colorsystem

In 1758 — 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» (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.