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Colour Theory by the Number

Zero           (or nearly so)
One (I)        A Spin on Colour
One (II)       Cyclops Vision
Two (I)        Binocular Vision
Two (II)       The Retinex Theory of Edwin Land
Three (I)      Additive Primaries and the Greyscale Example
Three (II)     Subtractive Primaries
Three (III)    CIE Colours
Four (I)        Printing Primaries:- CMYK
Four (II)       The Psychological Primaries / L*a*b
Five             The Munsell System
Six               The Artist's Palette / Colour Wheel 
Seven          Roy G. Biv:- Newton's Colours
Eight            D.o.D. / Colour in Black and White
Nine / Ten    The Pantone System
Eleven (or a Dozen) Colour Names

Zero (or nearly so)

Visible Spectrum    The electromagnetic spectrum consists of radio waves, microwaves, infra-red radiation, visible light, ultraviolet light, X-rays and gamma rays. The eye can see only 2% of this electromagnetic energy.  Alternately, of 108 octaves of detectable electromagnetic radiation, the eye is sensitive to only one octave. 

"The Rays to speak properly are not coloured."
"To what modes...Light produceth in our minds the Phantasms of Colours is not so easie."      Sir Isaac  Newton (1642-1727).

    More significantly, colour requires an observer.  Colour can be thought of as a persistent optical illusion.  It is the brain's way of interpreting the information that it receives from the three different types of cone cells in the eye.  The spectral sensitivity of each type of cone (Red, Green and Blue) is shown in the visible spectrum images.  Visible light is from 400 to 700 nm (nanometres).
    Another zero comes from the CIE's investigation of colour perception. There are no real-world colours that are universal primaries; i.e. able to make all other visible colours from their mixtures.
    People have asked "What wonderful new colours would be visible if we could see into the Ultraviolet?"  The answer is again zero.  The three cone system is the best compromise between visual acuity and the ability to avoid colour ambiguity.  The cones would be adapted to any spectral range that was visible and would present the same information to the brain.  We know that we would see some different patterns of colour (e.g. in flowers that have different reflectances in the ultraviolet than in the visible) but the spectrum of colours would be the same as we see now.
    What they often mean is "What colours would we see if we had a fourth colour receptor?" by assuming that we would need a new one to see into the ultraviolet.  If we had a fourth one for whatever reason, then we have no way to predict how the new visible spectrum would look.
    Finally, one experiment Newton tried was sitting in a dark room and stimulating the eye's nerves by applying pressure to the side of the eye.  He noted the colours thus created.

One (I)   A Spin on Colour

Spinning Colour Illusion    There is no colour information when only one wavelength of light is available for seeing.  You have likely experienced this under yellow sodium street lights or yellow bug lights.  Colour information is almost completely wiped out.
    This does not mean that the colour spectrum cannot be created from a single colour of light.  The disk image will show a variety of colours when spun using a variable speed drill or a vinyl record player.  The white/dark stripes will excite the different cones at slightly different times.  The cones' colour responses are at the 24 frames per second rate of a movie film.  This is not fast enough for all of the cones' responses to be summed up in the spinning pattern so a blurred colour sensation is created instead of the expected grey.

One (II)     Cyclops Vision

    Every discussion of colour vision deals with the individual eye.  Descriptions of cones, centre/surround opponent systems, and the organisation of colour information do not extend to how this information is integrated with the other eye when it reaches the brain.  There is the implicit assumption that both eyes see the same colours.  One case where this is not true is described in Science Magazine.

Two (I)     Binocular Vision

    An individual described the result of a minor stroke.  His right eye still had normal colour perception, and viewing with both eyes was also normal.  However the colour vision in his left eye was not normal and was described as skewed.
    The normal person has two eyes.  We assume the colour information from each eye is identical but the "Sky Blue" section can demonstrate otherwise.

Two (II)    The Retinex Theory

Retinex Link    Edwin Land, founder of the Polaroid-Land Camera Company, discovered that two wavelengths of light are sufficient to re-create the colours in an image.  He called this visual mechanism the Retinex Theory because he determined that both the retina and the visual cortex of the brain were involved in interpreting colour information.
     The colour image is re-created in a special manner using only black and white photographic slides.  Take one picture of a scene through a red filter and a second through a green filter.  You now have two black and white slides with different colour information.
    Put the slides into different projectors and align the images.  Now put a red filter over the lens of the slide that was taken through the red filter.  (Do not use a green filter on the other projector.)  Logically you should get an overall reddish image.  Surprisingly the image is coloured.  The colours are not as vivid as in the original scene but an entire spectral range of colours is clearly visible.  (The Retinex pictorial representation is here.)
    This is the local link to the Scientific American Retinex article (pdf) that introduced the theory to the public.   Here is the Retinex external link.

Three (I)   Additive Primaries

Additive Primaries    These are Red, Green and Blue - the RGB colour system for the monitor/screen you are using to observe this website.  The Secondary colours are Cyan, Magenta and Yellow.  The colours are created from excited phosphors in the monitor, or from coloured lights as in the  Additive Primaries image.
      All three primaries together create White, the brightest combination possible.  Alternately, one Primary and its complementary colour (one of the Secondaries) will also create white.  However, each secondary colour can be reproduced by a single wavelength of light rather than the two implied by the colour theory.  Therefore White can be created from only two wavelengths of light.  Once this is understood, many more two-colour complementary combinations can be found that make White than the original three pairs in the Additive Primary system.
    Because there are three additive primaries, they are often represented as a mathematical X,Y,Z co-ordinate system.  However, the visual response (the colour the eye actually sees) is not linear with the brightness represented by the RGB values.  Therefore the RGB system is not a suitable mathematical system for representing human vision or the corresponding colour theory.  See the Greyscale example.

Three (II)   Subtractive Primaries

Subtractive Primaries Link    These are Cyan, Magenta and Yellow.  The secondary colours in this system are Red, Green, and Blue.  Note the symmetry with the Additive Colours with the primaries and secondaries interchanged.
    Overlapping colour filters can achieve an almost perfect reproduction of the Subtractive Primaries image.


Three (III)   CIE Colours

CIE 1931    There is no real-world set of primary colours that will reproduce all of the colours that the eye is capable of seeing.  Manufacturers of monitors or inks imply that it is because of technological limitations:- the monitor/screen does not have the perfect phosphors, or the printing dyes absorb extra wavelengths thereby reducing their purity.
    In fact, the characteristics of the cones in the eye prevent perfect primaries.  The CIE (Commission International de l'Eclairage) has investigated the eye's response to colour.  The CIE Diagram has been constructed as a true mathematical co-ordinate system. This means that the visual response between any two colours (two points on the graph) is a straight line.  Since the boundary around the visible colours is for the most part curved, you cannot select three real-world colours that will create a triangle to enclose all of the colours that the eye can see.
    The CIE colours are designated as x, y, and z.   They are imaginary colour axes and only a subset of co-ordinates designate visible colours.

Four (I)   Printing Primaries CMYK

Printing CMYK    These are Cyan, Magenta, Yellow, and Black.  These make up the CMYK printing system.  The white of the paper is the starting point.  The CMY printing inks are applied as dots of variable size . The inks are transparent to allow colour mixing by overlap to create the secondary colours of Red, Green and Blue.   The Black is needed to create dark shadows because the other inks will only create a transparent grey when they all overlap.  Also, black ink made from carbon is a cheaper way to create the greys than by overlapping the more expensive coloured inks.  

Four (II)   The Psychological Primaries / L*a*b

Psychological Primaries    The psychological primaries are Red, Yellow, Green and Blue.  When people are asked if they can see red and yellow in orange, they say they do. There are also descriptions such as reddish-orange.  Similarly for purple.  However, yellow is a very delicate colour.  There is no colour that can be readily called greenish-yellow by an untrained individual.  As soon as yellow is mixed with blue, the new colour is a variant on green; i.e. yellow-green.  Because of this large change in visual response to a small change in colour, Green is considered to be a Psychological Primary.
    Next, there is evidence that the colours are not transmitted to the brain as RGB cone responses.  The information is reorganized into Red-Green, and Blue-Yellow opponent pairings with a Brightness value.  (See the York University description of colour vision.)       It has been formalized into the L,a,b colour system.  It is a mathematical co-ordinate system similar to the CIE system.   Light meters are made that give an objective measure of colour in this system (also called CIELab).
    The Ostwald classification system also uses four colours but was found not to be as versatile as the Munsell system because it did not have a good notation system for defining colours.
    Finally, this opponent pairing explains why colour-blindness is red-green or  blue-yellow, or total.  There is no such thing as, say, Red-Blue colour-blindness.

Five   The Munsell System

Munsell Colours    This copyrighted system is not a colour theory but a classification system.  It is used primarily in the paint industry.
    The five base colours are Red, Yellow, Green, Blue and Purple with provision for intermediate colours.  It uses colour chips provided by the company in their Munsell Colour Atlas.  The chips are chosen to create an equally spaced visual response for each of the colours.  Reasonably good mathematical agreement with the L*a*b measurement system is possible.

Six   The Artist's Palette / Colour Wheel

Artist's colours    These are Red, Yellow and Blue as primaries and Orange, Green and Purple as secondaries.   It is a practical Subtractive colour system that can be traced back to Renaissance painters.  These are the most vivid colours recognized as distinct by almost everyone.  (Here is information on artists' tube colours.)
    Theoretically, Magenta and Cyan would make better colour mixtures than Red and Blue - but they are not perceived as pure colours.  Thus the artist would be faced with extra work to make reds and blues.  Additionally, the secondaries Orange and Purple would require three colours in the mixture instead of just two.  More than two pigments in a mixture tends to make muddy colours.  This is why the artist prefers to use single-pigment secondaries rather than relying exclusively on primary colour mixtures.  Finally, there have not been acceptable Magenta and Cyan pigments available to the artist until recently.
    When the colours are arranged as a colour wheel, it is immediately obvious which colours are complementary; i.e. opposite colours on the wheel.  When mixed,  complementary colours produce grey.  To dull a colour, mixing a small amount of its complementary is preferable to adding Black.  This is because some blacks have a greenish undertone that muddies the colours.

Seven   Roy G. Biv

Newton's Colours    This is the mnemonic for the Red, Orange, Yellow, Green, Blue, Indigo and Violet colours described in Sir Isaac Newton's colour wheel.  Newton gave these names to the seven colours that he perceived to be distinct in the spectrum.   Although historically interesting, there is evidence that Newton chose the number of colours based on numerology (e.g. seven musical notes, seven days of the week) and named the colours to fit.
    The useful organizing principles of Primary-Secondary Colours (Hermann von Helmholtz (1821-1894)) and Complementary Colours (M. E. Chevreul (1786-1889)) were still in the future, so Newton (1642-1727) could postulate an odd number of colours.  We now classify colours as complementary pairs and we generally deal with an even number of colours.

Eight   D.o.D. / Colour in Black and White

Black & White in Colour Theory    The U.S. Department of Defense had specified eight colours for map-making purposes:- purple, dark blue, light blue, blue-green, lemon-yellow, orange, reddish-purple, and light reddish-purple.  These colours, plus black and white, give maximum clarity and visibility for graphics and maps.

    Three colour receptors in the eye imply eight excitation states (colours) that the eye is tuned to see.  These include White and Black in addition to the Red, Green, Blue, Magenta, Cyan and Yellow already discussed.  Until now I have skirted the issue of White and Black in colour perception.
    In fact there is an alternate set of light receptors in the eye called 'rods' discussed with the visible spectrum ('Zero' section above).  They can only 'see' in black-and-white.  They are excluded from the centre of the retina (the fovea) where the cones are densely packed.  Rods are more sensitive than cones to light and to the blue region of the spectrum.  Rods contribute to peripheral vision, motion detection, and night vision.  They do not directly contribute to colour vision.  (They are involved in the Purkinje Effect however.)

    Aristotle believed that colours were on a linear scale between black and white with violet being close to black and yellow closest to white.  Johann Wolfgang von Goethe postulated that colour was a result of the interaction of black and white contrasts with the eye's colour receptors.  Other investigators failed to distinguish between Additive and Subtractive colour systems.  (Recent thinkers have had speculations on black and white.)

    The spectrum is a linear display of colours but the full range of visible colours requires a three dimensional colour space for full representation.  Most colour systems use a Black-to-White scale to complete its three dimensional aspect.  The Munsell system calls it "Value".  The L*a*b meter gives a "Luminance" or "Lightness" reading.  The HSB system defines a "Brightness" in addition to Hue and Saturation.

Nine / Ten   The Pantone System

    Pantone is a proprietary printing colour system that includes inks, plastic film and markers to provide consistent colours for printing, graphic arts, and packaging.  The company sells catalogues that classify colours according to Pantone ink colour mixtures.  For example, Pantone 273C is a 1:1 mixture of Pantone Rubine Red ink and  Reflex Blue ink.
    There are nine Pantone Colors: Yellow, Orange, Red, Rubine Red, Rhodamine Red, Purple, Blue, Process Blue, and Green.  An abbreviated Basic Colors list adds a tenth colour, Warm Red, to replace the previous Orange and Red colours.  White and Black are also used in the colour mixtures
    Pantone uses their own ink colours for better colour control during printing.  Deficiencies associated with the simpler CMYK system limit the range of colours that can be represented.  Furthermore, the CMYK printing system is based on overlapping dots of transparent colour where colour intensity is related to the size of the dots.  (The white of the paper is also important.)  Pantone inks are opaque for solid colour printing (no dots).  The inks are premixed according to the Pantone system with White and Black added as necessary.
    On occasion, people have tried to use the Pantone System to specify transparent colours.  This is wrong because the Pantone system is for surface colour representation only.   

Eleven or a Dozen Colour Names

    English has eleven basic colour terms:- Black, Grey, White, Red, Pink, Orange, Yellow, Green, Blue, Purple, and Brown.  Russian adds 'Goluboy' (light blue).
    At the other end of the usage spectrum is the colour term 'Grue'.  Many languages combine the green and blue colour ranges of the spectrum into one word or concept.   Philosopherscolour theorists, and anthropologists have created the word Grue (green-blue) for discussion purposes.

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