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Pythagoras, Aristotle, Plato

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Date:

Basic colours:

Bibliography:

Antiquity.

Pythagoras: musical notes are assigned to colours; Aristoteles: colours throughout the day: white, yellow, red, violet, green, blue, black; Plato: white, black, red, "radiant".

Form: Aristotle: line

Related systems: Grosseteste, Alberti, da Vinci — Aguilonius — Fludd — Chevreul — Field —

C.M.N

Summary: An interpretation of Pythagoras ’s teachings, which maintained that the root of all harmony was to be found in the positions of the planets between the earth and sphere of fixed stars; the linear arrangement of colours according to

Aristotle , who was probably the first to investigate colour mixtures; and finally a personal intepretation of Plato ’s colour-system taken from his Timaios , according to which the eye does not receive light, but rather transmits a ray of vision towards an object.

Aristotle, De sensu et sensato , De anima , Meteorologica ; Plato, Timaios , 67D-

68C in the Stephanus numbering; A. T. Mann, The Round Art , London 1979;

Th. Lersch, "Farbenlehre", in: Reallexikon zur Deutschen Kunstgeschichte , published by the Zentralinstitut für Kunstgeschichte Münschen, Volume VII,

Munich, 1981.

In a reality so rich with colours, there are in reality no colours. The colours we see indeed depend on the light that enters our eyes from the outside world. Nevertheless, what we actually perceive as red or green originates deep within our brains. Colours are not, therefore, merely "Deeds of Light", as Johann

Wolfgang Goethe once claimed; colours are also a product of the self, and we decorate our own personal world with them.

We see and produce an apparently endless abundance of colours. Philo of Alexandria was the first to notice this when, in the first century, he marvelled at the colours around the neck of a dove as it moved in the light of the sun. At that moment, something may have dawned upon the man of antiquity which we now accept without question: namely, that the abundance of colours is actually so rich and plentiful that we cannot name all its shades and tones — at least, not without the aid of a systematic order. It is only natural, therefore, that throughout history we have endeavoured to invent a system for colours. We shall be investigating some of these attempts, and in so doing we shall see that there is no clear and final, nor even objective, solution to the problem of arranging the colours of our world into a distinct order. The history of colour systems remains as open as the history of human beings themselves.

Colours are ideas. As we progress, moving from the classical world towards the present day, we shall wish to acquaint ourselves with their origin, both in the world about us and within our own minds. At the same time, we shall gradually have to learn to deal with the vocabulary of colour in a more exact way — naturally, without sacrificing its range. To the physicist, "colour" can imply a determinable wavelength, but to the painter it is a brilliant substance on his palette. If we turn our attention to

"mixtures", we will be faced with so many possible variations that there will soon be confusion if we fail to determine exactly what, in each case, has been combined. Red and green light, for example, will together form a different colour than red and green watercolours.

Aristotle was probably the first to investigate colour mixtures — and in so doing, meet with failure. He arranged for daylight, which is seldom colourless in its effect (we shall be considering this later), to fall upon a white marble wall after passing through a yellow and a blue fragment of glass. After observing the two resulting patches of light and their colours, he then held the blue fragment between the wall and the yellow fragment. When Aristotle saw the green component in addition to the original yellow and blue, he came to the conclusion that green will be formed when yellow light and blue light are mixed together.

For a while we may tend to agree with such an addition. However, if we then consider these pieces of coloured glass more closely, we will soon see that something must have been subtracted from the light which passes here. Every time the apparently white light of the sun is made to pass through a piece of coloured glass, a component will be removed. (Using the techniques of modern physics, this can now be measured accurately). If this light has passed through both the yellow and the blue glass fragments, its remnant light will be seen by our brains as green.

We will, for a while, leave undisturbed the precisely measurable aspects of the science of colours, in order to explain more about the ideas of the Greeks — ideas which thrive on the experience provided by our senses. Their world is understood as an organic entity, with its colours arising from the continually observed struggle between the darkness of the night and the light of day. Any system of colours must therefore range from white through to black and, as with all first attempts, the simplest possibility is tried to begin with: namely, the straight line. Aristotle's linear sequence of colours can be observed during the course of the day: the white light of noon becomes tinged with yellow, and changes gradually to orange, and then to red. After sunset, this evening red becomes a purple violet, changing to a night sky which appears as dark blue. In between, green light can sometimes be seen.

(It is unlikely that many have observed a green glow at sunset, but there are numerous photographs documenting this).

Aristotle's system, where red is also able to occur less dramatically as a combination of black and white — as demonstrated by the reddish glow in a black steel reflector, for example — may well be as clear and convincing as the "Explanation of Colours" provided by Plato in the 30th chapter of Timaios is complicated. Plato's basic ideas about our visual perception have little in common with our modern explanation; they are not based on light rays entering the eye, but on rays of vision extending from the eye, thus interacting with particles emanating from objects. Accordingly, Plato introduces the first two basic colours: "It is the white which extends our visual rays, and black is its opposite". Regardless of the clarity with which he begins this exposition, the route leading us to his two further basic colours of red and "radiant" requires a highly sophisticated notion. Plato observes that our eyes become filled with tears when we are too close to a fire. Tears, understood as the unity of water and fire, provide the eye's moisture, and eventually create mixtures which lead to the diversity of colours. Objects thus acquire a radiance, and begin to glow. Red as the colour of fire is henceforth explained in the following way: because of the flames "by virtue of the ray of blended fire gleaming through the moisture, a colour similar to that of blood is created", and this colour "we give the name of red". With these four basic colours, further mixtures are possible: "The radiance associated with white and red is a golden yellow....The mixture of red with white and black produces the colour purple, but a deep violet will arise if the colour purple is burned and if black is then generously mixed in ... If white should combine with the radiance and should then encounter a saturated black, a dark blue colour will be formed, and through the mixture of this with white, a sky blue", and so on, to "yellow brown" and "leek green".

If we wish to sketch this construction and understand it as a geometrical pattern, we can proceed in a personal way, just as Plato did ( illustration I and illustration II . The radiance (Italian "Splendente", here abbreviated to S) must appear alongside the colours and have equal value, only white ("Bianco", abbreviated to B) being allowed dominance. If the tetrahedron is taken as a basis, three of these can be assembled, with their white tips interlocking around a central point to form a secondary triangular plane with a colour appointed to each of its corners. The white centre remains colourless and empty, attracting the tetrahedrons like a shadow, and allowing the colours to be mixed in the way familiar to us. Although he puts forward his construction as a rational theory of colour, Plato has not actually constructed a colour system, and the personal view presented here is only intended as an aid to understanding the colour mixtures he describes. A theory of colour was impossible in his time, although it was certainly understood that within the colours "hidden things concerning harmony and contrast" could be discovered "which rely, for their effect, on themselves alone, and which cannot be

expressed in another medium" — as Vincent van Gogh had writen in a letter to his brother Theo, in

1882. Harmony has always been the object of our searching, and a corresponding number of colour theories have been passed down to us. Most widely known is the Pythagorean design, which defined a relationship between the musical scale (in either full or half tones) and the position of the planets between the earth and the sphere of fixed stars. A first colour system could be created by representing this system of harmony as a semi-circle which incorporates the traditional signs of the planets, and then adding the corresponding sequence of colours to this image. To visualise this harmony, we have reproduced such a semi-circle here. A fully complete colour diagram by Pythagoras must have existed, however, because ancient commentators on the writings of Empedocles emphasise that he —

Empedocles — proceeded on the basis of such a pattern when he mixed red and  (óchron) with the primary colours black and white, but this Greek word remains vague and is not translated. (It implies a pale yellow, from which the colour "ochre" is derived.) Aristotle then took the ideas of

Empedocles a step further to create the base line, already described and occupied by seven colours, which applies to all colour systems up to the time of Newton. His basic assumption (which still persists in many people's minds) was to represent colours as actual characteristics of the surface of bodies and not as subjective phenomena produced by the eye or in the brain as a result of the properties of light.

Aristotle not only observed colours very accurately, but also their contrasts ("De meteorologica"). He was aware that the violet appearing on white wool appeared different when on black wool, and that embroidery appeared different in daylight and in the light of a candle. Aristotle, therefore, had already asked those questions which, only much later, were to be systematically examined and explained by the French chemist Michel Eugène Chevreul .

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Robert Grosseteste, Leon Battista

Alberti, Leonardo da Vinci

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Middle Ages to Early Renaissance.

Country of origin: Grosseteste: England; Alberti and da Vinci: Italy

Basic colours: Robert Grosseteste: 7 (unknown) basic colours between "Lux clara" and "Lux obscura"; Alberti: yellow, green, blue, red; Leonardo da Vinci: white, yellow, green, blue, red, black.

Related systems: Pythagoras — Aguilonius — Newton — Hayter — Chevreul — Field — Hering

— Ebbinghaus — Astrological connections — Ars magna — Islamic Tradition

Summary: Robert Grosseteste, first chancellor of Oxford University, was interested in the phenomenon of colour in an entirely fundamental way. He had no practical intentions and saw light as a "prima materia". Grosseteste developed a system of colours as part of his "grandiose metaphysical interpretation of light". The painter Leonardo da Vinci and the architect Leon Battista Alberti are more pragmatic in this respect, and seek a system that is suitable for the mixing of colours.

Bibliography: R. Grosseteste, De colore , ca. 1230; L. B. Alberti, Della pittura , 1435; L. B.

Alberti, Opere volgari , 3 volumes., edited by C. Grayson, 1960 / 1973; Ch.

Parkhurst and R. L. Feller, Who invented the Color Wheel?

, Color Research and Application 7, 217-230 (1982); Th. Lersch, "Farbenlehre", in: Reallexikon zur Deutschen Kunstgeschichte , published by the Zentralinstitut für

Kunstgeschichte M ünschen, Munich, 1981; John Gage, Colour and Culture,

Practice and Meaning from Antiquity to Abstraction , Thames and Hudson,

1993, (mention and comment), p. 117-120.

With Aristotle , as he himself expressly noted in his paper De sensu et sensibili ( On Sense and

Sensible Objects ), we required seven colours to connect the extremes of black and white. Aristotle does not always give the same names to the steps of his scale — grey can occur between blue and black, thus displacing yellow to the opposite end — but it is always seven colours. We find this number again, although without specifically allocated names, in the early 13th century with Robert

Grosseteste , the first chancellor of Oxford university. With the publication of his book De colore ,

Grosseteste added a new dimension to our cultural history. He had translated the works of Aristotle, and conceived a new view of the world which became known as a "grandiose metaphysical interpretation of light". As "prima materia", light provided him with the primary physical form, with space being a function of "lux", perceivable in its seven colours.

Grosseteste became aware that colours were not only to be defined according to their brilliance or saturation — we will explain more closely what is meant by these terms — but that their brightness or whiteness also seemed to play a part. A bright, shining red can be very easily distinguished from a grey, dark red, and is also described in another way. Grosseteste retained the black-white axis, but he removed them from the classical straight line, to turn them through a right angle. By placing his seven equal — value basic colours across the axis between white (Lux clara or Albedo) and black

(Lux obscura or Nigredo), he opens up a new dimension for colour systems. Grosseteste imagined that Lux clara descended to the colours — by means of a procedure which he named "remission" — and that Lux obscura ascended to the colours — by means of "intention".

We do not know which colours he wished to see arranged linearly at the midpoint between Albedo and Nigredo. Black and white were probably not among them ( illustration ), implying that Grosseteste was the first to distinguish between the two colour types nowadays known as achromatic (namely, black, grey and white) and chromatic (all others). A glance at the still linear scale of the six "colori semplici", which we also find with Leonardo da Vinci in about 1510, will reveal that this segregation of actual colours — as they are sometimes known — was in reality both difficult and disputed.

Noteworthy in Leonardo's straight — lined arrangement, however, is the series of chromatic colours

— giallo, verde, azzuro, rosso, thus yellow, green, blue and red — which form a contrast to the patterns of Antiquity and at the same time begin to resemble the established psychological sequence of modern times, which we will later explain in more detail.

Leonardo was interested in colours as a painter, hesitating at first to adopt green, since green can be obtained as a mixture of yellow and blue. Here, we can for the first time recognise a difference which was to become significant in later systems — the difference between primary and (corresponding) secondary colours. The allocation of colours is very much dependent on the originator of a particular colour system and the purposes he intended to fulfil. The colour green certainly belongs to both categories, since from a physical point of view it is a primary colour, but it is a secondary colour as far as the technique of painting is concerned (see above). In the course of examining other colour systems, we will often be confronted with such dichotomies. Colours are formed and blended in many different ways.

While Leonardo deliberated over colours, he was already aware of the arrangement put forward in

1435 by his fellow countryman Leon Battista Alberti . This makes do with four (actual) colours which form a rectangle in our illustration — yellow (giallo. G), green (verde. V), blue (blu. B), red (rosso. R)

— and thus serve as the base of a double pyramid with the achromatic extremes placed in the corners ( illustration ). It is clear that the seven colours used by Grosseteste had been abandoned by this time, the reason probably being a new theory of the rainbow which had been put forward in the early 14th century. In Antiquity, Aristotle had initially discovered only three colours, which he identified as red, green and blue. Other ideas first emerged in the year 1000 or thereabouts, as the Middle

Ages became occupied with optical experiments, and in about 1310 the Dominican monk Dietrich von

Freiberg finally linked many of his observations to his recognition that four colours are spread across the sky in front of dark clouds. He named them red, yellow, green and blue, and spoke of primary

"median colours", all of which can be mixed together.

However, it was not until the19th century that a distinction was drawn between the reflection of light from a surface and the refraction of light occurring, for example, in a rainbow. Nevertheless, what we experience here is an early form of scientific knowledge of colours, which the colour theorists of the

Renaissance were then able to adopt. Leon Battista Alberti wished to take this particular development a step further, in order to originate a suitable system for mixing paints, providing a "ratio colorandi", as he called it. He has not handed a pictorial representation of his ideas down to us, and only wrote a few lines on this subject in Della pittura , his 1435 book on painting. We have reproduced his arrangement, based on suggestions made by the American art historian Charles Parkhurst, who places the four basic colours within a closed system — for example a square, although a circle could equally take its place — since they can be mixed in pairs as paints to allow the artist to aim at all possible transitions. Again, black and white assume their own dimensions, with the four previously mentioned chromatic colours all having equal spacing. Because Alberti's four elements should correspond to the four "veri colori", there are problems with yellow, which cannot be allocated in a suitable way and was later replaced by Alberti with grey: red corresponds to fire, blue to air, green belongs to water and grey to the earth. In Alberti's case, there was no fourth primary colour, but a mean value between the absolute values of black and white, and the resultant grey was seen by him as the colour of the earth. If we now exchange this grey for yellow, we will depart from his system and return once again to Aristotle.

If the reconstruction is correct, then Alberti was the originator of a colour circle — at least at first glance. But when Parkhurst, together with his colleague Robert L. Feller, systematically researched the invention of the "colour wheel", they were able to show that Grosseteste's diagram can be understood spacially, in the way shown. (A circular arrangement of colours had also been mentioned by Albertus Magnus as early as the 13th century). Grosseteste himself remarks very generally that the entire cosmos arose from primaeval light, and that philosophy cannot be understood without

"figures". He had certainly — and demonstrably — understood the term "figures" to be threedimensional objects.

The Oxford academic otherwise had no special application for colours in mind, being concerned solely with general theory. In this respect, his contribution had actually succeeded because, well into the 20th century, we will once again encounter his basic concept of placing all colours at the same distance from white and black. Grosseteste's ideas anticipate all systems which take the form of a double cone based on colour hues of equal brightness. With colours, too, is there nothing new under the sun? Indeed there is, but on a less superficial level. As the two Americans discovered, the history of colour wheels appears to have neither beginning nor end — just like the circle of colours itself, made possible by the light of the sun and our own eyes.


Aron Sigfrid Forsius

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Date: The system originated in 1611 in a text by the author on physics.

Country of origin: Finland

Basic colours: (Black, white), red, yellow, green-blue

Form: Sphere

Related systems: Grosseteste, Alberti, da Vinci — Fludd — Newton — Wundt

"If, however, the origin and the relationship of the colours are to be correctly

Bibliography: observed, then one must begin with the five basic median colours, which are red, blue, green and yellow, with grey from white and black, and one must heed their grading, and whether they move nearer to the white because of their paleness or nearer to the black because of their darkness." This is

Forsius’ own description of his fundamental thoughts about his system . The construction is, as far as we can tell, the first drawn colour-system.

S. Forsius, Physica, published by J. Nordström, Uppsala Universitäts

Arsskrift, X, 1952; "A. S. Forsius, Physica Manuskript, 1611", published in

1971, ACTA Bibliothecae Regiae Stockholmiensis, pp. 315-321 (1971); C.

Parkhurst and R. L. Feller, "Who Invented the Color Wheel?", Color

Research and Application 7 , pp. 217-230 (1982); John Gage, Colour and

Culture, Practice and Meaning from Antiquity to Abstraction , Thames and

Hudson, 1993, p. 166 (mention and comment).

The oldest colour system known today that's worth its name originates from the Finnish born astronomer, priest and Neoplatonist Aron Sigfrid Forsius (died 1637), sometimes also known as

Siegfried Aronsen. Forsius became Professor of Astronomy in Uppsala (Sweden) in 1603, later moving as a preacher to Stockholm and beyond. He was removed from office in 1619, after being accused of making astrological prophesies.

Eight years previously, a manuscript had appeared in which Forsius expounded his thoughts about colours, concluding that they could be brought into a spacial order. This 1611 text lay undiscovered in the Royal Library in Stockholm until this century, to eventually be presented before the first congress of the "International Colour Association" in 1969. It was in chapter VII — which was devoted to sight — of this work on physics that Forsius introduced his colour diagrams. He first of all discusses the five human senses, explains (for us in rather complicated and incomprehensible terms) how colours are seen, and then arrives at his colour diagrams, on the basis of which he attempts to provide a three-dimensional picture. Forsius states:

"Amongst the colours there are two primary colours, white and black, in which all others have their origin." Forsius is here in agreement with Leonardo da Vinci who, more than three hundred years earlier, had included black and white amongst the colours, seeing them next to yellow, red, blue and green as primary colours. Forsius then continues:

"In the middle, between these colours (black and white), red has been placed on the one side since the classical antiquity, and blue on the other; yellow then comes between white and red, pale yellow between white and yellow, orange between yellow and red ..." and so forth, until Forsius has completed the whole circle which can be seen above right, around which are placed the English translations of the Swedish appearing within. (We have used American terms because the Forsius manuscript was unearthed by American academics.) Following this circle in Forsius' text is a drawing which is definitely intended to represent a colour-sphere. We have placed a smaller version containing the English translations next to the original Swedish version. Forsius uses four basic colours (red, yellow, green and blue) which he observes, together with grey as a "median colour", between the two extremes of black and white. With regard to his second diagram, he comments:

"If, however, the origin and the relationship of the colours are to be correctly observed, then one must begin with the five basic median colours, which are red, blue, green and yellow, with grey from white and black, and one must heed their grading, and whether they move nearer to the white because of their paleness or nearer to the black because of their darkness."

In other words, Forsius had the idea of introducing four basic chromatic colours, applying for each colour a grey scale which runs from bright to dark along the central axis of the sphere. The colours on the sphere's surface are arranged in such a way that three opposing pairs are created: red and blue, yellow and green, white and black.

As we shall see, Forsius had thus paved the way for modern colour systems (even though

complementary colours are later subjected to a more exact description). Nevertheless, from the colours of the Forsius sphere we can see that its author experienced some difficulty with the overall perspective:

White

Life colour — tree and wheat colour — chalk grey — pale blue

Pale red — pale yellow — apple mould — verdigris — sky blue

Red — yellow — grey — green — blue

Purple — flame yellow — mouse grey — grass green — dark blue

Violet — black brown — black grey — black green — indigo

Black

Forsius' colour sphere was just one of the widespread attempts made in the 17th century to create comprehensive colour scales, partly undertaken to enable very exact differentiation between the various styles of painters. A technical problem which initially remained unsolved — also in Forsius' case — concerned a coordinated relationship between the two parameters colour hue and colour value (or brightness). Pure yellow is simply brighter than unmixed blue. In 1677, the English doctor

Francis Glisson is credited with the creation of a colour-solid which, in this respect, was both coherent and of sufficient quality to become the ancestor of all colour systems of the New Age.

According to John Gage in his Culture and Colour , the success of this undertaking has unfortunately not been substantiated. Glisson operated with the primary colours red, yellow and blue, and his grey scale was composed of 23 steps between black and white, which he constructed using lead-white and black ink.

Scientific progress would soon surpass those mixtures developed by Glisson in his "scale for red"

(Scala Rubedenis) or his "scale for black" (Scala Nigredinis) — progress initiated by experiments conducted even while Glisson was mixing his pigments. And as we shall soon see, at the end of the

17th century in Cambridge, Newton separated the white light of the sun, to subject the colours to the scrutiny of physics.


Franciscus Aguilonius


Date: The colour diagram appeared in 1613 in a work on optics.

Country of origin: Belgium

Basic colours: Yellow, red and blue appear between white and black

Form:

Reference

Systems:

Summary:

Bibliography:

Bow

Pythagoras, Aristotle, Plato — Newton — Goethe

In this, possibly the oldest system to use the trio of red, yellow and blue, colours are defined within a linear division. Their mixing options can be deduced using bows. "One can see in his achievement the quietness of the monastery, which can permeate into the smallest detail of a work" was

Goethe’s comment on the work Franciscus Aguilonius, whom he rated highly.

F. Aguilonius, opticorum Libri Sex , Antwerpen 1613; J. W. von Goethe,

Geschichte der Farbenlehre , Part 1, Munich, 1963; F. Gerritsen,

Entwicklung der Farbenlehre , Göttingen 1984; John Gage, Colour and

Culture, Practice and Meaning from Antiquity to Abstraction , Thames and

Hudson, 1993 (mention and comment).

Franciscus Aguilonius (1567-1617) "was a Jesuit in Brussels and published his Optics in large format in Antwerp" — as recounted by Goethe in his History of the Theory of Colours , adding: "one can see in his achievement the quietness of the monastery, which can permeate into the smallest detail of a work". We could also add that the origin of the curved bow of his colour system can, if so wished, also be seen in the vaults and windows of the cloister.

It is clear that François d'Aguilon — his French name — also conforms fully to the tradition of

Aristotle, and he uses the bow as an addition to the classical, linear division to specify the possibilities that arise from mixing colours. It is important to note that in his optics textbook, which appeared between 1606 and 1611, Anguilonius did not merely wish to envisage the painterly

"colores concreti", but was more interested in the visible colour qualities which this revealed.

An attempt at transferring musical consonants into the area of colour formed the basis of his scale.

To this end, Aguilonius did not concern himself with harmonies, but simply the relationship between the colours. As a physicist, he had introduced the expression "simple colours", meaning any colour from which an infinite number of other colours could arise through mixing. As our illustration shows, there are five of these simple colours, and a further three can be directly composed from these.

"Quinque sunt simplicium colorum species, ac tres compositiae", states the propositio 39 of his work. Between the extreme colours ("colores extremi"), defined as brightness and darkness — named "albus" and "neger" — come the median colours ("colores medi"): "flavus — ribeus — caeruleus", thus yellow — red — blue. If, in accordance with their respective bows, in each case two of the simple basic colours are mixed, then "aureus, purpurus and viridis", in other words gold, purple and green will be formed. But Aguilonius explicitly warns against a mixture of all three simple colours, since in this case only a murky grey hue will result — a "corpse-like colour".

Aguilonius is praised by Goethe, since he expresses more clearly than usual "that the colours must be arranged according to the differing ways in which they appear". At the same time, Anguilonius differentiates — in Goethe's translation — between "true, apparent and intentional colours" which, in his History of Colour Theory , the poet explains in the following way: "The true colours are allocated according to the properties of the bodies, the apparent colours are seen as unexplainable, indeed a divine secret, but yet to a certain degree they are also to be regarded as coincidental." The intentional colours are still more difficult to substantiate, since, according to this interpretation, they are granted a will and a purpose — indeed a "spiritual nature, due to their delicateness and effect".

Goethe devotes an entire chapter to them, which we can here only refer to.

Aguilonius also applies the triple subdivision of colours to their mixtures, and in this respect the above concepts are easier to understand. The intentional mixing ("compositio intentionalis") merely involves the superimposition of numerous colours. In addition, Anguilonius also defines the combination of physical dyes ("compositio realis"), as well as the distribution of the smallest colour

patches ("compositio notionalis") which can be perceived by the eye as a mixture, although his diagram does not emphasise this clearly. His bows can certainly not be used in all three cases, since a mixture of yellow and blue light produces not green — as portrayed by Aguilonius and which applies to paints — but white.

As the jargon of the Neo-platonists, amongst whose numbers Aguilonius is counted, would have elegantly stated: "The colour diagram shows the relative position of the simple and composite colours on a scale which determines their respective status through a colour's participation in light".

In his case, in accordance with the added proportions of white and black, all colours also exhibit different grades of intensity.

The right-hand diagram suggests a continuous transition from the subdivision of the straight line, as indicated by the sequence of colours, to the continuity of the bow joining black and white. Colours, therefore, can also serve as an inspiration for geometrical patterns.

Anguilonius' system uses three basic colours, and can thus be seen as the forerunner of other systems which function in a similar way. In the pure combination of colours, he dispenses with the fourth, green, which had already caused difficulties for Leonardo da Vinci , but not without granting it a special position. In the same way as red (above), green is placed in the middle (although beneath). Both colours therefore stand opposite one another, and rightly so, since they do this in a complementary way, as Aguilonius quietly implies when he allocates a tip (a point) to red, whilst green is allowed to extend outwards as a bow. Thus, a restrained point of colour stands opposite the continuous coloured line, to be combined using the stepped diagram.

While working on his optics textbook Opticorum libri sex , Anguilonius had collaborated with the

Dutch painter Paul Rubens, who at that time (1611) was painting Juno and Argus , his famous visual allegory. Included in the picture are a rainbow and a peacock, and many have wondered at the fullness and abundance of their colours. In the second century A.D, the Gnostics had already made the surprising observation that the infinite fullness of colours in the tail of a peacock all emerge from a single white egg, and bestowed upon this the greatest of all mysteries. In our modern age, this has been reduced to a banality. The idea that the potential for all colours is contained in white alone is therefore ancient, and emerges clearly in a 13th century treatise attributable to Albertus Magnus, which states: "Appearing in white are absolutely all the colours which mankind can imagine on the face of this Earth". In 1669, before embarking on the experiments dedicated to this very insight,

Isaac Newton purchased the collected works of Albertus Magnus.


Robert Fludd


Date: The system appeared between 1629 and 1631 in a work on medicine.

Country of origin: England

Basic colours: Blue, green, red and two different yellows

Form: Circle

Related systems: Pythagoras,Aristotle, Plato — Forsius — Field

Summary: The colour-circle , probably the first to have been printed, operates with five colours (blue, green, red and two types of yellow) and gives their position in relation to black and white. An influence from the Antiquity, especially from Aristotle ( text ), reaches into the 17 th century and seems impossible to ignore. Accordingly, its history is represented in some detail.

Bibliography:

In the course of our journey, in addition to Aristotle we meet figures such as

Empedocles, Democritus, Plato, Avicenna, Alhazen, Roger Bacon und

Nikolaus Cusanus.

R. Fludd, Medicina Catholica , 2 volumes, Frankfurt, C. Rötelli, 16291631; J.

Godwin, Robert Fludd Hermetic philosopher and surveyor of two worlds ,

London 1979; John Gage, Colour and Culture, Practice and Meaning from

Antiquity to Abstraction , Thames and Hudson, 1993, pp. 9 and 171

(mention and comment).

In about 1630, barely twenty years after the publication by A. S. Forsius of the first hand-drawn colour-circle , the first printed colour-circle appeared in a medical work by the Englishman Robert

Fludd (1574-1637). His colour-wheel has a total of seven areas around its circumference, and thus points to its ancestral link with Aristotle's line. Fludd distorts this classical line, to join it back upon itself. He places black and white (Niger and Albus) firmly next to each other, with red (Rubeus) opposite them as a "medium". All three are granted the same status as the four other colours, which we know as green (viridis), blue (coeruleus), yellow (flavus) and orange (croceus). Fludd, who also referred himself De Fluctibus, was the author of a total of 20 works in the Latin language

— including the History of the Macrocosm and the Microcosm — which for us contain many incomprehensible ideas. He takes up the opposite view to Johannes Kepler in his writings, and introduces three principles of the world: darkness, water and divine light, the latter bringing life to everything. His work with colours appears in a book which attempts to create a "Medicina

Catholica", and although Fludd had intended to produce a universal medical textbook, only one volume ever materialised, between 1629 and 1631.

Throughout its 200 pages, Fludd occupies himself with a diagnosis of his observations on urine.

Through its colour and consistency, he attempts to draw conclusions about a patient's state of health. Fludd's basic approach, the course of which can be followed into the modern age, rests on a firm conviction concerning a metaphysical duality, manifest on earth by the opposite poles of light and darkness. The purpose of his colour circle (" Colorum Annulus ") is to trace each colour back to this duality. He also made the fundamental observation that colours are not mere coincidence ("as the ancient philosophers would maintain") but that essences were involved here with which the

Maker imbued his creations. The colours of things, in other words, are a part of their elementary make-up.

Fludd assigned values to the basic colours within his circle, in that he established how much

"brightness" (light) and how much "darkness" (blackness) was represented in them. White is light without blackness (Nigfedinis nihil), and black is an absence of light (Lux nulla). In green, there is an equilibrium of light and blackness, and in yellow there is a balance between white and red.

Orange originates if, in yellow, red increases in relation to white, and sky blue will arise if, in green, the blackness increases in relation to light. (We have shown these traces of Aristotle's theory in a second smaller diagram .)

The ideas of Aristotle thus remain influential well into the 17th century, and for this reason a short description — for which there was previously no space — is now worthwhile. In principle, it must be noted that colour theories from the Antiquity relate to a few basic colours and their corresponding mixtures. Our understanding of these theories is hindered because our language is almost incapable of expressing the terms used for colours by Greek or Latin. Translators of the Aristotelian texts, for example, have pointed out time and again that one and the same word was often used to describe various tints. This is partly because many colour names did not primarily describe a colour hue, but rather the material from which the colour can be extracted. Individual words thus cover a whole range of different brightnesses or brilliances not implied by our modern (standardised) colour phraseology.

Aristotle (384-322 B.C.) had three predecessors, who all commenced with four colours.

Empedocles (circa 500-430 B.C.) named white, black, red and yellow-ochre, to which he allocated the four elements: fire, earth, water and air. The only sure associations here, however unusual they may appear to us, are those of white with fire and black with water. Empedocles' interest was in

chemical composition, as it would nowadays be described, while Democritus (circa 460-370 B.C.) tended to adopt a physicists view, with the emphasis being placed on certain atomic relationships.

He likewise specified four colours, but replaced yellow-ochre with a greenish yellow. In addition to his primary colours, he specifies colour mixtures derived from these — seven in all: alongside yellow-red, purple, indigo, leek green and dark blue is a nut colour and a fire colour, which we are to imagine as a bright brown-yellow.

Plato (427-348 B.C.) stays with these four basic colours (white, black, red and "brilliant"). Neither chemistry nor physics are important to him. Colour is basically an element of beauty, and its shine should enhance its effect. Aristotle is in turn more practical. He restricts the basic colours to the two extremes of black and white, defined by either the absence or presence of light. Light on its own is thus white, and for that reason he assigns this to the element air. This is an important point: in

Aristotle's case, ("De sensu et sensibili") light itself is colourless. Light is only the medium by which colours can be seen — those colours, in fact, which objects possess. Colours appear at the point where a body is no longer transparent. Aristotles constructs the many colours of the world by mixing, which takes place on various levels. The five colours of his scale are formed from black and white-yellow, scarlet, purple, leek green and dark blue — which in turn can be mixed. The secondary colours arise from the juxtaposition of the smallest points of basic colours which are no longer perceivable by the human eye, from the superimposition of basic colour layers, or through blending coloured substances.

Aristotle's theories remain influential up until the time of Fludd in the early 17th century. They were not confined to Europe, having intensively occupied the Arabic philosophers, who were to reexamine the relationship between light and colour in the 11th century.

Avicenna (died 1037) disputed the existence of colours where darkness prevailed, since without light the vital "verum esse" would be denied them. His adversary Alhazen (died 1038) took the opposite view — that colours indeed exist in darkness, but did not reach the eye.

In the European Middle Ages, Roger Bacon (died 1294) looked into this question once more, declaring that light and colour only occur when combined ("Lux ... non venit sine colore"). He strongly opposed Aristotle, mainly objecting to the names of the colours and their translation. With

Bacon, the terms "albedo" (white), "rubedo" (red), "viritas" (green) and "nigredo" (black) emerge, but he also insists on a fifth colour which he calls "glaucitas", probably meaning a bright blue.

We shall close this study with a reference to the Nikolaus Cusanus (1401-1464), the Bishop of

Brixen, who was the first to express the idea that light did not so much reveal the colour of objects as create the colours themselves: "Omnis esse colores datur per lucem descendentum". And he said something delightful: the transient, earthly things, according to Cusanus' observations, change their colours when they change themselves. He thus concludes that the purpose of colours is to visually demonstrate an "ability to become". Colours, therefore, show what life can do.


Athanasius Kircher


Date: 1646

Country of origin: Germany

Basic colours: Red and blue in addition to black and white

Form: Semi-circle

Related systems: Waller — Newton — Astrological connections — Ars Magna

Summary: We will meet Athanasius Kircher once more in the metasystems, where an exciting cosmological construction has a scarab moving between the planets. His system shows a linear diagram with a trichromatic base with red, green and blue as the basic colours. Possible mixtures are indicated on half-circles. Kircher had also wondered why the sky was blue, but never reached a satisfactory answer. Our illustration shows science’s explanation of the blue sky, of which Kircher could not have known.

Bibliography:

Bibliography:

Kircher, Ars magna lucis et umbrae , Rome 1646; J. W. von Goethe,

Geschichte der Farbenlehre , Part I, Munich 1963; J. Godwin, Athanasius

Kircher A Renaissance Man and the Quest for Lost Knowledge , London

1979; John Gage, Colour and Culture, Practice and Meaning from Antiquity to Abstraction , Thames and Hudson, 1993, pp. 9 and 233 (mention and comment).

Jesuits and the Sciences (Loyola University of Chicago)

We shall encounter Athanasius Kircher (1601-1680) later, in connection with an exciting cosmological construction in which a scarab moves between the planets ( Astrological connections ). Kircher, who came from Fulda, was a versatile man whose activities included the teaching of mathematics and Hebrew. He also attempted to decipher hieroglyphs, and invented the concave burning mirror. More than 40 works by Kircher have been passed down to us, one of which appeared in 1646, and is specifically devoted to colours — The Great Art of Light and

Shadow (" Ars magna lucis et umbrae "). The first two words of the Latin title clearly point to the art of Raimundus Lullus, which will be described later ( Ars magna ). No wonder, therefore, that his system provides a firm idea of mixed colours, characterised by semi-circular bows.

The basis for all combinations is a linear construction which, apart from white (albus) and black

(niger), operates with three colours, namely yellow (flavus), red (rubeus) and blue (caeruleus). We have no need to account for all arrangements here, and neither should we attempt the translation of all the many new names — subrubeus, for example, or fuscus, or incarnatus. The special position of green (virides) is noteworthy, however: like red, green is placed in the centre, although on the plane of the mixed colours, and not the pure colours. Green is located at the overlap of yellow and blue. If we draw the bows running from white so that they are directed upwards, and the curves running to black so that they are directed downwards, an image will be created which resembles the Chinese Yin-Yang (to create this symbol, we need only retain the route through red, while omitting the lines passing through yellow and blue). As our illustration shows, all the colour points of the system can then be reached from white and black; with that it's author's fundamental view will become apparent. In fact, Kircher views colour as a "genuine product of light and shadow", as he says in the forward to his 1646 book, adding that colour is "shadowed light" and

"everything in the world is visible only by means of shadowed light or illuminated shadow."

Kircher's book contains eight chapters which deal with the multitude of colours, investigate the colours of transparent stones, or query those of plants and animals, for example. Accordingly,

Kircher wishes to know why four legged animals do not appear to be golden, and why insects and birds adopt all of the colours. Kircher also ponders why the sky appears blue — without arriving at a satisfactory explanation, however.

We know now that questions beginning with the word "Why?" always permit two kinds of answer, with only one usually being offered. Thus, the mechanical aspect of the sky's blueness can be explained by modern physics, which shows us that light reaching us from the sky is scattered. The rays of the sun collide with particles in the atmosphere and are diffused by them. If this process is examined in detail, it can be seen that different components of light are scattered in a different way, and mainly blue light will then predominate, because the wavelength of blue light is of a higher frequency. This occurs to such an extent that we are ultimately only aware of blue. (To be

more exact, physicists are able to demonstrate that if the particles on which light is scattered are sufficiently small, the intensity of diffused light is proportional to its frequency to the power of four.

That — at least according to the lessons of physics — is why the sky is blue.)

But Kircher was not, of course, seeking this kind of answer. Nor would he have understood, had it been available to him. In Kircher's day, the physics of light and colour had to bide their time. But it was not long before the appearance of the first optics which we, in our modern age, can begin to grasp. We will only tackle the question of optics properly, however, after Sir Isaac Newton takes a prism to separate the colourless light of the sun into its many colours. The prism, and its effect on light, was something already known to Kircher. He accounted for his colours by noting that the brightest occur after passing through the thinnest side of the glass, and the darkest after passing through the thickest side of the glass. He will, for the time being, be the last to consider the brightness of the basic colours and incorporate that brightness into his system. After more than

2000 years, the ordering of colours from bright to dark — as in Kirchers system — will then be lost to us, to re-emerge only during the 20th century.


Richard Waller


Date: The system was introduced in 1686 in a Catalogue of Simple and Mixt

Colours .


Basic colours: Yellow, red, blue and green

Form: Square

Related systems: Kircher — Newton — Goethe

Summary: Four basic colours —yellow, red, blue and green—are arranged on the sides of a square, the diagonals of which produce the mixtures. His square is the last "obstacle" on the way to Newton, who was occupied with optical experiments from 1670 onwards and substantiated the future arrangement of colours with a basic, physical concept. At this point, it is important to note that we find ourselves at the end of the old view which sees colours as modifications of white light through the addition of darkness. Later, of course, Johann Wolfgang von Goethe will revitalise these ideas of the turbid medium with great vigour.

Bibliography: R. Waller, "A catalogue of simple and mixt colours", Philosophical

Transactions of the Royal Society, XVI, 1686; F. Gerritsen, Entwicklung der Farbenlehre , Göttingen 1984; John Gage, Colour and Culture,

Practice and Meaning from Antiquity to Abstraction , Thames and Hudson,

1993, p.169 (mention and comment).

On the disappearance of the old order of colours from bright to dark — or from black to white — at the end of the 17th century, and at the time when Isaac Newton had introduced a new system of colours, the Englishman Richard Waller was attempting to discover if the colours could be arranged within a square. He published his attempts in order to provide a " Standard of Colours ", since he complained that until that time, standard terms of reference had not become established amongst the philosophers. This was regrettable, he said, because the science of colours exceeded the demands of medical diagnosis, and now had to serve the added purpose of

cataloguing the Creation.

We reproduce Waller's system with its four basic colours — yellow (Y), red (R), blue (B) and green (G) — which are not placed at the corners of the square, but in the middle of each respective side. The resultant mixtures can then be entered in the fields of the grid thus formed.

Waller did not determine these middle hues intuitively, but according to their weight. In other words, he mixed each basic pigment at equal proportions of weight. If we separate Waller's square into primary and secondary lines (below left, or right), the diagonals will reveal themselves as the loci of synthesis. The mixed colours — orange (O), yellow-green (YG), bluegreen (BG) and violet (V) — will then result, in the physical sense, from the forces which embrace the pure colours.

Waller published his system in about 1686 under the title Catalogue of Simple and Mixt Colours .

His square represents the final obstacle on the way to Newton , who had been occupied with his optical experiments since 1670, and had imposed a fundamental physical way of thinking upon the future order of colours. At this point, there was above all a change in the old viewpoint — which was to view the formation of colours as a modification of white light by mixing it with darkness. ( Johann Wolfgang von Goethe will, however, revitalise these ideas about the turbid medium with great vigour.) The idea that colours are not actually changes imposed on white light, but are in fact its original components, was gained through experiments with a prism. In 1648, the

Bohemian physicist Marcus Marci had used a prismatic glass for the first time, allowing sunlight to enter a darkened room through a small opening, and then directing the resultant ray through a prism. He saw a series of colours which we now call the spectrum: red, white and violet. Marci noted that the modification seemed dependent on the angle through which the light was deflected, and also remarked that coloured light cannot be subjected to further separation.

In Bologna of the same period (1650), F. M. Grimaldi discovered that small openings will leave a trail of coloured light traces. This is nowadays explained by so — called diffraction. The physics of colour — prior to Newton — then gained real momentum with Robert Hooke, who began to investigate the colours which occur if light is refracted on thin fragments of mica, or between glass plates. In his Micrographia , Hooke also made bold assumptions about the nature of light For him, a wave motion was involved, and he believed that a wave — surface perpendicular to the ray produced white light, and that the inclination of this surface gave rise to colour, which took effect on the edge of a light ray. Colours as the inclination of a wave surface — only a physicist could think of that! But the champions of science had yet more vivid ideas, and these will occupy us in some of the following plates.


Isaac Newton


Date: The famous circular arrangement of spectral colours appeared in 1704 in his central work: Opticks .


Basic colours: Red, orange, yellow, green, cyan blue, ultramarine blue, violet blue

Form: Circle

Application: Physics

Related systems: Grosseteste, Alberti, da Vinci — Aguilonius — Kircher — Waller — Mayer

— Harris — Schiffermüller — Sowerby — Goethe — Field — Maxwell —

Helmholtz — Wund t

Summary:

Bibliography:

After Newton had used a prism to separate daylight and count seven individual colours, it appeared to him that, when considering colour-hue, this was a closed system. By taking the violet end of the spectrum and linking it to the red start-point, he thus created a convincing circle of colours . With Newton’s circular shape, the transition between the one- and two-dimensional colour-system is complete. It is helpful to realise that although this step was made by a physicist, it actually has little to do with physics; it is our brain that, out of the straight line of physics, makes the circle first drawn by Newton

Newton, Opticks , London 1704 (numerous subsequent editions); K. T. A.

Halbertsma, A History of the Theory of Colour , Amsterdam 1949; R. S.

Westfall, "The development of Newton's theory of color", Isis 53 , pp 339-

358 (1962); John Gage, Colour and Culture, Practice and Meaning from

Antiquity to Abstraction , Thames and Hudson, 1993, pp. 201-203

(mention and comment).

"Newton created white from all colours. He's even fooled you, so that you will believe in secular world!" — with that, the great German poet Goethe came into conflict with Newton more than a hundred years after the British physicist had detailed a new order of colours. Newton had transformed the normal linear system into a circle, dispensing with the old organisation according to values of brightness and darkness. Using modern lettering and his original script, we can see that Newton's colour circle comprises seven colours in the sequence red (p) — orange (q) — yellow (r) — green (s) — cyan (t) — ultramarine (v) — violet (x). Black and white have been excluded, and the vacant centre of the circle has instead been expressly assigned to white in order to symbolise that the sum of all the specified colours will result in white light. Goethe protested vehemently against this idea, and therefore attacked the foundation of Newtonian optics, the basis of which is the separation of daylight by a prism.

Isaac Newton (1642-1726) can certainly be counted amongst history's most influential scientists, and his most productive period was during his youth. He had begun to develop his "method of fluxions" — nowadays known as infinitesimal calculus and making possible the mathematical treatment of speeds and accelerations — when he was just twenty two years old. Four years later, he constructed a reflecting telescope (to eliminate the irritating aberrations of its predecessors). It was also during these years that he gained the insights for which he was to become famous — Newton was able to demonstrate that an apple falling to the ground and the moon orbiting the earth both obey the same mechanical laws. In other words, he showed that the physics of the earth is likewise the physics of the heavens. The cosmos is not strange to us; our laws apply there, too.

In 1687, Newton published his greatest work, Philosophiae Naturalis Principia Mathematica , in which he propounded his ideas on gravitation and its mathematical treatment. By this time, he had also undertaken optical experiments, and had long understood that white light was made up of coloured rays. He submitted a work to the Royal Society in 1672, in which he presented "a new theory of light and colours". The plague had threatened London in the previous year, so Newton withdrew for several months to his parents' farm in the County of Lincolnshire. Here, he began by repeating Marci's experiments . In 1648, Marci had directed white light through a prism and observed its deflections. Newton took this a step further, becoming convinced that the deflected light rays ran on in a straight line after passing through the prism. In his "experimentum crucis",

Newton directed the rays which had been refracted by a first prism through a second prism. He observed that they were deflected once more, but were otherwise not altered (further separated into colours). For Newton, this was proof that colours are not modifications of white light, but are the original components of white light. White light is composed of coloured light: in fact (according to Newton), the seven colours which are located within the colour-circle. This coloured light is not a mixture. It is a single colour, and is pure. It can be mixed, of course, to produce secondary colours, but if the components combine in the correct proportions, the light will appear white.

The palette formed through the refraction of light by a prism is referred to as the colour spectrum,

the components of which are the spectral colours. The question now is, how do we explain them?

For what reason is blue light deflected (refracted) in a prism to a greater degree than red light?

An answer could only be provided if more was known about the nature of light. What actually was a light ray, which evidently moved in a straight line? Did it involve a wave, as could be seen running along a rope? Or did light comprise tiny particles (corpuscles)?

Newton attempted to clarify these questions in his second definitive work, his Opticks , which first appeared in 1704 and contained the colour-circle which we reproduce. The colours are marked here by circular figures, at their largest for red and becoming progressively smaller towards violet.

In this way, Newton reveals something of his ideas about the nature of light. He believed that light was composed of corpuscles which were deflected by a prism according to their size: the large red was subjected to the least deflection, and the small blue the most.

Let us now examine other details in Newton's colour circle . Its colours are allocated to segments, the sizes of which are proportional to their respective colour's intensity in the spectrum. Using this segment size, and the varying sizes of the light corpuscles, it was possible to calculate a type of concentration point for the circle — marked as Z by Newton — and mark it in. The straight line, which connected the white colour centre O and this centre of concentration

Z, intercepted the circle at Y. Bearing in mind Newton's love of mechanics, colour mixtures can then be represented by drawing a triangle of forces (below right), the three corners of which are formed by the three basic colours: rosso (red), blu (blue) and verde (green).

Newton's view that the nature of light was composed of corpuscles contradicted that of the

Dutchman Christian Huyge ns, who published his paper "Traité de la Lumière" in 1678. Huygens saw light as movement within a fine medium, with its motion being triggered by shocks within matter which in turn emanated light. A forerunner of this wave idea, by the way, dates back 400 years to Robert Grosseteste , who had envisaged light spreading as a "species" ("multiplicatio speciorum"). Unfortunately, in his idea, Huygens completely neglected the problem of how the spectral colours could be formed. The now accepted answer, pointing to an increase in wavelength from blue to red, remained illusive to him. It was only in the 19th century, through the diffraction of light through a grating, that measurements could be made with regard to the order of magnitude of the wavelengths involved here.

Newton's colour circle will remain inadequately explained if we ignore its inventor's belief that the propagation of both light and sound are comparable, and that they should therefore be treated harmonically in an identical way. Newton selected his seven colours because an octave displays seven sound intervals. He allocated segments to them in accordance to their value in the Dorian musical scale. The individual sound tones associated with this scale coincide with the borders between the colour grades: D, for example, with the border between violet and red; A with the border between green and blue. This mathematical-musical appropriation of colours makes it difficult for many to understand Newton's system which, with its seven (instead of five) primary colours, has more of an aesthetic basis than a scientific one.

With Newton's colour circle, the transition between the one- and two- dimensional colour system is complete. It is helpful to realise that although this step was made by a physicist, it actually has little to do with physics. The spectrum which Newton sees on the other side of his prism is a line which he can only transform into a circle because the colour tones merge into one another gradually. For this reason alone, and by dispensing with purple, the short-wave end (violet) can be joined onto the long-wave end (red). This omission in physics is overcome by our senses: out of the straight line of physics, it is actually the human brain which creates this circle, first drawn by Newton. We understand colours only when we also take into account those who see them.


Tobias Mayer


Date: In 1758, the mathematician Tobias Mayer attempted to define the number of colours that the eye can distinguish with accuracy.


Basic colours: Red, yellow and blue

Form: Triangle

Related systems: Lambert — Benson

Summary:

Bibliography:

Tobias Mayer's colour triangle was first published in 1775 by the

Göttinger physicist Georg Christoph Lichtenberg—more than 12 years after Mayer's death —in an edition which included other "opera inedita" at the suggestion of Johann Heinrich Lambert, who had used the Mayer triangle three years previously. A colour-triangle operates with the three basic-colours cinnibar, massicot and azurite and gives all mixtures in which at least one twelfth of another colour is added to a base-colour.

Black and white are treated as the representatives of light and darkness, which in turn either lighten or darken the colours.

T. Mayer, De affinitate colorum commentatio , Göttingen 1775; J. W. von

Goethe, Geschichte der Farbenlehre , Part II, Munich 1963; K. T. A.

Halbertsma, A History of the Theory of Colour , Amsterdam 1949.

In 1758 — more than half a century after Newton's Opticks had appeared — the German mathematician and astronomer Tobias Mayer (17231762) gave a lecture to the Göttingen

Academy of Science entitled "De affinitate colorum commentatio" ( historical system ), in which he tried to identify the exact number of colours which the eye is capable of perceiving. He chose red, yellow and blue as his basic colours, and vermillion, massicot and azurite as their representatives amongst the pigments. Black and white were considered to be the agents of light and darkness, which either lighten of darken the colours.

For Mayer, it is clear that very small variations in colour are not noticed by the eye, and for this reason the difference between mixtures cannot be selected freely. In order to have a basis for calculation, Mayer adopted twelve gradations — similar to an octave — between any two basic colours, and claimed that mixing of such a twelfth part of a colour into a base colour was essential in order to perceive the new mixture. He then made the following — although rather obvious — note: cinnabar is characterised by r12 (12 units of red), massicot by y12 (12 units of yellow), and azurite by b12 (12 units of blue). Mixtures are rated, for example, as r6y6 (6 units of red, and 6 units of yellow to give orange), b6y6 (6 units of blue and 6 units of yellow to give green), or r6b6 (6 units of red and 6 units of blue to give violet). Through placing the pure colours r12, b12 and y12 at the corners of a triangle, Mayer constructed a geometrical figure which systematically states how 91 chromatic colours, for example r4b5y3 or r2b8y2, were created.

Tobias Mayer's colour triangle was first published in 1775 by the Göttinger physicist Georg

Christoph Lichtenberg — more than 12 years after Mayer's death — in an edition which included other "opera inedita", at the suggestion of Johann Heinrich Lambert ( illustration ), who had used the Mayer triangle three years previously. Mayer's original showed a planar figure with 91 compartments, but at the close of his lecture had also mentioned that each of the constructed

(mixed) colours could be modified towards bright or dark by adding up to four parts of white or black. The aggregate of theoretically distinguishable colours in his system therefore rises by 2 x

5 x 91, to 910. The position that each colour could adopt is shown in the figure, with its superimposed triangles, as described by Mayer but not graphically illustrated. The basic triangle is located in the middle position, with grey at its centre. The proportion of black (BK) increases in the downwards direction, with white (W) being added in the upwards direction. R

stands for red, Y for yellow and C is for cyan. However, the construction does not work out — it contains an anomoly. The grey centre of the basic triangle is, in fact, already so dark that the central area beneath it can only be repeated, and offers no further opportunity for gradation.

Mayer is famous within the world of astronomy for his exact measurements, and he has earned great credit with his methods for detecting instrument errors. His most significant contribution was made in 1760, when he was able to show that fixed stars had their own motion, and are not actually quite as fixed as had been assumed up to that time. Although this observation owed something to the Theory of the Heavens , brought out in 1755 by the philosopher Emmanual

Kant, in nevertheless encouraged Lambert, the above mentioned Alsation naturalist, to attempt

— from 1761 onwards — to provide a new theory of the universe in his Cosmological Letters .

Thus, Mayer twice provided impetus to the contemporary world view — with the stars, and with colours.


Tobias Mayer


Date: In 1758, the mathematician Tobias Mayer attempted to define the number of colours that the eye can distinguish with accuracy.



Form: Triangle

Related systems: Lambert — Benson

Summary:

Bibliography:

Tobias Mayer's colour triangle was first published in 1775 by the

Göttinger physicist Georg Christoph Lichtenberg—more than 12 years after Mayer's death —in an edition which included other "opera inedita" at the suggestion of Johann Heinrich Lambert, who had used the Mayer triangle three years previously. A colour-triangle operates with the three basic-colours cinnibar, massicot and azurite and gives all mixtures in which at least one twelfth of another colour is added to a base-colour.

Black and white are treated as the representatives of light and darkness, which in turn either lighten or darken the colours.

T. Mayer, De affinitate colorum commentatio , Göttingen 1775; J. W. von

Goethe, Geschichte der Farbenlehre , Part II, Munich 1963; K. T. A.

Halbertsma, A History of the Theory of Colour , Amsterdam 1949.

In 1758 — more than half a century after Newton's Opticks had appeared — the German mathematician and astronomer Tobias Mayer (17231762) gave a lecture to the Göttingen

Academy of Science entitled "De affinitate colorum commentatio" ( historical system ), in which he tried to identify the exact number of colours which the eye is capable of perceiving. He chose red, yellow and blue as his basic colours, and vermillion, massicot and azurite as their representatives amongst the pigments. Black and white were considered to be the agents of light and darkness, which either lighten of darken the colours.

For Mayer, it is clear that very small variations in colour are not noticed by the eye, and for this reason the difference between mixtures cannot be selected freely. In order to have a basis for calculation, Mayer adopted twelve gradations — similar to an octave — between any two basic

colours, and claimed that mixing of such a twelfth part of a colour into a base colour was essential in order to perceive the new mixture. He then made the following — although rather obvious — note: cinnabar is characterised by r12 (12 units of red), massicot by y12 (12 units of yellow), and azurite by b12 (12 units of blue). Mixtures are rated, for example, as r6y6 (6 units of red, and 6 units of yellow to give orange), b6y6 (6 units of blue and 6 units of yellow to give green), or r6b6 (6 units of red and 6 units of blue to give violet). Through placing the pure colours r12, b12 and y12 at the corners of a triangle, Mayer constructed a geometrical figure which systematically states how 91 chromatic colours, for example r4b5y3 or r2b8y2, were created.

Tobias Mayer's colour triangle was first published in 1775 by the Göttinger physicist Georg

Christoph Lichtenberg — more than 12 years after Mayer's death — in an edition which included other "opera inedita", at the suggestion of Johann Heinrich Lambert ( illustration ), who had used the Mayer triangle three years previously. Mayer's original showed a planar figure with

91 compartments, but at the close of his lecture had also mentioned that each of the constructed (mixed) colours could be modified towards bright or dark by adding up to four parts of white or black. The aggregate of theoretically distinguishable colours in his system therefore rises by 2 x 5 x 91, to 910. The position that each colour could adopt is shown in the figure, with its superimposed triangles, as described by Mayer but not graphically illustrated. The basic triangle is located in the middle position, with grey at its centre. The proportion of black (BK) increases in the downwards direction, with white (W) being added in the upwards direction. R stands for red, Y for yellow and C is for cyan. However, the construction does not work out — it contains an anomoly. The grey centre of the basic triangle is, in fact, already so dark that the central area beneath it can only be repeated, and offers no further opportunity for gradation.

Mayer is famous within the world of astronomy for his exact measurements, and he has earned great credit with his methods for detecting instrument errors. His most significant contribution was made in 1760, when he was able to show that fixed stars had their own motion, and are not actually quite as fixed as had been assumed up to that time. Although this observation owed something to the Theory of the Heavens , brought out in 1755 by the philosopher Emmanual

Kant, in nevertheless encouraged Lambert, the above mentioned Alsation naturalist, to attempt

— from 1761 onwards — to provide a new theory of the universe in his Cosmological Letters .

Thus, Mayer twice provided impetus to the contemporary world view — with the stars, and with colours.


Johann Heinrich Lambert


Date: The astronomer J. Heinrich Lambert, strongly influenced by the work of

Tobias Mayer, presented the first three-dimensional colour-system in

1772.


Basic colours: Cin nibar, King’s yellow and azurite

Form: Triangle

Application: Determination of textile colours

Related systems: Mayer — Sowerby — Runge — Bezold — Wundt

Summary: The system attempts to explain the alternating relationships between the colours using a triangular pyramid . The base triangle is black at its centre and carries the basiccolours of cinnibar, King’s yellow and

Bibliography: azurite out to the corner points. The seven layers of the pyramid gradually increase in brightness to the white tip. Lambert believed that his system could help textile merchants decide if they stocked all colours; he also hoped that the dyers and printers of his time would find inspiration for their mixtures.

J. H. Lambert, Beschreibung einer mit dem Calaunischen Wachse ausgemalten Farbenpyramide , Berlin 1772; H. Matile, Die Farbenlehre

Philipp Otto Runges , 2nd edition, Munich 1979; W. Spillmann, "Color

Systems", in H. Linton, Color Consulting , New York 1992, pp. 169 -

183.

The Alsation mathematician and naturalist Johann Heinrich Lambert (1728-1777) is renowned amongst physicists as the founder of the theory of light measurement, which at that time was known as "photometria". In about 1760, Lambert originated the law governing the illumination of a surface by a light source which still bears his name. He also studied the ability of surfaces to reflect, and their transparency. His Cosmological Letters , written as a member of the

Academy of Frederick the Great in Berlin, are famous amongst astronomers. Lambert attempted to explain the structure of the universe in these writings — at that time it was not known just how extensive our galaxy, the milky way, actually is. In the course of his deliberations, he consulted measurements taken by Tobias Mayer in Göttingen, and thus became aware of Mayer's colour-triangle dating from 1758, the publication of which he was to subsequently support. Lambert recognised that Mayer had discovered a means of constructing and naming many of the possible colours, and at the same time also recognised that, to extend its coverage to include their full abundance, the only element missing from this triangle was depth. After carrying out his own experiments, Lambert suggested a pyramid constructed from a series of triangles ( historical illustration ) to accommodate the full richness of natural colours in one geometrical form. These differ from Mayer's triangles not only in their size, but also in the position of black.

As with Mayer's model , the corners of Lambert's base triangle are occupied by King's yellow, cinnabar (shown here as Y for yellow and R for red) and azurite. In each case, two basic colours are mixed (with varying proportions) to form seven hues along the sides, while on the inside all three basic colours contribute to the colour of each respective surface unit. A total of

45 colour-hues are thus formed in the lowest triangle, above which the others rise, tapering and becoming brighter as they proceed upwards. In turn, they contain 28, 15, 10, 6, 3 and finally 1 field. Lambert accommodates a total of 108 colours or their mixtures in his pyramid, the tip of which is white.

This construction succeeds in incorporating the various "tertiary colours" into one system, and logically links them with the neutral grey values appearing along its central axis. The colour created by mixing all basic colours — black — is found at the centre of the lowest triangle.

More colours can be distinguished on this plane than at the point where white predominates, demonstrating that the system of colours must taper upwards, and is a therefore a pyramid.

Lambert believed that textile merchants, after consulting his system, would know if they stocked all the colours, and if there were gaps in their range. He also hoped that the dyers and printers of his time would find inspiration for their mixtures.

As a naturalist, Lambert used his pyramid in his efforts to identify and classify all the colours which occur in animals and plants. Of course, this objective can only be achieved if a mixing system, operating with the three colours yellow, red and blue, is capable of creating each colour. Unfortunately, this is not possible. In nature, there are many tints of very colourful green, orange or violet which cannot be created by subtractive mixing of three primary colours.

Many colours in a butterfly, for example, are formed not by a mixture of this kind or specific dyes, but through the physical properties of light: interference, in other words, through thin leaflike structures. The abundance of colours thus created reaches far beyond the pyramid in

which Lambert wished to confine them.


James Sowerby


Date: Sowerby introduced his colour-system in 1809 as a tribute to the "great

Sir Isaac Newton".


Basic colours: Red, yellow und blue

Form: Modified triangle

Related systems: Harris — Lambert — Runge — Hayter — Maxwell — Ebbinghaus

Summary: The complete title of Sowerby’s work describes his main concern: A

New Elucidation of Colours, Original Prismatic and Material: Showing

Their Concordance in the Three Primitives, Yellow, Red and Blue: and the Means of Producing, Measuring and Mixing Them: with some

Observations on the Accuracy of Sir Isaac Newton . Sowerby’s system originated at the same time as the English doctor and physicist

Thomas Young submitted his theory (later to be confirmed) stating that the eye generates all colours by combining only three wavelengths.

This "Theory of Trichromatic Vision" is also based on the primary additive colours red, green and blue.

Bibliography: J. Sowerby, A New Elucidation of Colours, Original, Prismatic, and

Material: Showing their Concordance in Three Primitives, Yellow, Red, and Blue: and the Means of Producing, Measuring, and Mixing Them: with Some Observations on the Accuracy of Sir Isaac Newton»,

London 1809 . "Color Documents: A presentational Theory", organised by S. Wurmfield, Hunter College Art Gallery, New York 1985; John

Gage, Colour and Culture, Practice and Meaning from Antiquity to

Abstraction , Thames and Hudson, 1993, p. 221 (mention and comment).

At the beginning of the 19th century, the Englishman James Sowerby (1757 - 1822) — already distinguished as an author of books on botany and natural history — introduced his colour system , which he dedicated to "the great Isaac Newton". It had the lengthy title A New

Elucidation of Colours, Original Prismatic and Material: Showing Their Concordance in the

Three Primitives, Yellow, Red and Blue: and the Means of Producing, Measuring and Mixing

Them: with some Observations on the Accuracy of Sir Isaac Newton . Sowerby sets himself two tasks with this work, which appeared in London in 1809: he wishes to re-emphasise the significance of brightness and darkness, which after Newton had fallen into obscurity; and he wishes to clarify the difference which exists between colours. Johann Heinrich Lambert has already emphasised that the colours of light and the colours of materials behave in a different way when mixed. In his system, Sowerby assumes the existence of three basic colours, red, yellow and blue (he actually selects gamboge — a poisonous yellow sap from Asiatic plants — carmine and Prussian blue, which are then combined).

The sketches emphasise the three parts on which Sowerby's theory rests and express the stabilising continuity which can exist between them. Incidentally, Sowerby's attempt to

transform Newton's seven primary colours into three materially renderable basic colours attracted the attention of the English painter William Turner (the two were, in fact, acquainted).

Later, in about 1820, Turner followed the painter Otto Runge in trying to assimilate the system of the three colours red, yellow and blue into a diurnal pattern (for which there is more than just one possibility, as was soon apparent).

Sowerby's text describes the optical mixtures which result when narrow and tightly packed strips of primary colour are applied to paper. It was to be another few decades, however, before the difference between colours was correctly understood, enabling a more precise distinction between colour mixtures. Coloured light is mixed additively, to use the modern term.

That is to say, the sum of light rays with varying sprectral content (emanating, for example, from two lamps) will result in a new colour. Unlike the ear, the eye and the brain do not analyse the incident wavelengths; they create a new impression — in other words, a new colour.

The additive mixture of red and green will, for example, result in yellow. Violet-blue together with green will give cyan. Two colours which additively neutralise each other and combine to form white are called complementary colours. The appropriate experiments will show that there are three such pairs: green and magenta; violet-blue and yellow; and red and cyan — to use their most exact possible descriptions.

Coloured pigments have an effect that is very different to coloured light. Whereas yellow light comprises light of a definite wavelength, the colour of a yellow pigment is formed by the absorption of yellow's complementary colour: namely, violet-blue. The subtractive mixture of a yellow and a violet-blue pigment will not result in white, but black. This also applies for both remaining complementary colour pairs: red and cyan but green and magenta will result in a pigment which does not reflect light and is therefore black.

Here, we can point to a few distinctions which have traditionally always been blurred. To ignore them will always lead to confusion. Additively , the mixing of complementary colours will result in white; substractively , their mixture will result in black. Subtraction commences with all colours (white) and ends without light (black); addition begins without light (black), ending when all wavelengths are present (white). If — as is frequently the case — red, green and blue are regarded as the three additive primary colours because they deliver the largest palette of mixed colours, then for the same reason the subtractive primary colours should be pigments which absorb red, green and blue. In other words, the corresponding subtractive colours will be cyan magenta and yellow.

Of Sowerby's three basic colours — red, yellow and blue — we have exchanged yellow for green. Sowerby's system originated at the same time as the English doctor and physicist

Thomas Young (1773-1829) submitted his theory (later to be confirmed) stating that the eye generates all colours by combining only three wavelengths. This "Theory of Trichromatic

Vision" is based on the primary additive colours red, green and blue. Young first arrived at his ideas for a trichromatic theory in 1801, when he explained that the eye cannot record each of the almost infinite number of colours separately; most probably, it records them rather more sparingly: "Since it is hardly possible to believe that each light sensitive point on the retina contains an infinite number of particles, which must all be in a position to oscillate with the respective wave in full agreement, it is therefore necessary to assume that this number is, for example, limited to the three main colours red, yellow and blue".

This is not a typographical error. Young had first introduced the trio of colours with which the trichromatic theory is now linked in his "Lectures on Natural Philosophy and Mechanical Arts", dating from 1807. "It is necessary", he wrote at the time, "to modify the assumption which I made in my last paper ... and to replace red, yellow and blue with red, green and violet."

Because the violet used by Young appeared to his successors to be more like blue, for reasons of simplicity red, green and blue are now associated with the "Trichromatic Theory of

Vision".

The theory was brilliantly confirmed in the 1960s when a team of mainly English physiologists

and biochemists succeeded in proving that three different types of colour sensitive cells — the so called cones — exist on the human retina. They contain pigments which can chiefly receive

(absorb) blue, red and green light. Technical language refers to the absorption peak of photosensitive cells, and we can now specify the their wavelengths: 425 nanometres (nm) for blue,

535 nm for green and 570 nm for red. (The wavelengths of light were measured for the first time shortly before Young's death.)

The first step in the perception of colours is therefore exactly how Young had imagined it at the beginning of the 19th century; the second step, however, seems to be a very different matter.

Young had assumed a direct transmission of the received signals into the brain, imagining each nerve fibre that entered the brain to be composed of three parts, each responsible for transmitting one of the main colours which appear in the eye. Closer inspection reveals that the processing of colour information does not appear quite so straightforward. Although ideas suggested by psychologists at the end of the 19th century have also been confirmed — we will be looking more closely at this, but must adhere to the historical sequence, also with the route between the eye and the brain — the true process has only been understood to a greater or lesser degree during the last few decades.


Ignaz Schiffermüller

Navigation:

Date: The colour-circle was published in Vienna in 1772.

Country of origin: Austria

Basic colours: Red, blue, green and yellow

Form: Circle

Related systems: Newton — Lambert

Summary: red (Navigator) or bold (Explorer) = illustrations ///// blue = text

Bibliography:

A colour-circle based on four colours, red, blue, green and yellow, divided into a total of 3 x 4 = 12 segments. Orange and violet, which

Schiffermüller saw as being insufficiently strong, cannot be counted amongst the "subsidiary colours". In part, his colour-circle is provided with rather fanciful names: blue, sea-green, green, olive-green, yellow, orange-yellow, fire-red, red, crimson, violet-red, violet-blue and fire-blue.

Schiffermüller, Versuch eines Farbensystems , Vienna 1772; C.

Parkhurst and R. L. Feller, "Who invented the Color Wheel?", Color

Research and Application 7 , pp. 217-230 (1982); John Gage, Colour and Culture, Practice and Meaning from Antiquity to Abstraction ,

Thames and Hudson, 1993, p. 170 (mention and comment).

In the same year that J.H.Lambert constructed his colour pyramid and demonstrated for the first time that the complete fullness of colours can only be reproduced within a three dimensional system, another colour circle was published in Vienna by Ignaz Schiffermüller.

The circumference of Schiffermüller's circle is filled with twelve colours to which he has given some very fanciful names: blue, sea-green, green, olive-green, yellow, orange-yellow, fire-red, red, crimson, violet-red, violet-blue and fire-blue. The transitions are continuous — in marked contrast to Moses Harris — and the three primary colours of blue, yellow and red are not placed at equal distances from each other; between them come three kinds of green, two

kinds of orange and four variations of violet (excluding the secondary colour violet).

Schiffermüller selects a total of 12 colours and thus draws upon the system originated by the

French Jesuit Louis Bertrand Castel, who had published his Optique des couleurs in 1740 in order to extend Newton's circle with its seven colours up to twelve. His choice sounds unusual: bleu, celadon (pale green), vert, olive, jaune, fauve (pale red), nacarat (orange), rouge, cramoisi, violet, agathe (agate blue) and bleu violant. Castel linked his system to music

— more specifically, the twelve semi-tones of the musical scale.

But whereas Castel attempted to undermine Newton's theory and reject it, Schiffermüller's undertaking achieved the exact opposite: his system served to illustrate Newton's discovery that the pure colours could be arranged in a circle. The Viennese entomologist — a butterfly specialist — was one of the first to arrange the complementary colours opposite one another: blue opposite orange; yellow opposite violet; red opposite sea green. Schiffermüller also placed a sun (only suggested here) inside his colour circle in order to emphasise that he wished to show "the radiant colours" produced by nature. Whilst wishing to achieve "vivacious and gleaming colours" like the wondrous colours of the rainbow, he considered further combinations of "subsidiary colours" as aesthetically unsuitable.

By 1771, Schiffermüller had come to feel that it was time to treat colours as a natural system and bestow upon them a kind of natural order — exactly as had been done for so long with animals, plants and minerals. Such an order would have been an indispensable aid to the descriptive methods common amongst naturalists at the end of the 18th century. In his Colour and Culture , John Gage recounts the story told by the painter William Williams in 1787 about an entomological illustrator who, "living in a remote country, unacquainted with artists, or any rational system of colours, with a patience that would have surmounted any difficulties, had collected a multiplicity of shells of colour, of every various tint that could be discerned in the wing of that beautiful insect [the butterfly]; for he had no idea that out of two he could make a third, by this method he had collected two large hampers full of shells, which he placed on each side of him, and sometimes the individual tint he wanted, was half a day's labour to find out. What excellence must he have arrived at, had he known how to mix his tints."


J. W. von Goethe


Date: The problem of colours had occupied Goethe from 1791. His work Theory of Colours appeared in 1810.


Basic colours: Yellow, blue and red [purple]

Form: Circle

Related systems: Aguilonius — Waller — Newton — Runge — Chevreul —

Bezold

Summary: Goethe proesented a circular diagram in which the three primary colours of red, blue and yellow alternate with the three secondary colours of orange, violet and green. Red occupies the uppermost place in the circle, and green the lowermost.

The semi-circle from green, through yellow to red is known as the plus side; its opposite is the minus-side ( Original drawing of Goethe ). Goethe sought to surpass Newton’s system. With

Bibliography: his insight into the sensual-moral effect of colours, Goethe comes nearer to his initial objective: namely, to bring order to the more chaotic, aesthetic aspects of colour. He places colouration within the separate categories of "powerful",

"gentle" and "radiant" and, accordingly, sets down his concept.

J. W. von Goethe, Theory of Colours , Tübingen 1810; J. W. von Goethe, Geschichte der Farbenlehre , parts I and II, Munich

1963; J. W. von Goethe, Theory of Colours , didactic volume,

Munich 1963; W. Heisenberg , "Die Goethesche und die

Newtonsche Farbenlehre im Lichte der modernen Physik" in

Gesammelte Werke , Volume CI, Munich 1984, pp. 146-160;

John Gage, Colour and Culture, Practice and Meaning from

Antiquity to Abstraction , Thames and Hudson, 1993, pp. 201 -

205.

100 years after Newton, Johann Wolfgang Goethe (1749-1832) examined the problems of colour and although his Theory of Colours was intended to attain "a more complete unity of physical knowledge" by including all branches of the natural sciences, Goethe approached the subject primarily to gain some knowledge of colours

"from the point of view of art". In a letter to Wilhelm von Humbolt in 1798, Goethe explained that by embarking on his History of the Theory of Colours he had also hoped to create a "History of the Human Spirit in Miniature".

Goethe's first Contributions to Optics were produced in 1791 after experiencing the difficulties encountered by contemporary artists with colouration and colour harmony at first hand on his journey through Italy. "Indeed, I heard tell of cold and warm colours, and colours which enhance one another, and suchlike", but everything "turned in an odd circle ... of confusion".

Between 1790 and 1823, Goethe documented the subject of colours in some 2000 pages, most of which appeared between 1808 and 1823 under the title Theory of

Colours . He evolved his system from the elementary opposition of light and dark (which was not a part of Newton's work). In his paper On the Order of Colours and Their

Relationship to Each Another , Goethe establishes that, as totally pure colours, only yellow and blue "can be perceived by us without being reminiscent of something else".

The opposite poles are formed by the yellow most easily compared with brightness

("next to light") and the blue most related to darkness ("next to blackness"), between which all other colours can be grouped.

When, in 1793, Goethe sketched his colour-circle , he did not place this basic pair of yellow (giallo) and blue (blu) opposite each other but extended them into a triangle together with a red, which was originally described as purple (rosso). He described

"this red effect" as the "highest augmentation" of the series of colours leading from yellow to blue, and placed green (verde), arising from the mixing of yellow and blue, opposite. The circle is completed by an orange (arancio) on the ascending side and by a blue-red (porpora) on the descending side (often described as violet) ( Original drawing of Goethe ).

Next to the circle, in various small triangles , we have shown a few alternative possibilities for the layout of the large triangle — similar to Joseph Albers in his

Interaction of Color (1963) — in order to demonstrate an "expressive colour accord".

The first case shows the series of primary colours (1.1), secondary colours (1.2) and tertiary colours (1.3); in the second case, we give an impression of what, from the

"sensual-moral" point of view, Goethe explained as force (2.1), sanguineness (2.2) or melancholy (2.3). (The following paragraph will provide more on this subject.) The third case emphasises the three axes of the complementary colours: red (3.1), yellow (3.2)

and blue (3.3). Finally, we accentuate brightness (4.1) and intensity (4.2).

Goethe referred to the part of his circle running from yellow to red as the plus side and its continuation into blue as the minus side, and arrived at the following arrangement: the yellow was associated with "effect, light, brightness, force, warmth, closeness, repulsion"; and blue with "deprivation, shadow, darkness, weakness, cold, distance, attraction". It is suggested that Goethe's intention was mainly to ascertain the "sensualmoral" effect of individual colours "on the sense of the eye ... and the eye's imparting on the mind". He understands colours mainly as "sensual qualities within the content of consciousness" and thus transfers his analysis into the area of psychology. The colours on the plus side "induce an exciting, lively, aspiring mood". Yellow has a

"splendid and noble" effect, making a "warm and comfortable" impression. The colours on the minus side, however, "create an unsettled, weak and yearning feeling". Blue

"gives a feeling of coldness".

With his insight into the sensual-moral effect of colours, Goethe comes nearer to his initial objective: namely, to bring order to the more chaotic, aesthetic aspects of colour.

He places colouration within the separate categories of "powerful", "gentle" and

"radiant", and propounds the following ideas: the powerful effect will arise if yellow, yellow-red and purple predominate, with the gentle effect mainly being determined by blue and its neighbours. If "all colours are in equilibrium", an harmonious colouration will arise which can produce radiance and also pleasantness. (The philosopher Ludwig

Wittgenstein, by the way, notes in his Remarks concerning colours : "I doubt that

Goethe's remarks about the character of the colours would be much use to a decorator, let alone a painter").

Whoever should compare this short description of Goethe's Theory of Colours with

Newton's preferred approach will soon become aware of two completely different attitudes to the one, single theme. These attitudes do not oppose each other, however; they complement each other — alone, neither of the systems can cover all aspects of colour completely. Their relationship can best be described as "complementary", implying a deeper meaning here than the term used for colours. Newton's analysis of colours is to be seen as complementary to Goethe's. Neither of the theories is wrong; each independently reproduces a valid aspect of our world, and substantiates the other. Goethe is only wrong when he maintains that Newton was misled, indeed "twice and three times over".

In order to bring life to this idea of complementarity, we can compare the English scientist's and the German poet's beliefs: what for Newton is simple — pure blue, for example, being light with one wavelength ("monochromatic light") — is complicated for

Goethe, since pure blue must first of all be prepared by an extravagant means and is therefore artificial. In contrast, white light is simple for Goethe, since it exists completely naturally and without effort; Newton, on the other hand, sees in white light a mixture of all colours. White light is not simple for Newton; it is a combination.

Thus, what Goethe regards as a unity, a whole — "das Schauen" — disintegrates with

Newton (and his successors) into many parts. For Newton, the act of viewing colour commences with a reaction in the eye which, to be understood, requires more detailed knowledge of the retina; the circuit of nerve cells; the different stages which signals pass through on their way to the brain; and the regions in the brain which, through the generation of electrical signals, create sight.

The essential complementarity of both colour theories becomes evident when we consider the role of the subject — the human being. While Goethe, as a matter of course, views the human being as central, Newton omits him totally. Here, two complementary truths meet: Goethe presents the direct truth of sensuary perception as a counterbalance to the remote truth of Newton's science; Newton distances himself from a notion of the world ("the pure human sense" as Goethe would have it). Indeed,

Goethe expressively employs such a notion to obtain clarity about the nature of

colours. Something troublesome arises here, creating a certain tension. The opposite of one deep truth (in this case from Newton) is not something which is wrong; it is another deep truth (that of Goethe).


Philipp Otto Runge


Date: The painter Runge introduced his spherical construction in 1810 after eight years work with colours.


Basic colours: Blue, red and yellow

Form: Sphere

Related systems: Lambert — Goethe — Benson

Summary: The colour-sphere has the pure colours around the equator, starting with the three primary colours of red, yellow and blue.

Three mixed colours take their place in each of the equal intermediate spaces between the primaries, while white and black form the sphere’s poles. Runge wished to capture the harmony of colours —not the proportions of mixtures. He wished to bring a sense order to the totality of all possible colours, and sought an ideal colour-solid.

Bibliography: links:

Ph. O. Runge, Farbenkugel , Hamburg 1810; J. Pawlik, Theorie der Farbe , Cologne, 1976; H. Matile, Die Farbenlehre Phillip

Otto Runges , 2nd edition, Munich 1979; John Gage, Colour and

Culture, Practice and Meaning from Antiquity to Abstraction ,

Thames and Hudson, 1993, p. 221 (various illustrations; mention and comment). Catalogue , Runge Centre, Wolgast,

Germany.

xterna-net.de : Runge's colour system (interesting illustrations)

The system of Philipp Otto Runge built as a virtual colourspace .

In 1810, the year in which Goethe's Theory of Colours with its colour-circle ( original drawing of Goethe ) was published, the painter Philipp Otto Runge presented his work on a "colour-sphere". As suggested by its title, Runge was concerned with the

"construction of the proportion of all mixtures of the colours with each other, and their complete affinity"( original drawing of Runge ). Runge's sphere appeared in the year of his death — the painter died at the age of only thirty three. His colour system, once described in an encyclopedia as "a blend of scientific-mathematical knowledge, mystical-magical combinations and symbolic interpretations", represented the sum total of his endeavours. Runge's colour globe is seen as marking the temporary end to a development which had led from linear colours via the two-dimensional colour-circles to a spacial arrangement of colours in the form of a pyramid.

In the three basic colours of blue, red and yellow (which to Runge, as a painter, were

subtractive), Runge saw the "simple symbol of the Holy Trinity". He had written this in a letter in 1803. To him, black and white were not mere colours since "light is goodness, and darkness is evil".

The way to the sphere begins with the colour circle which he drew in a letter to Goethe in 1806 (extracts of which were quoted in the didactic part of Goethe's colour system):

"It is apparent that only three colours exist, and these are yellow, red and blue. If we accept these in all their potency, and if we imagine them arranged within a circle, then three transitional areas of orange, violet and green will be formed (I shall describe everything which falls between yellow and red as orange, or which inclines towards red from yellow or the reverse) and in their middle position these are at their most brilliant and are the pure mixtures of colours." The three pure colours as well as the mixed colours terminate in the grey of the centre. Grey, of course, can also be mixed from black and white. In 1807, Runge transferred his attention to his model of a "globe" so that the relationship of the colours to white and black could be made comprehensible in the geometrical sense. The colour-sphere originated from this in 1809, the poles of which are black and white. The pure colours run along the equator with equal spacing.

Each colour placed on the surface of the sphere can move in five directions: towards the colours to the right or to the left; up towards white; down towards black; and inwards to the pass the grey of the centre and continue in the direction of its complementary colour.

In the introduction to his colour system, Runge complains that artists have been abandoned by scientists because scientists ignored those effects of colour "not explained merely by the refraction of the ray of light". His objective was "to enquire into the mutual relationships of the given colours .... in order that our impressions of their compositions and the altered appearances arising out of their mixtures can be deduced in a definite way, and can each time be reliably repeated when using our materials." He viewed colours as "a fixed, indeed independent phenomenon" and for this reason his investigations can be regarded "as fully remote from science, in the same way as colours themselves originate out of light". Runge selected the perfect symmetry of the sphere (and not the restricted symmetry of a double cone) because he believed that only by this means could "a completely neutral grey" occur at its centre. Only in this way could the diametrically opposed colours on the surface of the sphere resolve themselves at its central point ( illustration ). Runge did not want his colour-sphere to be understood as "a product of art" but presented it as a "mathematical figure of various philosophical reflections".

Naturally, Runge knew of Lambert's pyramid ( historical illustration ), but he wanted to place the pure colours at the same distance from white and black and thus decided on a round construction which was also easier to associate with the divine order of the cosmos. Nevertheless, it was clear to him that his proposals could only be an imperfect representation of the ideal sphere, and he must also have been aware that the subtractive colour mixture (this being the only possibility with regard to his paints) did not produce the neutral, middle grey that was so vital to him. Runge may have had something different to Lambert in mind. Lambert had mainly wished to present a practical system as an aid to the mixing of colours, whereas Runge did not want to vividly record the proportions of mixtures, but rather the harmonies of colours. He wanted to bring a sense of order to the totality of all possible colours — an order which is defined by a means other than language, as he stated in a letter to Goethe: "If we try to think of a blueish orange, a reddish green or a yellowish violet, it is like trying to imagine a southwesterly north wind". His sphere aimed at the creation of a genuine colour-system, an attempt not surpassed during his century.


Charles Hayter

Navigation:

Date: red (Navigator) or bold (Explorer) = illustrations ///// blue = text

Charles Hayter’s work appeared in 1826 in London and described how all colours could be obtained from just three.



Form: Triangle

Related systems: Harris — Sowerby — Maxwell — Helmholtz — Pope

Summary: Based on physisist Thomas Young’s theory that all colours can be mixed from the three basic colours of red, blue and yellow,

Hayter composed a disc-shaped compendium with black at its centre. But Hayter does not here distinguish between additive mixtures of light and subtractive mixtures of pigments. From the point of view of scientific histroy, Hayter’s system belongs to an era in which the argument —which had continued since the time of Newton —about the nature of light and whether it was composed of waves or particles seemed finally to have been resolved. This is therefore a good time to comment on related research from the first half of the 19th century.

Bibliography: Ch. Hayter, A New Practical Treatise on the Three Primitive

Colours Assumed as a Perfect System of Rudimentary

Information , London 1826; F. Birren, Principles of Color , New

York 1969; W. Spillmann, "Color Systems", in: H. Linton, Color

Consulting , New York 1992, pp. 169-183.

In 1826, the English architect and painter Charles Hayter (1761-1835) published a book in which he recommended Young's trichromatic theory as a practical basis for colour reproduction (see text in plate 13). According to its subtitle, his "compendium" of colours was intended to "show as examples the natural and inevitable consequences of simultaneous combination which result through gradual and systematic concentration of the three primary colours according to the recommendations of Leonardo da Vinci ".

Hayter claims in his foreword that he already had a mental image of the diagrams and explanations (which he intended as a guide for painters) in 1813, and had previously never heard or seen anything of Moses Harris, who had touched upon much of what

Hayter now expounded. We must here point out a contradiction: although Hayter, as a painter, wished to provide a system for subtractive mixtures, he does not quote the appropriate forerunners of this line of thought, but refers to Leonardo, Newton and

Young, all of whom tended to think in terms of an additive system. Nevertheless, he sees with unusual clarity that a difference must be drawn "between the properties of such materials as give their colours in substances suitable to the purposes of art, and the transient effects of LIGHT, which must not be considered as belonging to a system of mixing colours for the purpose of painting." Although Hayter did not — either generally or in detail — analyse this difference for the purposes of painting, he comes to the conclusion that "all transient or prismatic effects can be imitated with the Three Primitive

Colours ... but only in the same degree of comparison as white bears to LIGHT."

Hayter's basic triangle , comprising the three subtractive primary colours yellow, red and blue, is naturally by this time no longer an unknown construction, and we can

recognise the black centre as being from Moses Harris at the latest. It is thus difficult to judge the originality of Hayter. We are already familiar with the Frenchman J. C. Le Blon .

In a short paper completed prior to 1731 Le Blon was the first to introduce the group of three — made famous by Goethe — of yellow - red - blue as a subtractive trio of primary colours. His view about the fundamental character of his primary colours has been available in print since 1756 under the title L'Art D'Imprimer Les Tableaux , in which he provides instructions about the use of his basic colours for printing, weaving and painting. Le Blon is proud of his construction, and specifically mentions that many of his colleagues did not believe that there were indeed such simple rules about art.

Hayter examines these concepts in greater detail (perhaps inventing new ones, too) and at the same time explains his mixed colours. We can follow him in three separate directions, starting at each primitive colour. Firstly, from blue upwards to orange, then from red to green at the lower left, and finally from yellow down to purple at the lower right.

The word "slate" appears three times between blue and black in the centre, which at the time probably also appeared grey. This slate colour appears at three levels as a mixture of purple and green, as a neutral grey and as a shadowy grey. Brightness increases again after the centre is passed, with a mixture of brown and olive between a neutral and a yellow-red orange.

The red changes towards the centre through three shades of brown, henceforth becoming a green, of which there is a neutral, an olive grey and a yellow-blue variant.

Yellow gives rise to the olive colour, which darkens via a neutral shade towards the centre, continuing then as purple towards a blue-red.

The adjacent sketches show how we can travel through the system, always crossing the centre (black) in order to pass from one colour to another. This interesting structure reproduces a spiral system in which both circular and radial movements coexist and in which both singularities and pluralities can therefore be found.

Seen within the context of scientific development, Hayter's system stems from a time in which the controversy — which had persisted since Newton — over the nature of light and whether it consisted of waves or particles seemed finally to have been resolved. On the one hand, Thomas Young, who we have already discussed, had proved that light rays can interfere with each other: under controlled conditions, light added to light can result in darkness. This property of interference applies only to wave formations, and not to particles. In the 1820s, the Frenchman A. J. Fresnel was also able to demonstrate that all optical phenomena can be understood if light is conceived as an oscillation in a

(hypothetical) medium, with the direction of oscillation being vertical to the direction of propagation (transverse). In 1821, the German physicist J. von Fraunhofer actually succeeded in measuring the length of the waves of which light consisted. He used a diamond to scratch fine, closely-spaced parallel and vertical lines on a sheet of glass, and then studied the "deflection" of light through this so-called "diffraction grating". By

1835 at the latest, the physicist F. M. Schwerd was able to take exact measurements of the visible spectrum with the aid of such a diffraction grating, and show that red light has a longer wavelength than blue light, and that yellow and blue light lie in the middle of the spectrum. (The nanometer — 10 -9 metres, or 10 -7 centimeters-has now become the standard unit of measurement, with the wavelength of the visible spectrum lying within a range of a few hundred nanometres).

We can see, therefore, that the first half of the 19th century was the heyday of wave theory. For the first time, it seemed that science could rest assured that something about the nature of light had been understood. But fundamental problems with regard to our conception of waves were to re-emerge at the beginning of this century. They remain with us to this day.


Michel Eugène Chevreul


Date: The chemist Michel Eugène Chevreul introduced his (incomplete) attempt at producing a systematic approach to seeing colours in

1839.

Country of origin: France

Basic colours:

Form:

Red, yellow and blue

Hemisphere, circle

Application: Organisation of colours for the manufacture of textiles.

Related systems: Field — Benson — Bezold — Wundt — Blanc

Summary:

Bibliography:

The purpose of the system is to establish a law of "Simultaneous

Contrast". Leonardo da Vinci had probably been the first to notice that, when observed adjacently, colours will influence each other.

Goethe, however, was the first to specifically draw attention to these associated contrasts. Chevreul designed a 72-part colourcircle whose radii, in addition to the three primaries of red, yellow and blue, depict three secondary mixtures of orange, green and violet as well as six further secondary mixtures. The resultant sectors were each subdivided into five zones and all radii were separated into 20 segments to accommodate the different brightness levels. This is the first time that we have been confronted with the active role of the brain in the formation of colours, and we should once more remind ourselves that colours are also effects which are created in the world inside our heads

M. E. Chevreul, De la loi du contraste simultané des couleurs et de l'assortiment des object colorés , Paris 1839; A. Hope und M.

Walsh, The Color Compendium , New York 1990; John Gage,

Colour and Culture, Practice and Meaning from Antiquity to

Abstraction , Thames and Hudson, 1993, pp. 173-176.

Although he had no interest in understanding or treating colours in the same way as artists, it is unlikely that any other chemist has influenced the development of art as much as the Frenchman Michel Eugène Chevreul (1786-1889). Chevreul trained as a chemist, and in 1824 was appointed as director of Gobelin, the famous carpet manufacturer. Here, he concentrated on the problems of dyeing, and therefore on the dyes themselves. As a chemist, Chevreul supervised the preparation of these dyes, and it occurred to him that the main problems had nothing to do with chemistry but were more related to optics. A colour frequently failed to achieve the desired effect. This was not caused by pigments, but by the influence of neighbouring colour tones. Chevreul decided to investigate the matter on a scientific basis, and in 1839 published his De la loi du contrast simultané des couleurs ( historical illustration ), a comprehensive attempt at providing a systematic basis to seeing colours. The work dealt with the so-called "simultaneous contrast" of colours, and contained Chevreul's famous law: "Two adjacent colours, when seen by the eye, will appear as dissimilar as possible".

Chevreul's work influenced the movements in art known as Impressionism,

Neoimpressionism and Orphic Cubism, with Robert Delaunay (1885-1941) using

coloured "simultaneous discs" in his paintings. Although Chevreul's work remained impractical and was never completed, he also in fluenced the views of both Eugène

Delacroix (1798-1863) and Georges Seurat (1859-1891) with regard to colours and the way in which they used them.

Leonardo da Vinci had probably been the first to notice that, when observed adjacently, colours will influence each other. Goethe, however, was the first to specifically draw attention to these associated contrasts and described them with such emphasis that they have continued to be born in mind. Whoever should simultaneously look at the same red, first on a yellow background and then on a violet background, will have two different impressions: in the first case a darker red; in the second case, a more orange red.

Chevreul was able to establish a difference between the two ways in which simultaneous contrast occurred and spoke of changes in intensity as well as "optical composition".

Nowadays, we know with greater accuracy that there are three components which can displace one another under the influence of surroundings of another colour. These three components correspond to the dimensions of a spacial colour system and are named brightness (or value), hue and saturation (or chroma). One and the same colour will have a brighter effect against a dark background, and a darker effect against a light background: a pure red will have a redder effect on a yellow background, and a yellower effect on a reddish background; a grey red will have a more colourful effect (less grey) on a grey background than on a coloured background.

This simultaneous interaction of colours can be easily understood or interpreted using the colour-circle or the colour-sphere if we accept that the background colour will repel the colour of the observed colour field. Of course, our perception must actually carry this out, and since it is therefore reasonable to assume that our eyes and brain will try to perceive the differences occurring in nature as clearly as possible, this explanation conforms with the displacement represented by the colour-circle.

This is the first time that we have been confronted with the active role of the brain in the formation of colours, and we should once more remind ourselves that colours are also effects which are created in the world inside our heads — this can be better envisaged by consulting the contributions of physiology.

Let us return to Chevreul, who in his 1839 work demonstrates that a colour will lend its adjacent colour a complementary tinge (of colour hue). As a result, opposing complementary colours will brighten, and non-complementary colours will appear

"contaminated", for example a yellow next to a green receives a violet tinge.

The laws of colour contrast occupied Chevreul during his search for an adequate organisation of colours, as required for the manufacture of textiles. For this purpose, he designed the 72 segment colour circle shown here. The circle defines the colour hues on the basis of the various changes which a colour undergoes in the direction of white

(higher intensity) or black (lower intensity). According to Chevreul, 10 steps are possible . It is worth noting that in his colour-circle, Chevreul arranges each of the saturated colours on a varying radius within its associated segment. Pure yellow lies nearer to the centre than pure blue. Pure red lies at point 15 on the scale. By this means, the values of colour hue for the different pigments are given a position more appropriate than in preceding systems.

In Chevreul's colour-circle we find three secondary colours (the primary mixtures orange, green and violet) alongside the three subtractive primary colours (red, yellow and blue), as well as six secondary mixtures. The segments arising in this way are thus divided into six zones, and each radius is divided into 20 sections in the form of a ladder, in order to specify the different brightness levels.

With his hemisphere, Chevreul attempted to provide us with a spacial representation of the colours appearing in his two dimensional colour-circle. The black axis of the hemisphere thus becomes a pointer, pivoting to select the different levels on a scale. The

numbering will then stipulate the proportions of a colour, for example 9B/1C will mean that 9/10 black and 1/10 of the corresponding (colour) hue are present.

Chevreul was convinced that the many different colour hues and their harmony could be defined by means of the relationships between numbers, and he wished his coloursystem to become a suitable instrument, available to all artists using coloured materials.

Although his harmony systems, which he described as "Harmonie d'analogues"

(harmony of analogy) and "Harmonie de constraste" (harmony of contrasts), were of great influence, he was unable to discover a law of colour harmony. It simply doesn't exist.


George Field


Date: The colour-circle appeared in 1846 in a book about "Chromatics", which dealt with the analogies and harmonies of colours.


Basic colours: Red, yellow and blue; Field also declared orange, green and purple to be primary colours.

Form: Circle

Related systems: Pythagoras, Aristotle, Plato — Grosseteste, Alberti, da Vinci —

Fludd — Newton — Maxwell — Helmholtz — Bezold

Summary: The chemist George Field constructed a colour-circle from the basic colours of red, yellow and blue, thus wishing to take up a position opposed to Newton. Secondary and tertiary colours arise through progressive superimposition. Meanings were allocated to the colours: hot (red) and cold (blue) stand opposite one another; likewise advancing and retiring. George Field also saw a connection between colour and sound, and so draws our attention to one of the stumbling blocks of the era: namely, an understanding of the carrier medium of light.

Bibliography: G. Field, Chromatics, of the Analogy, Harmony and Philosophy of

Colours , London 1846 (new issue of the 1st edition of 1817); G.

Field, Rudiments of the Painter's Art, or A Grammar of Colouring ,

London 1850; A. Hope und M. Walsh, The Color Compendium ,

New York 1990; John Gage, Colour and Culture, Practice and

Meaning from Antiquity to Abstraction , Thames and Hudson,

1993, pp. 214-216.

Throughout his life, the chemist George Field (1777-1854) occupied himself not only with the practical aspects of pigments and dyes, but also with the theory of their harmonic relationship. In Chromatics , his first work, an essay written in 1817 on the "Analogy and

Harmony of Colours" used the three subtractive primary colours red, yellow and blue, and was concerned with the arrangement of a colour harmony as an "aesthetic analogy" of the musical harmony system. In his essay, Field describes a "metrochrome", an equivalent of the musical metronome comprising three calibrated wedge-shaped glass vessels filled with red, yellow and blue liquids. For our purposes, it is enough to appreciate the reason

for the many numbers in his system, without the need for understanding each one individually.

In his Chromatography of 1835 — a title sounding to our modern ears like a scientific method — a second discourse on colours and pigments appeared, featuring the "colourcompass" shown. His compilation A grammar of Colouring followed, which was chiefly intended for artists, providing them with information on the origin, composition and properties of pigments, dyes and paints.

In all three works, Field establishes a link with the works of Jakob Christof Le Blon , who in

1730 had put forward a colour-circle of the three "primitive" colours red, yellow and blue, and the three mixed colours orange, green and purple (thus taking up a position opposed to Newton). Field declared the six colours of his circle to be primary colours, from which the secondary and tertiary colours arise through gradual change. Whilst Field characterised his secondary colours simply by using double names and saw the three tertiary colours as dark (dk) variations of the mixed colours already mentioned, three special names appear in his colour compass: the mixture of purple, blue and green is called "olive"; the mixture of green, yellow and orange is called "citron"; and the mixture of orange, red and purple is called "russet".

Different meanings or connotations marked along the circumference of the circle are assigned to the colours: hot and cold stand opposite one another, likewise advancing and retiring, and a high mean and a low mean value. Both the smaller sketches show us how we can pass through the main circle — from outer to inner, from bright to dark, and from concave to convex.

Perhaps at this point we can justify a brief explanation of the link between colours and sounds which George Field wished to establish. Attempts at relating light and music are ancient. Athanasius Kircher was the most recent to reiterate that everything visible to the eye can also be made audible for the ear. It was not until 1760, however, that a developed system for colour music was presented by the Frenchman Louis-Bertrand

Castel. He undertook the following, fairly random allocation: C was expressed by blue, and C-sharp by blue-green, D by green, D-sharp by yellow-green, E by yellow, F by yellow orange, F-sharp by orange, G by red and so forth to B, which is represented by indigo. From the triad blue (keynote C) — yellow (third E) — red (fifth G), he arrived at a twelve-step chromatic colour-music scale via different intermediate levels. In 1844, Field suggested an alternative allocation, leaving C with blue, but bringing D to purple, E to red,

F to orange, G to yellow, A to yellow green and B to green. His Analogous Scale of

Sounds and Colours was based on the triad blue-red-yellow.

Deep down, music and colours most probably are related, but their connection is not easily established — a colour piano certainly overwhelms our imagination — even if, with regard to wave motion, we manage to superficially conceive a common physical basis.

Sound and light waves are not comparable, indeed they are about as different as any two things could ever be. The principal difference lies in their respective mediums of propagation. Waves can only exist when a carrier — a medium — is available. Ocean waves are carried by water; waves of music and sounds are carried by air. This is demonstrated by the experiment in which an alarm clock is placed in a glass bell and the air is pumped out. The alarm clock can still be seen rattling, but there is silence, because the waves of sound no longer have a propagation medium. But although the sound waves capitulate to the relative vacuum of the bell, light waves manage to pass through it with ease — after all, we can still actually see the alarm clock. Air is not their medium. Indeed, if light waves could not cross the vast emptiness of the universe, we would see no stars.

At the time of Field's death, the scientific world was therefore confronted by a great mystery, namely the exact nature of the medium by which light waves are carried. The physicists had already named this mysterious substance "ether". But how could something which must be harder than steel in order to make possible the minute wavelengths which light was known to possess at the same time be so imperceptible that the planets could orbit within it undisturbed? An initial solution to this great difficulty

became apparent after 1860, through the work of the Scottish physicist James Clerck

Maxwell. He has not only profoundly influenced the history of light, but also the history of colours.

It has certainly now become evident that Field, despite his leaning towards music, considered the origins of colour in another way to Newton, viewing them more within the tradition of Aristotle. To Field, colours arise if the coexistence of light and darkness assumes a varying emphasis. If darkness is predominant, blue will occur; if brightness is predominant, then yellow will occur; if there is an equilibrium, there will be red.

As with this construction of polar principles with its positive white and negative black, much remained random with Field — his "chromatic equivalent" being one example. His ideas are not referred to later, and after the work and theories of Maxwell and Helmholtz ,

Field's ideas become obsolete — in spite of the beauty of his compass of colours.


James Clerck Maxwell


Date: James Clerck Maxwell, the physicist, presented his theory of colour mixing between 1855 and 1860.


Basic colours: Red, green and blue

Form: Triangle

Application: The system is a fundamental requirement for colorimetry.

Related systems: Sowerby — Hayter — Field — Helmholtz — Benson — Bezold —

Wundt — Rood — Jacobs — C.I.E.

— Gerritsen

Summary: It is difficult to explain to the outside observer just how famous

Maxwell is amongst physicists. In addition to his "Theory of Colour

Vision", which is seen as the origin of colorimetry, his name is linked to the four so-called field equations which are able to explain how light propagates, and thus point to the existence of electromagnetic waves. We make use of the reception of these waves today, for example when we listen to the radio. After discovering equations which could record colours, Maxwell placed the resultant combinations in a triangle , the corners of which were marked by the three primary spectral colours of red, green and blue. Each mixed colour lies on the line linking the separate components of the mixture.

Bibliography: J. C. Maxwell, "Experiments on colour", Transactions of the Royal

Society Edinburgh 21 , pp.275-298 (1855); J. C. Maxwell, "On the

Theory of compound colours", Philosophical Transactions 150 , pp.

57-84 (1860); E. G. Boring, Sensation and Perception in the

History of Experimental Psychology , New York 1942; C.W. F.

Everitt, James Clerck Maxwell Physicist and Natural Philosopher ,

New York 1975.

1859 is one of the great years in the history of science: the Englishman Charles Darwin

expounded his ideas on the origin of species, and so cleared the way for the theory of evolution; and in that same year, the Scottish physicist James Clerck Maxwell (1831-1879) published his Kinetic Theory of Gases , in which he introduced the statistical account of molecular motions and their mathematical treatment known today as Maxwellian distribution and contributing to our fundamental knowledge of physics.

In the same year, Maxwell, then 28 years old, presented his Theory of Colour Vision , acknowledged as being the origin of quantitative colour measurement (Colorimetry). In this work, Maxwell demonstrates that all colours arise from mixtures of the three spectral colours — red (R), green (here abbreviated to V [verde]), and blue (B), for example — on the assumption that the light stimulus can be both added and subtracted. He allocates each of the three main colours to a corner of a triangle , into which we have then placed a curve of spectral colours which is provided with technical data. A line of this type will reappear later in the CIE System . This is important, because all associated insights go back to Maxwell who, with his triangle, introduced the first two-dimensional colour system based on psychophysical measurements.

It is difficult to explain to the outside observer just how famous Maxwell is amongst physicists. In addition to Maxwellian distribution (see above), his name is also associated with the four so-called field equations which are able to explain how light propagates, and point to the existence of electromagnetic waves. We make use of the reception of these waves today, for example when we listen to the radio. Maxwell showed that light waves are to be understood as oscillating electrical and magnetic fields, and he explains how light waves can travel across the vast emptiness of the universe and reveal the stars.

Before moving even closer to the true nature of light, Maxwell attempted to gain more exact access to colours. Physics and the measurement of light and colour re-emerge in post-Newton history as a result of his contribution, with his triangle being in part an attempt to improve on Newton's methods of mixing light. In the preceding decade physicists had learned to determine wavelengths in the region of 10 -7 m with the aid of microscopic diffraction gratings. Nowadays, wavelengths can be more accurately expressed in nanometres (1 nm = 10 -9 m). The wavelengths of visible light are now known to lie in a range between 760 nm for red and 380 nm for blue, with green at approximately 550 nm.

(These values are located along the length of the curve.)

Maxwell's observations of colours are based on propositions made by Thomas Young , who had already noted that no more than three colours of the spectrum were required in order to bring all others into being. At the time when Young submitted his trichromatic theory, many artists had long known that they could mix all colour shades by using three primary pigments; physicists, however, were still influenced by Newton's claim that the seven colours emanating from a prism are elementary (and therefore not mixable).

Young's three receptors gained in credibility when, in 1855, George Wilson of Edinburgh presented the first statistical analysis of colour blindness. In the appendix, Maxwell was able to show that the observations made sense if the individual concerned was assumed to have one or two receptors that were ineffective.

Maxwell had begun his own experiments into colour mixing at Edinburgh, in the laboratory of J. D. Forbes, who worked with rapidly rotating discs. Using this method, Forbes wished to mix the spectral colours to create grey, and was unsuccessful in his attempts to mix grey from red, yellow and blue. He soon saw why: under these circumstances, blue and yellow do not result in green, but rather a kind of pink. As a result, Maxwell chose red (R for rosso), green (V for verde) and blue (B for blu) as his basic colours (clearly stressing, however, that any other trio of colours can be selected which combine to give white). We find these basic colours again in his triangle.

In his experiments into the measurement of colour, Maxwell engaged test subjects, who judged how the colour of a sample compared with a mixture of the three basic colours.

Nowadays, the test subjects are themselves allowed to change the mixture of red, green

and blue (with the aid of standardised light sources) until the impression of the colour corresponds to that of the sample ("colour match"). The respective proportions of the mixture can be recorded using three numbers, identified as R, V and B and known since

Maxwell's time as "tristimulus values".

Maxwell now became aware that the brilliance of a multicoloured surface is relatively insensitive to changes in brightness, and was able to totally eliminate this as a determining factor by introducing new parameters r, v and b, arrived at by dividing each tristimulus value by their total value: r = R/(R+V+B), v = V/(R+V+B), and b = B/(R+V+B). These new colour coordinates fulfil a simple condition-their sum is one (r + v + b = 1). This means that all their possible combinations can be represented as the points of an equilateral trianglethe Maxwell triangle. A few examples can be seen in the series shown to the right; here, the white neutral point is located in the centre of the construction.

Since their tristimulus values, or their colour coordinates, add up to one, the triangle enables us to predict the result of a mixture of two colours ( triangle 1 — triangle 2 — triangle 3 ). All possible combinations of any two colours will lie on the line connecting their respective positions within the triangle. Naturally, Newton's circle had already specified the results of colour mixing. But Maxwell's achievement was that the geometrical relationship and spacing between the colours in his triangle have a precise meaning, based on psychophysical measurements.

In his colour mixing experiments, Maxwell was able to demonstrate that Newton's circle of seven colours, with white as a middle point, implicitly satisfied the trichromatic theory since it equates to a model which allocates a point within a three-dimensional space to each colour. On entering the experimental results into his colour triangle, he located a point for white. With the aid of this point, Maxwell was able to specify three new variables — similar to H. von Helmholtz — which characterise a colour: the "hue", the "tint" and the "shade".

Maxwell also showed how easy it is to form a link between these variables and portray colours as the sum of three primaries.

The limitations of this triangle, incidentally, soon became apparent: its values are based on comparisons of pigments, but the light of spectral colours can be much more intense. For example, if we seek the location of saturated yellow, we will see that it must lie outside the line between V and R. If all the spectral colours, together with the purple hues, are to be recorded in Maxwell's diagram, then his triangle must either be extended or reconstructed.

An attempt at this dates back to Helmholtz . Nowadays, we resort to a sophisticated method where the line in the triangle is already attuned ( CIE System ). Even today, because machines alone cannot distinguish between yellow or red, the measurement of colours continues to be a difficult task. As always, the human being is alone in his ability to decide. It is into his eyes that light falls, and from his eyes that the world is viewed.


Hermann von Helmholtz


Date: The colour diagram appeared in 1860 in the now famous Manual of

Psychologocal Optics .


Basic colours: Simple colours: red, green and blue violet

Form: Modified triangle

Application: Colorimetry

Related systems: Newton — Hayter — Field — Maxwell — Bezold — Jacobs —

Pope — C.I.E.

— C.I.E.-Stiles — Astrological connections

Summary: Both Helmholtz and Maxwell concentrated on selecting the most suitable diagram to explain the observed facts with regard to colour mixtures. Because the trichromatic theory was both available and accepted, their attention was turned towards the geometry of the triangle, without any consideration of the phenomenological aspects. However, after noticing that the spectral colours must have varying distances to white (which must, in turn, lie at the centre of the triangle), Helmholtz pur forward a modified version of

Maxwell ’s construction.

Bibliography: H. von Helmholtz, Manual of Physiological Optics , Volume II,

Section 20 (1860); A. König and C. Dieterici, "Die

Grundempfindungen in normalen und anomalen Farbsystemen",

Zeitschrift für Psychologie 4 , pp. 241-347 (1892); E. G. Boring,

Sensation and Perception in the History of Experimental

Psychology », New York 1892.

Hermann von Helmholtz (1821-1894) was the absolute master of the natural sciences of his day. He both dominated and understood. His first great achievement, in 1847 at the age of 26, was to formulate the principle of the conservation of energy. Helmholtz also demonstrated great practical talent by inventing the opthalmascope, and his Theory of

Sound Sensitivity (1862) both propounds a theory for the combination of tones and analyses the timbre of musical instruments, even venturing toward a theory of harmony.

His famous Manual of Psychological Optics appeared between 1856 and 1867, with the

English translation appearing 60 years later to world acclaim. Here, Helmholtz introduces the three variables which are still used to characterise a colour: hue, saturation and brightness. He was the first to unequivocally demonstrate that the colours which Newton had seen in his spectrum are different from colours applied to a white base using pigments. The spectral colours shine more intensely and possess greater saturation. They are mixed additively, whereas pigments are mixed subtractively. In each case a different set of rules governs their combination.

Helmholtz's investigations were guided by the ever present analogy of the eye and the ear.

The three - above mentioned variables of colour sensation were chosen to correspond to the three parameters of sound: amplification, pitch and timbre. The only difference between acoustic phenomena and the perception of colour is that the eye can not differentiate between the components of a mixed colour, while the ear can easily identify the separate elements of a complicated sound. As Helmholtz himself said in 1857: "The eye cannot separate combined colours from each other; it sees them as an unresolvable, simple sensation of one mixed colour. It is therefore of no consequence to the eye whether basic colours of either simple or complicated conditions of oscillation are combined in a mixed colour. There is no harmony in the same sense as with the ear; there is no music."

In line with Thomas Young , Helmholtz also advocated a three-colour system , and demonstrated that each colour could be composed as a mixture of three basic colours — for example red, green and blue-violet as the so-called "simple colours". In his manual, the great physiologist then submits several proposals for the arrangement of these simple, or pure, colours — thus covering the entire spectrum. He also attempted to intervene — rather casually, but nevertheless vividly formulated — between Newton and Maxwell. For

Helmholtz, Maxwell's triangle is too small to accommodate the saturated spectral colours and Newton's circle does not explicitly refer to the trichromatic theory, which contains a deep insight.

Helmholtz first of all arranges the spectral colours on a curved line in order to achieve a better understanding of their mixtures. He imagines a kind of force field of colours — the colour field — with white in the middle, corresponding to Newton's gravitational centre.

Helmholtz noticed that in order to obtain white, he did not require equal quantities of violetblue and yellow, for example. He thus arranged his colours in such a way that those complementary colours which were required in greater amounts were given greater

"leverage".

Newton's circle forms the basis of a second construction by Helmholtz in which two triangles are plotted after omitting the part which intersects the line between red (R) and violet (V). This truncation is only possible without detriment because the two colours concerned mark both ends of the spectrum. (at the CIE-system we will encounter this line once again as purple.) In the figure, we are left with two triangles whose corners have been determined in each case by the two possible combinations of three basic colours, between which Thomas Young had wavered at the beginning of the 19th century. The triangle with the violet, red and green (VRG) corners thus contains all colours which are formed from mixing violet, red and green, and the same applies for the red, yellow and cyan cornered triangle (RYC). It is apparent from the figure, and also from Maxwell's triangle , that not all colours can be recorded in this way, and that a large portion of the colour-circle remains remote.

There was, of course, no doubt about the trichromatic theory in Helmholtz's time, and this encouraged the belief that there really must be an ideal triangle with a place for all the mixed colours of the spectrum. With his remaining construction , Helmholtz returned to that first curve of simple colours which he had drawn on the assumption that quantities of light of varying colour can be regarded as being the same when, at set intensities, they appear to the eye as equally bright. Based on the pure basic colours of red and violet, without further explanation Helmholtz moves the point representing our perception of pure green to A, to form a triangle AVR which now contains all sensations of colour.

Subsequently, Helmholtz draws the conclusion that, in his view, the pure red and the pure violet of the spectrum do not occur as a simple sensation of a fundamental colour, and for this reason the lower line must be displaced to the values V1 and R1. The colours which can be directly attained by means of light entering a normally sighted eye will then lie on the closed curve V1ICGrGR1 (the abbreviations refer to indigo, cyan, green and yellow).

The triangle otherwise contains colours which are located at a greater distance from white, and are therefore more saturated than all customary colours.

Helmholtz and Maxwell concentrated on selecting the most suitable diagram to explain the observed facts with regard to colour mixtures. Because the trichromatic theory was both available and accepted, their attention was turned towards the geometry of the triangle, without any consideration of the phenomenological aspects. The question concerning the position of the spectral colours in each triangle was only finally resolved at the end of the

19th century when A. König and C. Dieterici examined "the basic sensations in normal and anomalous colour systems and the distribution of their intensity in the spectrum" and specified the course of the line which we have plotted in Maxwells triangle . This will only be scientifically correct if we imagine an ideal triangle whose colours possess greater saturation than the spectral colours (E marks the point of equal energy, and this can be also interpreted as white). The results of the spectral mixtures illustrate how Newton had simplified matters when he assumed that the saturation of mixed colours will be less if, within the sequence of colours, their components are located further apart.

The work of König and Dieterici appeared in the Zeitschrift für Psychologie in 1892, and it was evident that the pre-eminence of colours had become lost to contemporary physicists.

But the power of perception will in the end prevail; without it, the technical game with colours would remain all too trapped within geometrical constructions, even when practiced by a genius like Helmholtz or Maxwell.


William Benson


Date: The architect William Benson published his cuboid system in 1868, in London.


Basic colours: Red, green and blue

Form: Cube

Related systems: Mayer — Runge — Chevreul — Maxwell

Summary: The first colour-system to be based on a cube . William Benson attempted to master both the additive and subtractive mixing systems. The cube stands on its black corner, and three edges extend outwards to the basic colours of red, green and blue. From the white tip, the edges lead to a yellow, a "sea-green" and a pink corner. Benson preferred the unusual pink to the violet one would normaly expect; this, in his opinion, was too dark.

Bibliography: W. Benson, Principles of the Science of Colour, Consisely Stated

To Aid and Promote Their Useful Application in the Decorative Art ,

London 1868; Color Documents: A Presentational Theory , organised by S. Wurmfeld, Hunter College Art Gallery, New York

1985.

In Maxwell's triangle , we have seen that three slightly darker primary colours are located opposite three brighter colours which are reached by moving from each corner through the white centre point. Green-blue (or cyan) lies opposite the red corner, with purple (or magenta) opposite green and yellow opposite blue. If we then wish to create a spacial colour-system from this more explanatory triangle, we can do so in a similar way to the

English architect William Benson. In 1868, Benson proposed the first of his many colourcubes . He considered this arrangement to be the "natural system of colours", as the title of

Chapter 7 of his Principles of the Science of Colour states. At the outset, Benson cited the preliminary work of Mayer, Runge and Chevreul, but then proceeds in long sentences to justify his own preference for an alternative geometry.

"In order to use the normal methods of geometrical representation of all combinations which can be formed from three independent variables, a point must be chosen which represents zero or black — the absence of all light. From this point, three lines must be drawn at right angles to each other. Along these lines, and on all parallel coordinates, the colours red, green and blue shall increase in intensity, commencing at zero. The intensities of red, green and blue, which collectively give white, shall be the same, and are therefore represented by equal distancing along the three right-angled coordinates. The end points of these three lines will thus be the places for the full red, the full green and the full blue, while the lines themselves contain the shades of these three colours towards black... The corner of the cube opposite the black would be the full white, and the corners lying opposite red, green and blue would be sea-green, pink and yellow. The central point would be a medium grey."

The fact that pink is given priority over purple is probably connected with its brightness.

Benson's cube contains 13 main axes which he divides into three groups (in order to differentiate between contrasts, shades and harmonies). There are three axes connecting the central points of opposing sides and, because only one of the primary colours changes

on them, these are termed primary axes. In the figure they are shown as solid lines

(together with the lines parallel to them). There are a further six axes connecting the middle points of opposing edges. By following these, two primary colours will change, and for this reason Benson talks of secondary axes. Both they and their corresponding parallels are shown by broken lines. Finally, the four axes which join opposing corners are named tertiary axes, since in this case all three primary colours will change. These are also shown with broken lines. Benson gave exact colour names to all the many points, but we shall only sample them along the line from m1 to m6: m1 is pink; m2 is yellow-red; m3 is pink-blue; m4 is yellow-green; m5 is sea-green; and finally, m6 is sea-green-green.

We can pass back and forth through this cube along many routes. It can also be divided into many levels. To illustrate the potential diversity of colours in the cube , we have plotted a few main positions (middle drawing). The column to the outer right represents various horizontal projections which are obtained when passing from white to black. The mirror image of the triangles is here a geometrical phenomenon.

William Benson's system attempts to master both additive and subjective colour mixtures.

As a colour-system, a cube will always be confronted with one basic problem: it does not fully allow for the significance of brightness, and therefore places the colour hues wrongly.

Benson's system appears to the eye of the critical observer more as a confusion of colours.

If, however, we are not required to use the cube with all the complicated descriptions on its edges and the many straight lines inside, and if we find Benson's approach acceptable, we will still find our own pleasure in it.


HLS System


Date:

Basic colours:

Form:

No exact date; the system was developed in conjunction with television technology.

Red, green and blue

Double cone

Application: Colour-order for phosphorescent television screens

Related systems: Munsell - RGB

Summary: The three letters H, L and S represent the classic colour variables of hue, luminance and saturation. Regardless of such identification, the system provides a possible application of Henry Munsell's system to the colours created on television screens by the process of phosphorescence.

Bibliography: "Computer Graphics CAD/CAM Image Processing", Editrice il

Rostro , Milan, 1981; David Travis, "Effective Color Displays",

Computer and People Series, Academic Press, London 1991.

The three letters H, L and S represent the classic colour variables of hue, luminance and saturation. Intensity (I), which would create an HIS system from the HLS system , is often used in place of luminance.

Regardless of such identification, the system provides a possible application of Henry

Munsell 's system to the colours created on television screens by the process of phosphorescence. The expression "phosphorescence" comes from the Greek "phosphoros", meaning "morning star" or "Venus". It could also be translated as the "carrier of light". The light effect — the phosphorescence in other words — is created when energy delivered in the form of an electron beam is first of all stored by substances on the screen (molecules) and then released in the form of light.

The coloured picture on a television screen is actually produced by using three lightabsorbing and light-carrying molecules which are concentrated into tiny patches of approximately 0.2 mm diameter. When they glow, a particular type of additive light mixing — a partitive mixture — will occur, which is normally created using the three colours red, green and blue (RGB). This will be explained when we examine the associated RGB system .

In the HLS system, colour-hue is identified by an angle which can vary in an entirely conventional way between 0 and 360 . As with saturation, intensity is measured on a scale of

100 units , read off along the axial line between the black and white tips. (Saturation is extracted along the radial lines running from grey to the full colour.)

Naturally, the problem of mediation between purely numerical (metric) and chromatic

(psychological) scales is still present in the HLS system. But then, nobody is perfect — not even the carrier of light.


RGB System


Date:

Basic colours:

Form:

Application:

Red, green and blue

Cube

Colour-order for phosphorescent television screens

Related systems: HLS

Summary:

No exact date; the system was developed in conjunction with television technology.

Colours on the television screen are created by a special form of additive light mixture known as a partitive mixture. The surface of the screen is covered by tiny points, each with a diameter of approximately 0.2 mm, containing phosphorescent materials

(molecules). Normally, three types are selected to transmit red, green or blue light after excitement by beams of electrons; in other words, after they have absorbed energy. The screen colour-system introduced here is named RGB after these three colours.

Bibliography: "Computer Graphics CAD/CAM Image Processing", Editrice il Rostro ,

Milano 1981; David Travis, "Effective Color Displays", Computer and

People Series, Academic Press, London 1991.

Colours on the television screen are created by a special form of additive light mixture known as a partitive mixture. The surface of the screen is covered by tiny points, each with a diameter of approximately 0.2 mm, containing phosphorescent materials (molecules).

Normally, three types are selected to transmit red, green or blue light after excitement by

beams of electrons; in other words, after they have absorbed energy. The screen coloursystem introduced here is named RGB after these three colours.

The partitive light mixture is created because the human eye is incapable of perceiving the many hundreds of thousands of points — the triads of red, green and blue patches into which they are organised — individually, and can only register the mixing effect of all RGB-triads together, with brightness being regulated by the intensity of the electron stream which triggers the phosphorescence.

The colours on the screen are created by partitive mixing of red, green and blue. These are in turn able to produce only a limited number of all possible colours. The cube construction has been verified as the most suitable system for this particular range of colours, with each of its edges being divided into 16 equal parts numbered 1 to 15. These numbers are sufficient to specify the trichromatic composition of each colour. The eight corner-points of the cube are occupied by red (R), green (G) and blue (B), the subtractive primary colours magenta (M), yellow (Y) and Cyan (C), and the achromatic colours white (W) and black (B).

All colours in the RGB system can be concentrated into two subgroups , one centred on white and the other on black. The chromatic form extends from black (0, 0, 0) along the edges of the colours to reach the white tip (15, 15, 15) — the maximum intensity — after passing two corner points.


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Navigation: red (Navigator) or bold (Explorer) = illustrations ///// blue

Pythagoras, Aristotle, Plato

Robert Grosseteste, Leon Battista

Alberti, Leonardo da Vinci

Aron Sigfrid Forsius

Franciscus Aguilonius

Robert Fludd

Athanasius Kircher

Richard Waller

Isaac Newton

Tobias Mayer

Tobias Mayer

Johann Heinrich Lambert

James Sowerby

Ignaz Schiffermüller

J. W. von Goethe

Philipp Otto Runge

Charles Hayter

Michel Eugène Chevreul

George Field

James Clerck Maxwell

Hermann von Helmholtz

William Benson

HLS System

RGB System

Chronological

Bibliography

Part I

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Navigation: red (Navigator) or bold (Explorer) = illustrations ///// blue

Pythagoras, Aristotle, Plato

Robert Grosseteste, Leon Battista

Alberti, Leonardo da Vinci

Aron Sigfrid Forsius

Franciscus Aguilonius

Robert Fludd

Athanasius Kircher

Richard Waller

Isaac Newton

Tobias Mayer

Tobias Mayer

Johann Heinrich Lambert

James Sowerby

Ignaz Schiffermüller

J. W. von Goethe

Philipp Otto Runge

Charles Hayter

Michel Eugène Chevreul

George Field

James Clerck Maxwell

Hermann von Helmholtz

William Benson

HLS System

RGB System

Chronological

Bibliography

Part I

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