PART 7. THE DIMENSION OF HUE

7.1 FROM ARISTOTLE TO NEWTON

• Hue before the hue circle
• Newton's hue system

Hue before the hue circle

Figure 7.1.1. Seventeenth century diagrams of colour order systems¹ (click to enlarge). A, B. Two-path and five-path multilinear systems illustrated by Sigfridus Forsius (Physica [unpublished manuscript], 1611). C. Compound (linear-multilinear-trichromatic) system by Francois D'Aguilon from the Opticorum libri sex (1613). D. Diagram by Robert Fludd (Medicina Catholica, 1629), formed by joining the white and black ends of a linear system as a circle. E, F. Later compound systems based on D'Aguilon's, published by Athanasius Kircher (Ars magna lucis et umbrae, 1646) and Johannes Zahn (Oculus artificialis, 1685) respectively. G. Multilinear system illustrated by Francois Glisson in his Tractatus de ventriculo et intestinis (1677). For details of the original publications see Kuehni and Schwarz (2008).

Among earlier systems, the most influential was the linear scale devised by Aristotle, based on the idea that colours might be formed by the mixing in various proportions of white and black. In his Peri Aistheseos kai Aistheton (On sense and what is sensed, c. 330 B.C.) Aristotle arranged five chromatic colours on a line between white and black, with the lighter colours beginning with yellow close to white, and the darker colours beginning with blue close to black (Fig. 7.1.2A). The fundamental difficulty with such a system, obvious to us in the light of Newton's discovery of the hue circle, is that we can proceed from yellow to blue by two different hue series, passing through red or through green, which makes it impossible to define a single satisfactory hue sequence. Thus while many later authors adopted Aristotle's idea of a linear scale between white and black, most felt at liberty to vary the order of the intermediate hues (Fig. 7.1.2B-E).

Figure 7.1.2. Linear colour order systems. A. Aristotle, c. 330 BC, Peri Aistheseos kai aistheton. B. Chalcidius, c. 325 AD, from his commentary on Plato's Timaeus,. C. Bartholomaeus Anglicus, c.1245, from his encyclopaedia De rerum naturalis (Of natural things). D. Leonardo da Vinci,c. 1500, Trattato della pittura. E. Robert Fludd, 1629, Medicina Catholica. All diagrams based on purely verbal descriptions, except E (after Fig. 7.1.1D). For details of the original publications see Kuehni and Schwartz (2008, pp. 31-33, 37-38).

Beginning with the Persian philosopher Avicenna in the eleventh century, various writers resolved this dilemna by devising what I refer to here as multilinear systems, in which from two to seven sequences ("paths" or "families") of colours stretch between black and white. There are no contemporary illustrations of Avicenna's simple system (Fig. 7.1.3A) or of the more elaborate one by his 13th century commentator Al Tusi (Fig. 7.1.3B), but the Finnish mathematician Sigfridus Forsius (1611) used circular diagrams to illustrate a comparable pair of systems, a two-path "ancient" system (Fig. 7.1.1A, 7.1.3D) and a five-path "right" system (Fig. 7.1.1B, 7.1.3E) respectively. These diagrams and that of the English physician Glisson (Fig. 7.1.1G, 7.1.3F) independently show the multilinear sequences as straight and curved lines stretching between black and white. Several writers have interpreted the array of arcs in Forsius' second diagram as a sphere, but neither the diagram nor the accompanying text provide evidence that Forsius intended this (Kuehni and Schwartz, 2008, pp. 45-46). In the simpler multilinear systems each sequence includes more than one hue in the modern sense, but in others the sequences are effectively tint/shade scales of a single major hue category. Tint/shade scales are described in painter's practical manuals from the twelfth century (Kuehni and Schwarz, 2008, p. 35), and continue to feature prominently in later colour order systems, such as the colour "stars" of Lacouture and Itten (Fig. 7.2.4L, 7.2.6H).

Figure 7.1.3. Multilinear colour order systems. A. Avicenna, 1015, Liber de anima, with "paths" through pallidus (uncertain, either yellow-green or grey), rubeus (red) and indicus (indigo blue). B. Al Tusi, 13th c. commenatary on Avicenna. C. Alberti, 1435, Della Pictura, with "genera" passing through red, blue, green and grey/beige (bigia et cinericia). D. Sigfridus Forsius, 1611 manuscript Physica, "ancient" system (see Fig. 7.1.1A), with colours in two series, through red and blue. E. Forsius' second system (see Fig. 7.1.1B), with five series through red, yellow, green, blue and grey. F. Glisson, 1677, Tractatus de ventriculo et intestinis, (cf. Fig. 7.1.1G). Diagrams A, B and C, which were not illustrated by their authors, are modeled on the later diagrams by Forsius and Glisson. For details of the original publications see Kuehni and Schwarz (2008).

The elaborate diagram by the Jesuit mathematician Francois D'Aguilon (Figs 7.1.1C, 7.1.4) ingeniously reconciles three disparate systems: (1) a linear scale of the Aristotelian kind, (2) multilinear genera like those of Avicenna and Forsius, and (3) the newly ascendant trichromatic system of three primary colours - yellow, red and blue. The latter are arranged in order of tonal value between white and black in a linear scale of five "simple" colours. The graceful arcs in the upper part of the diagram resemble similar arcs in medieval musical diagrams (Kuehni, undated), but their function here is to represent Avicenna/Forsius-style colour sequences passing between white and black through yellow, red, blue and grey respectively. The ancient dilemna of where to put green relative to red on the linear scale is resolved by removing it entirely, as the compound of yellow and blue. The two remaining compounds complete the possible pairwise combinations of yellow, red and blue. By following the arcs of the lower part of the diagram from yellow through gold, red, purple, blue, green, and back to yellow, one can trace the succession of hues of the familiar colour wheel, but this colour wheel "foetus" was to remain attached to its linear Aristotelian parent until Newton published his hue circle in 1704. Later seventeenth century compound systems illustrated by Kircher (Fig. 7.1.1E), Traber (Kuehni and Schwartz, 2008, Fig. 2.21) and Zahn (Fig. 7.1.1F) are in essence identical, except that some lines do double-duty for the superimposed trichromatic and multilinear systems.

Figure 7.1.4. Interpretation of D'Aguilon's diagram from the Opticorum Libri Sex (see Fig. 7.1.1C) as a compound linear-multilinear-trichromatic system.

Newton's hue system

Newton presented his circular diagram in the Opticks of 1704 as an approximate guide to the additive mixing of coloured lights, explaining that the colour resulting from such mixing would lie at the "center of gravity" of the component lights, weighted according to their relative "number of rays" (Fig. 7.1.5). He further stated that colour mixtures on the circumference would be "intense and florid in the highest degree" and that other colours would be intense in proportion to their distance from the centre, thus making his diagram the first graphical representation of the dimension of saturation, as well as hue. Newton's hue scale, which is still widely given as the colours of the spectrum and the rainbow, consisted of seven hues, red, orange, yellow, green, blue (or "blew"), indigo and violet, spaced around the circle according to the intervals of a musical scale. This scale is not one of the modern tonal (i.e. major or minor) scales, which had become standard by the beginning of the eighteenth century, but is a Dorian scale, one of eight older traditional modal scales.

Figure 7.1.5. A. Colour circle from Newton's Opticks (1704), showing a desaturated orange light mixture (z) at the "centre of gravity" of its seven unequal spectral components, indicated by circles of differing size. Source:Posner Library. B. Coloured version of Newton's diagram, showing the interpretation of Newton's hue names adopted here. The spacing of the red through violet hues is taken unchanged from my linear RGB circle (Fig. 4.3.4), so that opposed spectral hues in the diagram are true additive complements.

Two additional discoveries are implicit in Newton's diagram: (1) the concept, later named metamerism, that the same colour can result from any number of different combinations of spectral components, and (2) the relationship, later termed complementarity, that lights having opposite colours on the circle, such as Newton created experimentally by splitting the spectrum in various ways, will mix to make white light (Fig. 7.1.6). Newton himself stopped short of asserting that the latter rule applied to opposite pairs of monochromatic lights, ostensibly because he had not succeeded in demonstrating this result experimentally, but perhaps also because it would have meant conceding a point to his early critic, Huygens. It is difficult to overstate the importance of Newton's discoveries, which contributed directly or indirectly to a huge part of our conceptual framework of colour in science, technology and art - not to mention the discovery of radio waves, microwaves, and the rest of the electromagnetic spectrum! Once hue and saturation had been added to brightness as independent dimensions, it was only a small step (first taken by Brook Taylor in 1719) to recommend an explicitly three-dimensional conception of colour. The hue circle and the concept of complementarity were particularly important developments for artists, and even the concept of "warm" and "cool" hues does not seem to have taken hold until after artists saw their hues laid out in a circle.

Figure 7.1.6. Generalized illustration of Newton's various experiments showing that splitting the spectrum produces coloured lights with opposite "centres of gravity" that can be recombined to make white light.

Though Newton's circle first appears in the Opticks of 1704, the musical comparison to which we apparently owe it is contained in De Colorum Origine (The Origin of Colours), the second part of the Latin manuscript of his Cambridge optical lectures deposited at that university in 1672. Throughout this document, translated by Shapiro (1984), Newton refers to five "principal" or "most conspicuous" colours (like Aristotle before him, and Munsell after him): red, yellow, green, blue and violet/purple. However when discussing a very cleanly separated spectrum (Lecture 3) and again when discussing the mixing of adjacent spectral colours (Lecture 8), he uses a finer scale of ten "gradations" in which typical representatives of the five principal colours alternate with intermediate colours (Fig. 7.1.7). He then claims in Lecture 11 that because the most typical representatives of four of the five principal colours are off-centre in the spaces assigned to them, the spectrum can be subdivided more "elegantly" by giving two of the intermediate gradations, orange and indigo, their own spaces (Fig. 7.1.7, right). Then in the following part of Lecture 11 Newton reports the similarity between the spacing of the colours in his seven-hue spectrum and the spacing of the stops in a Dorian scale.

Many have suggested that Newton settled on seven spectral hues because of a preconceived attachment to his comparison with a musical scale (which is plausible), or because of a supposed "obsession" with the number seven (which is groundless). However, one could equally well speculate that the common alternative of seeing six spectral hues originates from a preconceived attachment to a symmetrical colour wheel based on the three historical primaries. Before that idea gained hold, Aristotle saw three or four colours in the rainbow in the Meteorologica (Fig. 6.2.1A), and recognized five principal chromatic colours in De Sensu, and Theodoric of Freiberg (c. 1310) saw four rainbow colours (Kuehni and Schwarz, 2008). In any event, Newton correctly recognized that the number of colours seen in the spectrum was a function of how closely you looked, and depending on the latter might be five, seven, ten or "indefinite".

Partly because the traditional "artists' colour wheel" has a place for orange but only one blue, the spotlight of skepticism has mostly fallen on Newton's indigo, although some relief has arrived in recent decades in the form of the RGB(CMY) hue circle, which recognizes a deep "blue" and cyan as separate hues. The modern meaning for "cyan" of greenish blue dates from Helmholtz (1866), who suggested renaming Newton's "blue" and "indigo" as "cyan-blue" and "indigo-blue" respectively. Newton had used the Latin name cyaneus (derived from the ancient Greek for "blue") in his ten-hue spectrum for the presumably typical gradation of blue between the intermediate gradations thalassinus (sea green = the green-blue gradation) and indicus (indigo = the blue-violet gradation), but in his seven-hue spectrum, indicus includes the blue-violet boundary (the "most perfect indigo") plus an adjacent part of the blue of the five-hue spectrum, while caeruleus (blue = Helmholtz's cyan-blue) extends from the most typical blue up to the blue-green boundary (Fig. 7.1.7). Newton's indigo might therefore be expected to include the deep, violet-tending "blue" of modern technology (the "B" in RGB), while his blue would include the hue range of process cyan inks up to digital cyan. This correlation is compatible with Newton's placement in his circle of indigo as the complement of yellow to yellow-orange, and blue as the complement of middle red and orange, but not yellow, and also agrees with the opinions of earlier writers including Helmholtz, von Bezold, Rood, and Evans, who related Newton's indigo to the hue of ultramarine (though cf. McLaren, 1985, who argued that Newton's indigo was an indistinguishable division of violet).

Figure 7.1.7. Newton's colour terminology in the manuscript of his Cambridge optical lectures, De Colorum Origine (1772). A, one of the passages of the latin text giving the names of ten "gradations". B, Newton's spectral subdivisions aligned with the reproductions of Newton's optical lecture diagrams by Shapiro (1984).

Newton admitted in his optical lectures that a match between the precise boundaries of the spectral intervals and those of a musical scale could not be conclusively demonstrated from the evidence, but said that he favoured his subdivision for two reasons: (1) "because it may perhaps suggest analogies between harmonies of sounds and harmonies of colours" such as are known to painters, and (2) because "the affinity between the extreme red and violet, the ends of the spectrum, is of the same kind as between the first and last notes of the octave". The suggestion of "analogies between harmonies of sounds and harmonies of colours" was not unreasonable at the time, particularly in the context of Newton's hypothesis that colour stimuli were conveyed to the brain by vibrations in the optic nerve.

More compelling apparent support was in store for him when he came to arrange his colours in a circle (Fig. 7.1.8A, B). Like all modal scales, the Dorian mode can be sounded by stopping a plucked or bowed string at points at simple fractions of its length: in this case 8/9, 5/6, 3/4, 2/3, 3/5, 9/16 and 1/2 (Fig. 7.1.8A, blue fractions). An approximation of these notes can be heard by playing the white notes on a modern keyboard ascending from the note D. In introducing his circle in the Opticks, Newton gives this scale in the form of the intervals 1/9, 1/16, 1/10, 1/9, 1/10, 1/16, and 1/9, which refer to the proportion of the remaining part of the string occupied by the space to each note (Fig. 7.1.8A, red fractions). The relative sizes of these proportional intervals therefore differ from the absolute spacings on the string, and it is the former that Newton used to derive the angular divisions of his circle, in line with its music theory progenitors. The use of interval spacing rather than absolute spacing happens to substantially improve the alignment of the additive complementaries, for example placing middle green instead of blue-green - the actual middle of Newton's spectrum - opposite extraspectral "purple" (magenta), and blue-green opposite spectral red. It may have been this serendipitous circumstance that ultimately convinced Newton to publish his surprisingly daring analogy.

¹ Historical diagrams in Figs 7.1.1, and 7.2.1-3 sourced from Kuehni and Schwarz (2008), Spillman (2009), various public domain sources, and the collection of the author.

Modified April 15, 2013. Original text here.

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