describing the position of green with respect to these 2 endpoints by referring to the diatessaron and the diapente, and defining the distance between white and yellowish by a tone "neither consonant nor discordant," his spectrum does not arrange to the diatonic scale as well every bit Mocenigo's does (Scarmiglioni 1601, 148, 174, 180, 187, 199). It is not surprising that he included no illustration of the arrangement.

De Boodt's Natural History of Gems and Precious Stones likewise emerged from the Paduan context, and also suffered a significant delay in publication. It mentioned the notion of chief colors just twice, and merely in passing, equally if citing a truism rather than a indicate of contention. In his preface de Boodt (1609) stated that "from the colors white, blackness, red, blueish, and yellow, painters tin make a variety of hues," and later on he noted that "the chief colors, and those which are non made from the mixtures of others, are white, black, blue, yellowish, red, and minium, which is made from calcined lead" (8, 25). In calculation this last color—a bright orangish pigment prized by painters—de Boodt provided a corrective to Scarmiglioni'due south recommendation of a water-based procedure, and more important, an example of the use of heat, rather than mixing, to produce an unadulterated hue. xviii

Mocenigo, Scarmiglioni, and de Boodt do not seem to have offered a color system sufficiently robust to attract disciples. We might infer that Galileo Galilei's claim in May 1610, just after the publication of his Sidereus Nuncius , to have already written a short treatise "On Vision and Colors," involved an effort, or peradventure merely the intention to make such an effort, to improve upon an organisation whose basis was the work of his father'due south cracking rival Zarlino. xix The discussion of colors written by the prominent physician Epiphanio Ferdinando, which was published in early 1611 by the press from which Galileo'southward Sidereus Nuncius had emerged only eight months earlier, is notable for its tacit resistance to recent innovations. Its chartlike format, deployment of terms such as "diapason," "diapente," and "diatessaron," and ordering of the colors were zero merely a retreat to the proportional units of dark and low-cal advocated 60 years earlier by Mainetti (Ferdinando 1611, 193). xx

In these various efforts to reformulate and preserve the traditional connection of Pythagorean ratios with colors, we are far indeed from the antics of the pigment grinder, the brass merchant, and the dice cutter, and nevertheless Malaspina captures a hit mutual denominator. Published in 1609 by the same Venetian printing consortium used by Galileo in 1610 and Ferdinando in 1611, Two Hundred Novellas begins with a transparent fiction of anteriority much remarked by its original audience: even every bit it masquerades every bit a collection of tales told by speakers gathered in a villa to escape the plague of 1576, information technology blithely relates countless celebrated events of much more contempo vintage. Malaspina lived in Venice from 1580 to 1591, but what is more crucial than the writer's biographical particulars is the way in which his tale of the pigment grinder, opening with the formulaic "it is already many years ago," and treating the association of number with color equally farce, mimics the familiar combination of prior discovery and deferred revelation. Just as Scarmiglioni and de Boodt alluded to a debate several decades quondam, and only "being printed for the first time" in 1601 and 1609, and Ferdinando and Galileo coupled bygone analyses of color with publications of 1611 or even so to come, so the mocking Malaspina presented the tale of the pigment grinder equally an account of events long predating their moment of disclosure.

YELLOW, Cherry, AND BLUE

While Malaspina's gesture to this temporal lag suggests a kind of smug stasis in early mod color theory, a significant development soon followed. In 1613 the Jesuit François Aguilon offered a coherent discussion of the painter'south primaries in his Opticorum libri sex activity (Six Books on Optics), published in Antwerp and accompanied by engravings designed by Peter Paul Rubens. 21 A crucial feature of visible phenomena, colour emerges early on as a topic in this seven-hundred-page treatise. Despite his ultimate rejection of the Aristotelian explanation of color, Aguilon invoked several of the argu ments of On Sense and Sensible Objects , noting, for instance, that chromatic mixtures might occur through a layering of a translucent hue over a darker ane, or every bit an optical impression of minute spots seen from a distance or, finally, as a 18-carat admixture of ii different substances (Aguilon 1613, 39). He also distanced his discussion from the organic color changes addressed in pseudo-Aristotle'southward On Colors , and warned his readers that "we are non dealing here with concrete colors such every bit minium, dark royal, lake, cinnabar, indigo, ochre, orpiment, lead white, and the other things with which painters cover canvases, but rather with the visible qualities that inhere in them" (38).

His organization had an elegant simplicity. "Yellow, red, and blue number, strictly speaking, as the three intermediate colors," Aguilon asserted. "Forth with white and black they form a quintet of primary colors. Moreover, from these intermediate colors just as many secondary colors arise through three combinations. Orange is thus made of yellow and red, purple of red and bluish, and from yellow and bluish, finally, there is dark-green. And from the mixture of all three of these intermediate colors a certain unpleasant hue is born, something livid and pulp, like a cadaver" (twoscore).

Figure 2. François Aguilon S. J., Opticorum libri sexual practice (Antwerp: 1613), forty.

The figure accompanying Aguilon's explanation is clearly a modified version of that traditionally deployed in discussions of consonance and dissonance. Aguilon wholly abandoned, even so, the minute examination of various Pythagorean proportions: his arrangement is characterized by symmetry, and stripped of terms imported from the discourse of harmony. Though he never alluded to the efforts of Mainetti, Werro, Mocenigo, or Scarmiglioni, Aguilon elsewhere suggested a sure resistance to efforts such as theirs. The preface of his work includes a passing condemnation of the obscurity of Pythagorean mysteries; more substantively, the discussion of colors is preceded by the censorship of those who insisted on commonalities between the senses (Aguilon 1613, "Lectori S[alutem"], 2d unnumbered page). "That which is perceived through color has only to practice with sight; that which is discerned through sound, just with hearing; that which is known by scent, merely with the sense of smell, and then forth," Aguilon warned (30). Even more mistaken than the erroneous comparison of sensible objects, he argued, was the belief that the difference between colors could be explained by reference to transparency, opacity, darkness, and shadow (ibid.). Worst of all, however, was the assumption that aesthetic judgments were other than matters of taste and opinion: "for dazzler consists in harmonic division, which human reason barely recognizes; ugliness, in a sure obscure asymmetry of lines and qualities" (31). Put differently, consonance and racket could non exist established by arithmetical means, and figured not at all in a discussion of the relationships between colors.

By Inductive

Aguilon's theory of chief colors was parroted in the specialized ambit of the Jesuit thesis 2 years later (Felix and Denich 1615, xx). In general, however, his simultaneous rejection of the Aristotelian caption and of the traditional clan of colors with musical intervals seems to have gone unnoticed, unacknowledged, or unaccepted past natural philosophers. 22 As if in conformity with the design of tardy revelation of bygone findings, the Florentine physician Guido Guidi'due south work, written in the 1560s and based on Mainetti's accommodation of the Pythagorean ratios to color theory, was posthumously published in 1626; the Venetian dr. Valerio Martini'south De colore libri duo sua aetate iuvenilia collecti (Two Books on Colour Equanimous in His Youth) emerged in 1638, looked back several decades to discussions at the University of Padua and concluded, "based on reason, experiment, and the authority of those who are expert in painting," that the six principal colors—white, gray, yellow, orange, blue-light-green, and blackness—were produced through admixtures of black and white (Martini 1638, 2:ii). Without specifying its relationship to his prior and still unpublished "On Vision and Colors," in his Assayer of 1626 Galileo gestured in passing to his view that colors, similar particular sounds, tastes, tactile sensations, and odors, were an antiquity of the senses, and that ours is a monochrome world configured by indivisible quanta. In insisting that "a very long fourth dimension would non be enough for me to explain, or rather shade in on paper, what little I sympathise of these matters, and thus I pass over them in silence," he avoided, to a degree, the problematic elaboration of an atomistic doctrine, and reverted to his pattern of infinitely deferred disclosure (Galilei 1967, half-dozen:350).

Whether these debates were of any importance to the true protagonists of color mixing, the painters of early on modernity, is by no means clear. Thus far, simply a few works such as Peter Paul Rubens's Juno and Argus (ca. 1611) and Nicolas Poussin'southward Christ Healing the Bullheaded Man (1650), where sight and light are overtly addressed, are considered directly responses to emergent color theory as formulated past Aguilon, though one might possibly add to this meager list Guido Reni'southward Union of Design and Color (ca. 1620–25) and those cocky-portraits in which artists deliberately display a restricted palette (see Kemp 1990, 30–44). That said, it seems entirely possible that the most pronounced reactions to Aguilon's solution do not necessarily inhere in the expected genres or arise in conventional thematic treatments. Like Malaspina'southward narrative response to those prior attempts to mathematize color through Pythagorean ratios, they appear equally a cluster of complimentary details in a scenario whose ultimate referent is the original story of the forge.

Past manner of conclusion, and then, I would similar to consider the legacy of the debate over colour in two works past Diego Velázquez, Joseph's Bloodstained Coat Brought to Jacob , and Apollo at the Forge of Vulcan , both completed in Rome around 1630 during his beginning Italian sojourn. I will argue that this effect is the crucial component of both paintings: the ostensible subjects, biblical and mythological, merely provide the pretexts. In that location are a number of contextual reasons to doubtable that color theory would have been of involvement to Velázquez in this period. The young and ambitious creative person'south first journey to Italy had been prompted by Rubens'south visit to Madrid in 1628–29; before arriving in Rome he had spent a brief menstruum in Venice; his travel throughout the land was facilitated by the Venetian ambassador to Espana, Alvise Mocenigo, cousin to Filippo Mocenigo; and when in Rome he resided in the Villa Medici, where Galileo was besides staying (run across Goldberg 1992, 453–56; Palomino 2007, 37–44, 76–86). Though these coincidences probable indicate no more the relatively restricted number of participants in the cultural life of early modernity, it is also true that Velázquez acquired at some unknown point Aguilon'south 6 Books on Eyes , likewise as an unidentified work, possibly authored past Vincenzo Galilei, on music theory (Sánchez Cantón 1925, 3:389–91). 23 The best evidence for the importance of the argue over color, however, comes from the paintings themselves.

Effigy three. Joseph's Bloodstained Glaze , 1630 (oil on canvas), Diego Rodriguez de Silva y Velázquez (1599–1660). Monasterio de El Escorial, El Escorial, Kingdom of spain. Bridgeman Images.

In his 1724 biography of Velázquez, Antonio Palomino (2007, 83–86) presented Joseph'due south Bloodstained Coat and Apollo at the Forge as companion pieces painted without committee but later offered to the Castilian king; autonomously from two landscape sketches of the villa where the creative person may or may not have met Galileo, these are the only two canvases known to take been completed during the stay in Rome. 24 While scholars have emphasized their shared field of study of charade, it must be noted that dishonesty enjoys very different treatment in the ii works. In Joseph'southward Bloodstained Coat , the stunned patriarch Jacob is deceived by his sons, who use the garment to convince him that his youngest and favorite child has perished. Apollo at the Forge is likewise a tawdry domestic drama in which Apollo tells Vulcan the unhappy truth about the infidelity of his consort Venus.

What the paintings exercise share is a set of formal resemblances and sustained attention to the medium itself. 25 That Joseph'due south Bloodstained Coat has something to do with color is not surprising, given that the tunica polymita in question was generally understood in the early modern period to accept been woven "of diverse colors" (run into Beyerlinck 1617, 216; de Mariana 1620, 28; 1617, 385; Cornelius a Lapide 1616, 258). Considering that this splendid garment was the catalyst of Joseph'due south quarrel with his brothers, and that it is the sole prop in their ruse, the minor white item shown to the patriarch is much less impressive than one would expect. Its significance lies in this economy: flecked with faint crimson and yellow stains, and shadowed with blue and black, the coat recapitulates the emergent theory of main colors. As if to reinforce the bespeak, Velázquez distributed the primaries nigh the blackness and white tunics, the brightly lit, strongly modeled triad of blue, scarlet, and yellow cloths on the left finding a subdued mirror paradigm on the correct. While white and black are clearly crucial to the different tonalities of the left and right sides of the canvas, their new status every bit something other than the source of all colors is indicated in two dissimilar means. The rich gray cloak over the patriarch's robe, neatly posed confronting the juncture of light and dark walls, is the merely hue that could be said to derive from those erstwhile primaries. And the black robe of the brother who bears the tunic "of diverse colors" is nothing other than the dark basis of the canvas itself, at in one case a representation, accordingly somber, of the liar's garment, and an entirely unworked section of the painting (see Brown and Garrido 1998, 40–45; Garrido 1992, 230–31).

Figure 4. Apollo at the Forge , 1630 (oil on canvas), Diego Rodriguez de Silva y Velázquez (1599–1660). Prado, Madrid, Spain. Bridgeman Images.

Joseph'due south Bloodstained Coat incorporates a series of last efforts: after this painting, Velázquez never again used a night ground, he abandoned the coarsely woven canvas for a finer fabric, and the brilliant Naples yellow next to the tunic "of diverse colors" does not reappear in later works (Brown and Garrido 1998, 43, 45). While any of these three developmental steps is plausibly associated with his artistic apprenticeship in Rome, they as well appear crucial to Velázquez'south insistence on the very nature of his medium in this painting. This emphasis reappears, albeit in a slightly different annals, in the then-called companion piece of Apollo at the Forge. Here for the offset fourth dimension Velázquez prepared a luminous basis of an opaque atomic number 82 white mixture. This modification, in tandem with the much denser weave of the canvas, contributes to the slightly more than finished and even quality of this second work.

Despite these differences, the paintings share several features; both compositions include the device of the mural in the upper left quadrant, and both involve a dramatic moment in which a group of five men confront a sixth graphic symbol. While the focal point of Joseph's Bloodstained Coat was necessarily that pallid garment "of many colors," in that location is no such object in Apollo at the Forge . Rather than the double series of block-like primary colors, moreover, this work featured the secondary hues of orange, green, and royal, though merely the kickoff of these retains its initial intensity. The dark-green of Apollo's crown, made of admixtures of azurite, iron oxide, and lead white, was reproduced, with varied tonality, in the garments of Vulcan and his centrally placed companions, while the clothing of the man working on the armor at the far right, originally a muted violet, was composed of lead white, atomic number 26 oxide, vermilion, and a pale blue pigment, mayhap smalt, notoriously prone to discoloration (Brown and Garrido 1998, 46–56; Garrido 1992, 243). 26 Inevitably, the placement of these iii secondary colors replicates the organisation in Aguilon'south diagram, a central arc of green falling between the orange and violet extremes. Except for the bluish heaven beyond the forge, the chief colors do not appear in this painting, though blackness, white, and gray figure naturally in the metal objects produced by Vulcan and his assistants.

While the bright orange of both the metal on the anvil and of the burn down recalls the occasional presentation of this color, when derived from calcined lead, as a chief hue, the context itself is puzzling. And then, as well, are Vulcan's four companions, traditionally identified as a trio of Cyclops, for they are neither giants nor 1-eyed. 27 Nor is this Vulcan a deformed god, but merely a shocked cuckold. The easy translation of this episode to a vernacular idiom, though typical even of the young Velázquez, should non obscure the importance of that other forge where the fusion of color with consonance began. Simply put, the complimentary details of this painting serve to evoke the moment when Pythagoras, routinely described as Apollo's son, entered a foundry where five hammers had been pounding molten metal; discarding one, he discovered the crucial ratios between the other four. 28

Velázquez offers no way to assess the importance of this fable. Equally the groundwork figure in Apollo at the Forge tends the bellows, and the man on the far right is using tongs, there are but three who wield hammers. These instruments differ noticeably in size, as in the Pythagorean story. They are complemented, however, not by one discordant and summarily discarded tool, but past at least five, and possibly more, scattered well-nigh the enclave. The pan of a residue, entirely unsuited to the oversized hammers, lies abandoned on the flooring; a steelyard dangles unused side by side to the chimney. The apparent irrelevance of these weighing devices in Apollo at the Forge corresponds, roughly, to something like a visual pun in Joseph'south Bloodstained Coat , the baculus Jacobi or "Jacob's staff" being a traditional instrument for calculating angles. This studied emphasis on a kind of inadequation between the physical world and our means of numbering and measuring its phenomena would seem the very antithesis of the Pythagorean episode at the forge, and a definitive break with that early on attempt to measure out and codify aesthetic production.

But we might but as easily conclude that the painting involves non a rejection of the neatness of Pythagoras's approach to sound and by extension to color but rather an uncanny prelude to that foundational moment. In such a reading, the emphasis is less on the evident disorder of the forge than on the very fact of its reduction to an image. Put differently, the scene at this forge, anterior to that of the origins of music, can be rendered only through visual means; similar the banal motif of marital disharmony with which information technology is seemingly concerned, it cannot be captured through consonant ratios of sound. While clearly adhering to a vestigial or rather incipient version of the Pythagorean intervals in his handling of color in both paintings, here Velázquez would accept insisted on the absolute autonomy, priority, and permanence of his art. The work would have thus stood as a corrective to the long-standing subordination of color to sound and, past implication, of a crucial feature of painting to the strictures of musical harmony. If such was his intention, it is a matter of some irony that this aspect of the painting—its bid for priority and longevity—has been compromised by the instability of the medium.

In either guise, finally, Apollo at the Forge would appear remote from the tale of the tormented pigment grinder, and yet Malaspina's chestnut anticipates both readings. The decorous wreckage strewn about the forge, the disconcerting mismatch between the instruments depicted and the celebrated story of Pythagoras'south discovery, and the suggestion of an irremediable incommensurability betwixt the painter'southward medium and the harmonic ratios all figure as a sequel to the brass merchant'southward initial exposure of the strange place of number in the pigment grinder'south shop. But every bit nosotros might expect in a work whose focus is the antecedent to the Pythagorean moment in the forge, the canvas likewise articulates a corrective to the temporal feature parodied in Two Hundred Novellas and promoted without irony in early modern discussions of color. In the interest of undoing the priority claim of music, it refashions that insistence on a pronounced gap, typically on the club of a generation, betwixt the discovery of something near the mathematization of nature under the custodianship of sound and its disclosure in print. "Exist like a begetter to me," the hapless pigment grinder asked the brass merchant, equally if to avail himself of a previous generation'south wisdom; "you volition exist similar a son to me," Velázquez'due south Apollo might have observed to the as notwithstanding unborn Pythagoras.

NOTES

1 . This and all subsequent translations are mine unless otherwise indicated.

2 . More generally, see Fideler (1988); for some other version of the story, run across "Life of Pythagoras," in Guthrie (1988, 86–87); for background on Boethius's debt to Pythagorean and Ptolemaic arguments, run into Goldberg (2011, 19–30). On the legend, its presuppositions, and consequences, run across Heller-Roazen (2011, xi–59); on the place of Pythagorean mathematics in the globe of Galileo Galilei, see Peterson (2011, 33–42, 57–65, 149–73, 257–58); on the importance of early modernistic music theory in the evolution of number theory, come across Pesic (2010).

3 . On the history of efforts to pair musical consonance with colors, see Gage (1993, 227–46) and Kuehni (2007).

4 . On the relationship between artisanal knowledge of color mixing, particularly that of painters and dyers, and Isaac Newton'south eventual treatment of white light, see Shapiro (1994).

five . On the traditional resistance to colour mixing, and on the emergence of the practise of layering in the early on modern menstruation, see Hall (1992, 15–xvi, 52–57, 71–73, 211–17).

6 . Salviati'due south illustrations were for Guidi (1544). On Ghirlandaio'southward resistance to experimentation with colour mixing, his reversion to the older mode of unbroken colour established by Cennino Cennini, and on Salviati'south imitations of various color modes, see Hall (1992, 57, 61, 67, 163–66).

7 . Come across also Kirby, Nash, and Cannon (2010, 67, 147–48, 151, 244). As Gage notes, Alexander of Aphrodisias referred in passing, and dismissively, to the artificial production of royal and green effectually 200 AD; see Gage (1993, 31).

8 . On the trade in early mod pigments and dyes in Venice, see Matthew (2002). On the prices of pigments in early mod Italy, and on their relation to genre, see Spear and Sohm (2010, 65–66, 101–iv).

ix . "Spoken communication on Bringing in a Neb against Abuses in Weights and Measures," in Bacon (1868, xviii).

10 . Galilei's associate Ercole Bottrigari took upwards the argument in 1609 in his unpublished Enigma of Pythagoras .

11 . On the commerce in colorants in Venice, run across Matthew and Berrie (2010); Krischel (2010). For an overview of developments in the Venetian treatment of color, run across Hall (1992, 199–235).

12 . On the ongoing conflict between Zarlino and Galilei, see Heller-Roazen (2011, 61–69); Palisca (2006, 29–47, 142–44, 150–52); and Peterson (2011, 153–73); on Zarlino's senario in particular, see also Wienpahl (1959, 27–41). For a contempo in-depth study of the entire dispute, see Goldberg (2011): on Zarlino's dedication to Alvise Mocenigo, come across (2011, 44–45, 49), on his alleged attempt to delay Galilei's Dialogue on Ancient and Modern Music in 1581, run across (2011, 220–21, 265–67).

13 . On the emergence of the major and minor thirds, see Heller-Roazen (2011, 62, fourscore–81).

14 . On the traditional discussions involving the status of the tone, see Heller-Roazen (2011, 28–29, 32–40, 53–54).

xv . On the syntonic diatonic scale, and on Galilei's criticism of this choice, see Goldberg (2011, 57–64, 101–49, 240–48, 272–393).

16 . For similar combinations, come across Erizzo (1558, fol. 30v); Curaeus (1567, fol. 69 r–v); Caracciolo (1589, 257).

17 . De Boodt's doctoral caste was awarded in 1586 or 1587; Scarmiglioni was awarded a degree in June 1589; encounter Zonta and Brotto (1969, 4:3; 1469–70; 4:4, 2354). On de Boodt and Scarmiglioni, meet Parkhurst (1971); Shapiro (1994, 606–ix); Cuff (1993, 34–37, 93–96, 153–56, 165–68); Kemp (1990, 266, 275–76, 281–82).

xviii . On the confusion over this substance, run across Falloppio (1564, 152–54, 164–66); Guidi (1626, 369); on the departure of minium and the paucity of orange in the quattrocento palette, run into Hall (1992, xv, 208, 257); see farther Kirby, Nash, and Cannon (2010, 84n40, 305, 457).

19 . Galileo Galilei to Belisario Vinta, May 7, 1610, in Galilei (1967, 10:352). Curiously, the entry on Galileo written past Count Angelo de Gubernatis and published in an encyclopedia of 1901 refers to the work as "an essay, now lost, [establishing] the profound truth of the laws of consonance and racket, or the unity and diversity of colors" (Adams and Rossiter 1901, 5:13).

twenty . The fact that Mainetti would be misidentified in the 1620s in Jacopo Soldani's poem "Contro gli aristotelici" as an exemplar of Paduan philosophy is perhaps an index of the particular impact of his arguments in the celebrated university of that city.

21 . On Aguilon, see Parkhurst (1961); Kemp (1990); Shapiro (1994, 606–ix).

22 . On the resistance or indifference to Aguilon's statement, come across Shapiro (1994, 615–eighteen).

23 . The piece of work on music theory is generically described as "De arte música," and attributed to "Lipo Gailo," perhaps a misreading of "V zo Galilei."

24 . On the landscapes, run across Brown and Garrido (1998, 57–61).

25 . On the limited number of pigments favored past Velázquez, see Brown and Garrido (1998, 17–19).

26 . On smalt, see Zahira Véliz, "In Quest of a Useful Blue in Early Modern Spain," and Nicola Costaras, "Early Modern Blues: The Smalt Patent in Context," in Kirby, Nash, and Cannon (2010, 389–414); on Velázquez's early apply of smalt every bit a colorant (rather than as a siccative), see p. 393, as well as Brown and Garrido (1998, 39).

27 . In his Life of Velázquez , Palomino notes that in the much subsequently depiction of Vulcan painted by Juan Carreño and overseen past Velázquez, the Cyclops were three in number and named "Brontes, Steropes and Pyracmon" (Palomino 2007, 155).

28 . Pythagoras's biographers generally ascribe belief in his divine nature and his descent from Apollo to reckless poets and to common people; oc casionally he is said to exist Apollo himself. For such references in the accounts of Iamblichus, Porphyry, and Diogenes Laertius, see Guthrie (1998, 57, 58, 59, 61, lxxx, 83, 97, 101, 109, 123, 128, 129, 144, 147). At to the lowest degree one early modern writer identified the workers encountered by Pythagoras in the forge as the Cyclops (Ringhieri 1551, fol. 144).

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