Von Löwen Designs

The physics of light and colour plays a crucial role in humankind’s search for knowledge. In the light that falls upon the earth, we can find answers to the most fundamental of all questions – namely, the nature and origins of our known universe.

Equally, through our habitual imposition of order upon a world we would otherwise perceive as random, we run the risk of distorting our vision. What we perceive as chaos may be an illusion. Our desire for a supreme order may serve more to reassure us in our incomprehension than provide a firm and logical structure for our discoveries; ultimately, we may succeed only in bringing disruption to the unity and harmony that surrounds us.

In our obsession with scientific analysis, these methods to organize colour become a symbol. In the same way as they seek justification and meaning through the creation and definition of an extraordinary diversity of barely discernible shades and hues, our analysis appears at times to cause confusion; as we find no real answers – only more questions.

Our world and the distant, scattered beauty of the universe seem unwilling to yield their secrets to the onslaught of science. Nevertheless, science has assumed that it alone can nurture the human soul, and has declared itself independent. Modern society’s beliefs in self-redemption as creative faith has been described as the real delusion of our secularized age, and at the same time the declaration of all its failures. Is it now science, as the spearhead of human endeavor, which represents that delusion?

We can also see these systematic attempts as a catalog of failure, a chronicle of our culture’s constant inability to emulate the perfection of the world around us – a world that seems to defy analysis. Although we will find much here about the fundamental scientific principles that help us appreciate its wonders, we should, perhaps, not search too diligently for information that could tempt us to impose our own personal order; but appreciate the efforts and collective of those trials from the past.

Indeed, seen as a whole, and despite their individual shortcomings, these theories still contain truths and help us trace the changing views of civilization and culture. Representing not only a desire for order, but also a genuine (although sometimes misguided) search for wisdom and knowledge, they also show how we can lose ourselves in the closeness of inspection and analysis. Without physics, we can attain no insight into the nature of the universe; but do we at the same time lose sight of other truths? It may be wiser, in the end, to view these ideologies as a game – just as the many pieces in a puzzle. Each can be confusing, decorative or whimsical; we should accept them as so, in the same way as we should, perhaps, accept our world as the most complete and perfect system of them all.

1350-1400 – Pythagoras: musical notes are assigned to colours; Aristotle: colours throughout the day: white, yellow, red, violet, green, blue, black; Plato: white, black, red, ‘radiant’. 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 interpretation 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.

Middle Ages – Early Renaissance (England/Italy) – 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.

1611 (Finland) – The first drawn colour system is credited to astronomer, priest and Neoplatonist Aron Sigfrid Forsius (1569-1637). In his colour-circle, between the 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. 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 that was devoted to sight and 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.

1613 (Belgium) – Franciscus Aguilonius (1567-1617) was a Jesuit priest in Brussels when his colour diagram appeared in 1613 in a work on optics. It is possibly the oldest system to use the trio of red, yellow and blue wherein colours are defined within a linear division. “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.

1630 (England) – 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.

1646 (Germany) – Athanasius Kircher (1601-1680) 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. Kircher was also recognized for his connection with the cosmological construction theory that 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.

1686 (England) – 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.

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 revitalize these ideas of the turbid medium with great vigor.

1704 (England) – 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. 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.

“Newton created white from all colours. He’s even fooled you, so that you will believe in a 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 symbolize 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.

1758 (Germany) – More than half a century after Newton’s Opticks had appeared the German mathematician and astronomer Tobias Mayer (1723-1762) gave a lecture to the Göttingen Academy of Science entitled ‘De affinitate colorum commentatio,’ 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 that systematically states how 91 chromatic colours 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, 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.

1766 (England) – One hundred years after Newton’s separation of white light through a prism, a book appeared in England with the title The Natural System of Colours. In this work, Moses Harris (1731-1785), the English entomologist and engraver, examines the work of Isaac Newton and attempts to reveal the multitude of colours that can be created from three basic ones. As a naturalist, Harris wishes to understand the relationships between the colours, and how they are coded, and his book attempts to explain the principles, “materially, or by the painters art”, by which further colours can be produced from red, yellow and blue.

Harris builds upon the discovery by the Frenchman Jacques Christophe Le Blon (1667-1742). Le Bon is credited with the invention of colour printing. In 1731, during the course of his work, he observed something, which every school child now learns, namely – that three paints coloured red, yellow and blue are sufficient to produce all other colours. Although Le Blon invented the fundamental three-colour palette and demonstrated his system with many dyes, he did not extend his ideas to a properly organised colour-system; that was for Harris to accomplish. Harris introduced the first printed colour-circle in 1766, specifying his primary colours very exactly – red was cinnabar, which could be made from sulphur and mercury – yellow was King’s yellow (an artificial orpiment); and ultramarine was used for blue. Harris distinguished between the harmony of the ‘prismatic or primitive colours,’ which are assigned a ‘prismatic circle’ and ‘compound colours’ which are allotted their own circle. The word ‘prismatic’ could at first lead to confusion. In fact, Harris did not mean the spectral colours observed by Newton after light had passed through his prism and then arranged in a circle; he meant the unmixed pigments (‘grand or principal colours’). A mixture (‘compound’) of the three basic colours will result in the three intermediate colours (‘mediates’) mentioned: orange, green and purple, which also appear in the prismatic circle and are all brought to life with natural descriptions (‘fruit or flower’). According to Harris, the three main colours, red, yellow and blue, are: “the greatest opposites in quality to each other and naturally take their places at the greatest distance from each other in the circle”. In order to arrange this ‘greatest distance’ evenly within the circle, Harris requires an even number of circle segments, and Newton’s seventh colour, indigo, is therefore dispensed with.

1772 (Germany) – 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 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.

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 basic-colours of cinnibar, King’s yellow and 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.

1772 (Austria) – 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.

1809 (England) – 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 emphasized 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).

1810 (Germany) – 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 presented 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. Goethe sought to surpass Newton’s system 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, accordingly, sets down his concept.

1810 (Germany) – In the same year in which Goethe’s Theory of Colours with its colour-circle 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.” 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.

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.

1826 (England) – 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. 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.”

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 center. 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 the19th century.

1839 (France) – 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, 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”.

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 colour-circle 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.

1846 (England) – 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.

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.

1859 (England) – 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. 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.

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.

1860 (Germany) – 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 analysis the timbre of musical instruments, even venturing toward a theory of harmony.

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.

1868 (England) – 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 colour-cubes. 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.

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.

1874 (Germany) – Wilhelm von Bezold (1837-1907) was Professor of Meteorology in Munich as well as Director of the Prussian Meteorological Institute. His main interest as a scientist was the physics of the atmosphere and he contributed much to the theory of electrical storms. His uncle Gustav was a prominent art historian, and this may well have been instrumental in the appearance, in 1874, of his Farbenlehre im Hinblick auf Kunst und Kunstgewerbe in which Wilhelm von Bezold introduces a colour-system in the form of a cone. Although reminiscent of Lambert’s pyramid, this cone is conceived differently – similar, in fact, to the Chevreul’s hemisphere.

In spite of the attention he pays to science and scientific quantification, von Bezold is primarily concerned with art and design and wishes his circle to assist painters and colourists. A colour-cone is put forward with the fully saturated colours lying on the surface at various levels of brightness and becoming darker towards the black point. The circular base is divided into twelve segments of different size, with green being allocated the largest area and red the smallest.

1874 -1893 (Germany) – Psychology emerged as a new science towards the end of the 19th century. One of its early pioneers, Wilhelm Wundt (1832-1920), helped establish the experimental branch of psychology and secure it as an empirical science. He had studied physiology and philosophy and, during the course of his life as a researcher, prepared the foundations for a Physiological Psychology, the title of his twin-volume textbook dating from 1887, which is still on the market today as a standard work. Wundt was able to return to a form of psychophysics mainly developed by Gustav Fechner (1801-1887), and investigated the relationships between the measurable phenomena of the physical world and their experienced (psychic) image i.e. perception. The fact that smaller differences in brightness can be perceived in the dark made Fechner risk the conclusion that the visible increase in stimulation (increase in brightness) maintained a constant relationship to the basic stimulus (brightness itself). Fechner also envisaged that the effect of this relationship was continuous and also applied to the tiniest ‘infinitesimal’ changes. He thus derived the famous Fechner’s Law, which establishes a relationship between differences in the sensation of brightness on the one hand and intensity or corresponding differences between colour hues on the other. (To be more exact, we must talk of the Fechner-Weber Law, which states that an arithmetic progression in perceptions requires a geometrical progression in their stimuli.)
Wundt’s 1874 colour-sphere has eight basic colours around the equator, each assigned to equal-sized segments and changing in steps towards the white or black poles. The colour-cone of 1893 is constructed around only six basic colours which all progress to a black tip. Varying complimentary colours face each other in both systems.

1878 (Austria) – In the middle of the 19th century, it was accepted that only three variables, in other words three receptors, are required to explain the colour mixing which formed the basis of experiments carried out by both James Maxwell in 1867 and Hermann von Helmholtz in 1859. Modern physiologists can confirm only that three types of molecule (photo-receptors) exist, and that each type is particularly sensitive to either short, medium and long waves. Although this observation can help explain why a few wavebands of incident light cannot be distinguished from others and thus why many mixtures result in the same colours, we are nevertheless unable to explain those colour-hues, which we can see.

It was Helmholtz who had assumed that there must be three receptors, each directly signaling a definite colour-hue, and he consequently named these receptors ‘blue,’ ‘green’ and ‘red’ in the belief that the blue receptor, for example, produced the sensation of blue and so on. He was, of course, aware that the spectral sensitivity of the receptors had to overlap, so that each wavelength could give rise to varying colour relationships (and another perception). Between 1872 and 1874, the physiologist Ewald Hering (1834-1918) had delivered ‘six communications’ entitled On the Theory of Sensibility to Light at the Academy of Sciences in Vienna, privately published in 1878, in which Hering opposed the Helmholtz view of the phenomenon of colours. (From 1905 onwards, he published his Principles of the Theory of Sensitivity to Light. These appeared in four instalments of which, incidentally, the third was broken off in mid-sentence, leaving the reader to wait years for the full meaning!)

Although he also spent considerable time investigating the eye’s perception of three-dimensional space, Hering was more concerned with the introspective aspects of colours. He also spent considerable time investigating the eye’s perception of three-dimensional space. His work on colour refers to the problem of yellow in the three-colour-system, for example. According to Helmholtz, yellow was of necessity produced from a mixture of red and green, but this – so Hering realised – was not in line with human experience. The sensation of yellow is elementary, and not traceable to a mixture. Hering states that there are, in addition to black and white, four colours which “can occur without a tinge of another colour” and recommends that “each visual perception” can be seen as a “mixture of the six basic sensations” which oppose each other and thus interact.

1879 (France) – After the revolution of 1848, the French art critic Charles Blanc (1813-1882) was for some years Director of the Department of Decorative Arts at the Ministry of the Interior in Paris. After a political career, he developed an interest in art, and in 1881 presented his Grammaire des arts décoratifs which was widely read by artists who included Gaugin, Seurat and van Gogh. Blanc’s writings are considered the most influencial texts on colour theory to come from the second half of the 19th century.

In 1879, two years before the publication of his Grammaire, Blanc designed a colour-system based on Chevreul’s ‘laws of simultaneous contrast.’ A few ideas were also borrowed from the painter Eugène Delacroix, who had attempted to put Chevreul’s theory of contrast into practice. For Delacroix, half tones, which for him are the dominating principle of painting, do not occur as a result of the pure colours being mixed with ‘dirty-making’ black, but because neutralising complementary colours are used. To outline his ideas about colours, Blanc took an equilateral triangle with yellow, red and blue at its corners and violet, (between red and blue), green (between blue and yellow) and orange (between yellow and red) on its sides. Hence, Blanc constructs his colour-circle from triangles without including black or white – three chromatic triangles, therefore, one for each of the additive primary colours red (rouge), yellow (jaune) and blue (bleu) and one for each of their complementary partners orange, green (vert) and violet (violet).

1879 (USA) – The American Nicholas Odgen Rood (1831-1902), who had studied physics, started to paint during a visit to Germany. His interest in colours thus encompassed the scientific and artistic points of view, and both these aspects underlay his attempts to impose a systematic order on colours. His book Modern Chromatics appeared in 1879, its subtitle promising ‘Applications for Art and Industry.’ Rood announces: “an introduction to the facts, in a simple and comprehensive way, which form the basis of the artist’s use of colours”. A second edition of the work appeared two years later, this time with the less interesting title Student’s Textbook of Colour, in which he instructs artists on the insights of Helmholtz, and encourages them to ‘paint with light.’
Rood’s colour system proposes concentric colour-circles for the first time, based on the primary colours red, green and blue, and possessing a total of 12 outer segments of equal size. The colours of these segments are red, orange, orange-yellow, yellow, green-yellow, green, green-blue, cyan, blue, ultramarine-blue, violet and purple. The circles become paler as they progress inwards, with the centre of the rings finally containing white.

1890 (France) – Répertoire Chromatique, by the French botanist and naturalist Charles Lacoutre (1832-1908), was published in Paris. Lacoutre was Professor at the Collège Clément in Metz and had already written many books on moss and other non-flowering plants when he presented his work on colours. In Répertoire Chromatique, Lacoutre promised ‘reasonable and practical solutions’ to the problems occurring with the multiple use – thus mixing of colours, and constructed a figure which he called his ‘trilobe synoptique,’ which if we translate the term with due respect, contains the three ‘ear lobes’ which its name implies and provides a comparative view of colours. Lacoutre looked towards the three basic colours of red (R), blue (B) and yellow (J, jaune) and in his original 1890 figure uses these colours to plot the fine lines running in a bow-shape from the field J at the bottom left, for example, to the opposing field J at bottom right. Although not shown here, Lacoutre does not reproduce the various colour-hues and tints by altering the colour of the ink with which he works but varies both the thickness and the number of lines placed across his colour fields, in each case progressing from white in six steps: R1, R2 … R5. R stands for red, and accordingly B for blue and J for yellow (jaune). Each of the three primary colours appears as a generator of colour-fields, all of which overlap.

1897 (Austria) – Alois Höfler (1853-1928), the Austrian educationalist and philosopher, produced many texts on both psychology and general science and made a name for himself by publishing the Berliner Kant-Ausgabe (1903). In 1897, his textbook Psychologie appeared, in which he introduced his first colour system – a double pyramid with rectangular base (an octahedron). He later proposed a further, derivative colour solid with a triangular base (tetrahedron). White (W.) and black (BK.) are found at the tips of both constructions, with grey appearing in the middle.

Höfler also sought a relationship between the harmony of colours and music. In his books, he explicitly points to the sequence white-grey-black since he discovers here a ‘quasi-straight line,’ meaning a straight line limited at both ends. Such a line, however, appears unfamiliar to music and musical notes.

The rectangle – the system of four – operates with the four elementary perceived colours: yellow (Y), red (R), blue (B) and green (G). Of these four psychological colours, only the yellow reappears, along with cyan (C) and purple (P), in the artists’ triangle, which thus contains the subtractive primary colours.

The purpose of Höfler’s arrangement is not to provide an organisational or identification system, and neither does he consider that colour variations can be subordinated, for instance to the geometrical properties of a sphere. He is more concerned with “certain alternative internal relationships” between the colours. His colour-octahedron not only represents Hering’s basic colours, but also their relationship as opposing colours.

Höfler’s solid should be seen as an expression of the relationship between coloured sight on the one hand and the psychological effect of colours on the other. For this reason, many psychological textbooks have adopted his pyramids to provide information on our perception of colours.

1902 (Germany) – The concept of the double pyramid gained in popularity at the turn of the century, with the German cognitive psychologist Hermann Ebbinghaus (1850-1909) also constructing a colour system on this basis. He rounded off the extremities, however, and inclined the central plane. The colour-solid thus formed, containing the four primary colours red, yellow, green and blue, linked an idea of Leonardo da Vinci to the realisation that the chromatic colours vary in brightness, and can thus be separately distinguished.

Ebbinghaus rounds off the corners of his solid because the transition between the colours is not sharply defined. The base-square of the double solid is tilted in such a way that yellow hues, which are relatively bright, are nearer to white, and the blue tones, which are relatively dark, are nearer to black. For a long time, the Ebbinghaus double-pyramid represented the last stronghold of phenomenology and resisted the increasing dominance of physiology and its attitude toward the nervous system. With Ebbinghaus, an era came to a close in which colours were simple. From that point onwards, the world of physics could no longer be quite so certain about the nature of light.

1912 (USA) – The American ornithologist and botanist Robert Ridgway (1850-1929) encountered an almost infinite number of colours on his many voyages of discovery through the world of nature. In the course of time, he also became aware that the accuracy required for a scientific description of colours would only be possible through some form of standardisation. He therefore proposed a colour-system, which was published in 1912 under the title Color Standards and Nomenclature.

Ridgeway’s system exploits the possibilities of additive colour mixing. The basis for the required systematic order of colours is a circle subdivided into 36 pure, solid colours (full colours), which, from the perceptual point of view, are given approximately even spacing. While each basic colour loses saturation towards the centre by means of the progressive, additive mixing of a medium grey, its hue remains virtually unchanged. Ridgway achieves his set of colour standards by placing five steps, identified by concentric lines, between the outer ring of full colours and the central grey. In order to maintain their visual equidistance, the six concentric rings do not contain the same number of colours. Through progressive, additive mixing of white or black to each of the 159 colours within the full colour-circle, Ridgway eventually succeeds in attaining the three-dimensional diversity of non-self-illuminating colours. Three steps are involved in each direction. Towards black these are called shades, and towards white they are tints. Ridgway thus creates a register of 7 x 159 = 1113 colours, which, with the two tips, give 1115 colour standards, intended for use in the identification of the colours of birds.

Alternatively, the three-dimensional arrangement of these standard colours can be illustrated by the (dissected) double cone. The full colours are placed around the equator, with the grey colours running along the central axis from white through to black.

1905 – 1916 (USA) – Of all the attempts at constructing a colour-system with the aim of providing standard samples according to a logically organised plan while at the same time catering for the perceived affinity of colours, the effort by the American painter Albert Henry Munsell (1858-1918) is generally considered the most successful. Based on the principle of ‘perceived equidistance,’ to use the correct, although rather long-winded technical term, is certainly one of the most widespread and commonly used. When he proposed his rather inconspicuous colour-sphere (A Colour Notation, 1905), Munsell was still influenced by N. O. Rood’s ‘Modern Chromatics’ (1879). As he began with his painted samples, however, he realised that a geometrically symmetrical solid was unable to portray the opposing relationships between the colours, as we perceive them. The variation between the brightness of pure chromatic colours is too great to be arranged in sequence along the equator: yellow, for example, is brighter than red, which is in turn brighter than violet. Munsell’s efforts at constructing a system in which the spacing between each colour and its neighbour could be perceived as equal culminated in the publication of his Colour Atlas in 1915. He introduced an order of colours, also known as a ‘colour tree’ due to its irregular outer profile, grouped around a ‘naturally grown’ central vertical grey-scale.

Munsell constructed his system around a circle with ten segments, arranging its colours at equal distances and selecting them in such a way that opposing pairs would result in an achromatic mixture (compensativity). Munsell organised the hues of the hand-painted panels, which make up the tree according to three variables, as included in his rather individual system of naming. His parameters are hue, value (the index for brightness) and chroma (the gradations of saturation). Each colour is characterised by a triple block, symbolically understood as H/V/C (to be more closely explained). With this as his basis, Munsell went on to develop the entire system using spinning colour-tops to define the mixtures while entrusting the final judgement to his eyes.

The vertical value-scale divides the area between black and white into 10 steps (which Munsell determined using a photometer of his own construction). He does not simply define these gradations according to linear changes in reflection but selects a scale in which the square root of the measured reflected intensity is subjected to uniform change.

After setting up his value-scale, Munsell selected samples from red (R), yellow (Y), green (G), blue (B) and purple (P) which to him, and his painter’s eye, appeared equidistant not only from each other, but also from a grey of the same value. These became the basic hues of his system, and he provided an additional five mixtures – yellow-red (YR), green-yellow (GY), blue-green (BG), purple-blue (PB) and red-purple (RP) – arranging them in a circle around the previously mentioned neutral grey (N). The parameter Chroma 5 was arbitrarily assigned to all these ten main colours and their mixtures. The chroma scale is an open-ended scale and can reach values of up to 12 and 14 depending on the intensity of the colours used. Vermillion, for example, reaches this extreme position and is correspondingly abbreviated to 5R 5/14 in the Munsell notation, while pink, which is less saturated, is defined as 5R 5/4.

The outer graduations of the colour-circle show how a total of 40 hues are created by dividing the original five colour-hue intervals between the main hues, first into 10 then 20 and finally into 40 segments, once again in such a way that they will be perceived as equidistant. Their individualistic sounding names are also included.

A new Colour Atlas appeared in 1929, after Munsell’s death, this time under the title The Munsell Book of Colour. We still use this edition today. In 1942, the American Standards Organisation recommended its use for specifying the colours of surfaces. The approximate identification of Munsell’s parameters, namely hue, value and chroma, could be confirmed through direct visual comparison with the colour panels themselves. A refinement of Munsell’s notation was, however, recommended (to be later implemented in association with the Optical Society of America and known as ‘renotation’).

1916 (Germany) – In 1909, Wilhelm Ostwald (1853-1932), who came from the Baltic, received the Nobel Prize for chemistry for his work on catalysis, an area on the fringe of physics, which promised applications in industry. Ostwald, who had been instrumental in the foundation of the first Zeitschrift für Physicalische Chemie, was also something of a pioneer outside his own immediate field: in addition to the history of his special subject, he showed great interest in the physical sciences as a whole, as is evident in Ostwalds Klassiker der exakten Naturwissenschaften.

Although not always successful, Ostwald explored many new approaches to scientific thought, at one time attempting to refute the existence of atoms, which he maintained, were an uncalled for hypothesis since their structure was invisible.

His final passion, however, was the theory of colours, and after his retirement (at the age of only 53), he devoted himself to the laws of colour in the hope of developing a scientific basis for their perceived harmonies. His Farbfibel ‘The colour primer,’ which appeared in 1916, introduced a colour system devoted to this task (and survived for 15 editions).

The word ‘harmony’ in the title aptly symbolises what Ostwald wanted to achieve with colours. Experience had shown him (and others) that some colour combinations could be seen as pleasant (or harmonious), while others were unpleasant. The question was why, and whether a law could be formulated. With his analysis of colour-harmony, Ostwald proceeds on the basis of his conviction that harmony is created by colour-order. A double-cone is put forward with one white and one black tip between which a stepped grey-scale is arranged, modelled according to a fundamental psychological law. The double-cone extends from a colour-circle divided into 24 segments (the full colours), which in turn stem from the four proto-colours of yellow, red, blue and sea-green.

1923 (Canada) – Canadian-born sculptor and painter Michel Jacobs (1877-1958) wrote The Art of Colour, a book in which be presented a few rather individualistic theories on the harmony of colour. While studying the decorative arts in Paris and New York, Jacobs came to realise that although art students learn first to draw and then how to apply colour, to him the reverse seemed more sensible. To this end, he presented his theory of colours, which was not intended to introduce a new viewpoint (Jacobs was a supporter of the ideas of Thomas Young and Herman von Helmholtz). He thus operated with three colours, although his selection of red, green and violet was peculiar. These he called ‘spectrum primaries.’ The violet which he used is actually the type of blue-violet used by Wilhelm von Bezold and the physiologist Hermann von Helmholtz.

Michel Jacobs arranged his spectral primary colours around the outside of a circle, placing them opposite three secondary colours, which extended from the centre towards the periphery. These were yellow, blue and crimson, which Jacobs named ‘pigmentary primaries’ and which, together with his spectrum primaries, form three pairs of complementary colours – the so-called ‘complementaries.’ The circle is laid out in such a way that this opposition also involves the opposition of concave and convex.

Using these reference colours, six mixtures are possible, which Jacobs names within structures unfolding like the calyx of a flower. These are, clockwise: orange, yellow-green, blue-green, blue-violet, purple and scarlet. The complementary pairs may indeed flow into one another – purple and yellow-green, for example, but their separation is also emphasised. Generally, the many lines of the three calyx shapes actually maintain the separation of sharp extremes of complementary colours and reduce their contrast.

1924 (Austria/Vienna) – “There is only one correct colour system, and that is the three-dimensional system of nature with its three separate and independent effects of the three natural and original colours of pure yellow, pure blue and pure purple as organising and guiding principles which order all colours,” such was Max Becke’s creed.

Becke was director of the textile industry’s research institute in Vienna, and in 1924 presented a ‘Natural Theory of Colours’ in which he demonstrated with total conviction “that the scientific basis for the theory of colours is without question laid down in an irrefutable law of nature”. Becke establishes that “the innermost essence of colours” shows through “as the objective properties of matter” and that “inevitably, through the process of sight in combination with this property, colour terms identical to the colours” will be formed. The justification of his ‘natural colour equation xyz’ is thus inferred “because only this equation can accurately and scientifically express the actual relationships between cause and effect in the natural order of events.”

Becke’s stirring enthusiasm for the omnipotence of nature has long been relegated to the distant past, and in spite of all its proclaimed clarity and exactness, his ‘natural’ theory of colours remains just one of many. As stated, it operates with three basic colours, which the Viennese chemist and colourist also concisely names using pigments. Pure yellow should appear “as chinolin yellow on wool”, pure blue “somewhat less pierced with green, as patent blue on wool” and purple should be “something like sulphurhodamine B extra on wool.”

The objective of Becke’s system is “to examine the laws of material colouration and the effect of colours”. In other words, to cope with the subtractive mixtures of coloured materials just as effectively as physicists deal with the additive mixtures of coloured light. To this end, he constructs a ‘natural trichromatic solid’ in planar form in which “the totality of the material colours in the world around us, and the notional colour terms which are identical to them, is characterised and organised by means of their constructive content, according to the three original or basic colours – pure yellow, pure blue and pure purple”. Becke then goes on to describe both the construction and his idea more exactly. With our modern attitudes, however, we may be surprised at the simplicity with which the chemist sees the notional world within us:

“The natural colour-solid – shown as a cube – can be separated into three systems of vertical square surfaces of pure yellow, pure blue and pure purple, which are graded from 0 to 120. Each material colour in the outer world is, as a notional colour-term, mathematically and geometrically arranged at the intersection of the three basic colour surfaces to which they have been allocated as a result of the inevitable disintegration of their objective general effect into these three independent and objective partial effects during the process of sight. The allocation of each colour attains clear expression through the colour equation xyz , as entered into the triangular shape.”

Using this method of notation, white becomes 000, black 120120120, with the three pure colours being expressed as two zero’s and a 120. Becke refers to them as ‘one third colours,’ and middle grey is characterised as three times 60.

1929 (USA) – Although the American educationalist and art-theorist Arthur Pope (1880-1974) constructed his colour-solid in 1924, another twenty-five years were to pass before it was finally published. His system is centred on a grey axis, divided into 9 gradations running between white (W) and black (B) (as shown to the right). The solid itself can be envisaged as a series of triangles which vary in both size and shape. The two-dimensional projection of the three-dimensional arrangement results in a circle which is divided into twelve segments, one for each of the main colours: yellow (Y), green-yellow (GY), green (G), green-blue (GB), blue (B), blue-purple (BP), purple (P), red (R), orange-red (OR), orange (O) and yellow-orange (YO). Hue, saturation (which he calls “purity”) and brightness are chosen by Pope as the main features of colour perception. Tryggve Johansson’s colour system selects a similar layout to show the colour qualities which apply for any given colour hue, and Sven Hesselgren attempts to synthesise other similar experiments, all of which have Hering’s psychological approach as their origin and pave the way for the NCS system. From a geometrical point if view, Pope’s system falls somewhere between Ostwald’s graphic double-cone and the calculated solid from Luther and Nyberg.