Visual Art

Theory

Colour Wheel

How did the Martian Colour Wheel evolve?

You may, quite rightly, be wondering how my colour wheel came to be the way it is. Did I simply invent the colours as I pleased and then name them? Well, not exactly... I went through a logical and reproducible process based on colour theory which I now lay down for you here.

Step 1 - The 6 primary hues

My colour wheel starts with the 3 additive primary colours: Red, Green and Blue and the 3 subtractive primaries: Yellow, Cyan and Magenta. These 6 colours are placed 60° apart around the wheel with Red at 0°, Yellow at 60°, Green at 120°, Cyan at 180°, Blue at 240° and Magenta at 300°. These are the 6 primary hues and they anchor the wheel. Their position may not be altered. All colour wheels that purport to follow modern colour theory must start like this.

Since colour depends on intensity and saturation as well as hue, I set up 5 rings on the wheel to add these dimensions. The 3rd, or central, ring is the "true" representation of the hue: 100% saturated at 100% intensity. The 2nd ring, (the adjacent ring closer to the centre), is 100% saturated at 65% intensity and the 1st, (the most interior), ring is 100% saturated at 35% intensity. The 4th ring is a medium "tint" of the true colour, 100% intensity and 50% saturated and the outer ring is a light tint, being 100% intensity and 22% saturated. Low intensity desaturated colours are less important at the moment and I will deal with them elsewhere.

You may notice at this point that the second ring in the case of the hues blue, magenta and red seems too close to the 3rd ring, (especially for blue). However that is not the case for the other 3 hues so for the moment I will leave the intensity value for this ring at 65%. This apparent variation in tone for a constant value is due to various things and will be addressed later.

The outer ring without colour is simply there to name the "hue" as opposed to a specific "colour" within that hue. Thus we must be able to distinguish between "yellows" the hue and "Yellow" the colour. "Olive", "Butter" and "Yellow" (the colour) are all colours that belong to the hue: "yellows". For the purposes of this wheel I will use initial caps for colours and lower case for hues.

Step 1 - The 6 primary hues, uncorrected (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Comment
Ham	0°	22%	100%	Additive primary
Pale Raspberry	0°	50%	100%	Additive primary
Red	0°	100%	100%	Additive primary
Dark Red	0°	100%	65%	Additive primary
Maroon	0°	100%	35%	Additive primary
Cream	60°	22%	100%	Subtractive primary
Butter	60°	50%	100%	Subtractive primary
Yellow	60°	100%	100%	Subtractive primary
Olive	60°	100%	65%	Subtractive primary
Olive Drab	60°	100%	35%	Subtractive primary
Pale Green	120°	22%	100%	Additive primary
Green Hellebore	120°	50%	100%	Additive primary
Granny Smith	120°	100%	100%	Additive primary
Green	120°	100%	65%	Additive primary
Zucchini	120°	100%	35%	Additive primary
Pale Cyan	180°	22%	100%	Subtractive primary
Blue Spruce Light	180°	50%	100%	Subtractive primary
Cyan	180°	100%	100%	Subtractive primary
Dark Cyan	180°	100%	65%	Subtractive primary
Pthalo Green	180°	100%	35%	Subtractive primary
Forget-Me-Not	240°	22%	100%	Additive primary
Corn Flower	240°	50%	100%	Additive primary
Blue	240°	100%	100%	Additive primary
Ultramarine	240°	100%	65%	Additive primary
Dark Blue	240°	100%	35%	Additive primary
Extra Light Magenta	300°	22%	100%	Subtractive primary
Light Magenta	300°	50%	100%	Subtractive primary
Magenta	300°	100%	100%	Subtractive primary
Dark Magenta	300°	100%	65%	Subtractive primary
Purple	300°	100%	35%	Subtractive primary

Step 2 - The Secondary Colours And Their Shades & Tints

6 hues do not provide a detailed enough colour vocabulary so another 6 hues are inserted, each one midway between each pair of primary hues. These may be regarded as the secondary hues and they flesh out the wheel providing a rough approximation to most of the famous colours that we know.

One might think that by placing the 6 secondaries at 30° offsets from the 6 primaries that their hues would also appear perfectly halfway in a subjective sense, but this is not the case as you can see below. Yellow, Cyan & Magenta appear more distant in hue to their neighbours than do the Red, Green and Blue.

This apparent "hue contraction" about the additive primaries is perhaps due to the fact that the human eye can only sense red, green and blue... or perhaps it is due to mapping a 3D colour space onto a circle... or perhaps it is something else... In any event it must be compensated for and that is done in step 3.

The apparent brightness boost around the subtractive primaries on a computer screen is quite real. The subtractive primaries are each composed of two pixels of additive primaries, so at maximum brightness they are indeed twice as bright as the additive primaries which use only 1 pixel. There is also the effect of the differential sensitivity of the human eye's 3 colour sensors. These tonal quirks also need to be compensated for and this is done in step 4.

Step 2 - 12 hues uncorrected (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Comment
Ham	0°	22%	100%	Additive primary
Pale Raspberry	0°	50%	100%	Additive primary
Red	0°	100%	100%	Additive primary
Dark Red	0°	100%	65%	Additive primary
Maroon	0°	100%	35%	Additive primary
Parmesan Cheese	30°	22%	100%	Secondary
Peanut Butter	30°	50%	100%	Secondary
Orange	30°	100%	100%	Secondary
Brown	30°	100%	65%	Secondary
Dark Brown	30°	100%	35%	Secondary
Cream	60°	22%	100%	Subtractive primary
Butter	60°	50%	100%	Subtractive primary
Yellow	60°	100%	100%	Subtractive primary
Olive	60°	100%	65%	Subtractive primary
Olive Drab	60°	100%	35%	Subtractive primary
Pale Cabbage	90°	22%	100%	Secondary
Green Cabbage	90°	50%	100%	Secondary
Green Pea	90°	100%	100%	Secondary
Basil	90°	100%	65%	Secondary
Rhubarb Leaf	90°	100%	35%	Secondary
Pale Green	120°	22%	100%	Additive primary
Green Hellebore	120°	50%	100%	Additive primary
Granny Smith	120°	100%	100%	Additive primary
Green	120°	100%	65%	Additive primary
Zucchini	120°	100%	35%	Additive primary
Pale Variscite	150°	22%	100%	Secondary
Variscite	150°	50%	100%	Secondary
Chrysolite	150°	100%	100%	Secondary
Light Emerald	150°	100%	65%	Secondary
Brunswick Green	150°	100%	35%	Secondary
Pale Cyan	180°	22%	100%	Subtractive primary
Blue Spruce Light	180°	50%	100%	Subtractive primary
Cyan	180°	100%	100%	Subtractive primary
Dark Cyan	180°	100%	65%	Subtractive primary
Pthalo Green	180°	100%	35%	Subtractive primary
Powder Blue	210°	22%	100%	Secondary
Light Azure	210°	50%	100%	Secondary
Azure	210°	100%	100%	Secondary
Cobalt Blue	210°	100%	65%	Secondary
Prussian Blue	210°	100%	35%	Secondary
Forget-Me-Not	240°	22%	100%	Additive primary
Corn Flower	240°	50%	100%	Additive primary
Blue	240°	100%	100%	Additive primary
Ultramarine	240°	100%	65%	Additive primary
Dark Blue	240°	100%	35%	Additive primary
Rose De France	270°	22%	100%	Secondary
Lavender	270°	50%	100%	Secondary
Han Purple	270°	100%	100%	Secondary
Dark Han Purple	270°	100%	65%	Secondary
Dioxazine	270°	100%	35%	Secondary
Extra Light Magenta	300°	22%	100%	Subtractive primary
Light Magenta	300°	50%	100%	Subtractive primary
Magenta	300°	100%	100%	Subtractive primary
Dark Magenta	300°	100%	65%	Subtractive primary
Purple	300°	100%	35%	Subtractive primary
Baby Pink	330°	22%	100%	Secondary
Pink Hydrangea	330°	50%	100%	Secondary
Dragon Fruit	330°	100%	100%	Secondary
Chinese Strawberry	330°	100%	65%	Secondary
Red Plum	330°	100%	35%	Secondary

Step 3 - Correcting The Secondaries For Hue Contraction

Compensating for apparent hue contraction involves dragging the secondary hues closer to the subtractive primaries. 10° seems to be about right. Compare with the step 2 wheel to see the difference. Note that this entails a movement of 1/3 of a division, quite a substantial change! In most cases such a change in hue necessitates a change in name. For example the place that was occupied by "Orange" is now occupied by "Turmeric". Yes there is the loss of famous colours from the wheel at this point, such as "Brown", "Green Pea" and "Lavender" but don't worry, they will come back when the tertiary colours are added. In the meantime their absence is compensated for with new classic colours such as "Pink", "Chartreuse" and "Violet".

Note that in the cases of the Azures and the Emeralds there is no need to change the name. This is because, thanks to a happy accident, the real world exemplars for those hues were already slightly shifted to cyan.

Note the fully saturated rings, (ie the 3 closest to the centre), seem evenly spaced regards hue but the outer 2 do not. The unsaturated outer rings appear to show a predominance of yellows, cyans and magentas at the expense of reds, greens and blues. This effect is well known and is called the Abney Effect. This hue shift is physiological rather than physical in nature. I will be compensating for it in step 5.

Step 3 - 12 hues, secondaries corrected for hue contraction (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Comment
Ham	0°	22%	100%	Additive primary
Pale Raspberry	0°	50%	100%	Additive primary
Red	0°	100%	100%	Additive primary
Dark Red	0°	100%	65%	Additive primary
Maroon	0°	100%	35%	Additive primary
Pale Buff	40°	22%	100%	Secondary
Buff	40°	50%	100%	Secondary
Turmeric	40°	100%	100%	Secondary
Yellow Ochre	40°	100%	65%	Secondary
Milk Chocolate	40°	100%	35%	Secondary
Cream	60°	22%	100%	Subtractive primary
Butter	60°	50%	100%	Subtractive primary
Yellow	60°	100%	100%	Subtractive primary
Olive	60°	100%	65%	Subtractive primary
Olive Drab	60°	100%	35%	Subtractive primary
Pale Avocado Flesh	80°	22%	100%	Secondary
Avocado Flesh	80°	50%	100%	Secondary
Chartreuse	80°	100%	100%	Secondary
Sage	80°	100%	65%	Secondary
Oak Leaf	80°	100%	35%	Secondary
Pale Green	120°	22%	100%	Additive primary
Green Hellebore	120°	50%	100%	Additive primary
Granny Smith	120°	100%	100%	Additive primary
Green	120°	100%	65%	Additive primary
Zucchini	120°	100%	35%	Additive primary
Variscite	160°	50%	100%	Secondary
Pale Variscite	160°	22%	100%	Secondary
Chrysolite	160°	100%	100%	Secondary
Light Emerald	160°	100%	65%	Secondary
Brunswick Green	160°	100%	35%	Secondary
Pale Cyan	180°	22%	100%	Subtractive primary
Blue Spruce Light	180°	50%	100%	Subtractive primary
Cyan	180°	100%	100%	Subtractive primary
Dark Cyan	180°	100%	65%	Subtractive primary
Pthalo Green	180°	100%	35%	Subtractive primary
Powder Blue	200°	22%	100%	Secondary
Light Azure	200°	50%	100%	Secondary
Azure	200°	100%	100%	Secondary
Cobalt Blue	200°	100%	65%	Secondary
Prussian Blue	200°	100%	35%	Secondary
Forget-Me-Not	240°	22%	100%	Additive primary
Corn Flower	240°	50%	100%	Additive primary
Blue	240°	100%	100%	Additive primary
Ultramarine	240°	100%	65%	Additive primary
Dark Blue	240°	100%	35%	Additive primary
Mauve	280°	22%	100%	Secondary
Kunzite	280°	50%	100%	Secondary
Violet	280°	100%	100%	Secondary
Dark Violet	280°	100%	65%	Secondary
Spectral Violet	280°	100%	35%	Secondary
Extra Light Magenta	300°	22%	100%	Subtractive primary
Light Magenta	300°	50%	100%	Subtractive primary
Magenta	300°	100%	100%	Subtractive primary
Dark Magenta	300°	100%	65%	Subtractive primary
Purple	300°	100%	35%	Subtractive primary
Light Pink	320°	22%	100%	Secondary
Pink	320°	50%	100%	Secondary
Dark Pink	320°	100%	100%	Secondary
Prickly Pear	320°	100%	65%	Secondary
Elderberry	320°	100%	35%	Secondary

Step 4 - Correcting The Wheel For Tone

The next thing you notice is that the tone, or brightness, of each hue is not constant around a ring. Most obviously: the yellow hue is very bright and the blue hue is very dark. Closer inspection reveals that 1) the subtractive primaries are brighter than the additive primaries and 2) The segment from blue to red is darkest, the segment from red to green is brightest and the segment from green to blue is medium.

You can see this best by examining the wheel in a "grey scale" representation.

Grey scale representation after step 3 (click to enlarge)

There are two reasons for this unevenness of tone around the wheel:

1. Subtractive primaries have 2 pixels while additive primaries have only one.
   
   Standard LCD and LED colour display devices produce light and thus use the additive colour theory, creating all colours and shades from pixels composed of red, green and blue sub-pixels. To create any of the subtractive primaries on a given pixel the device needs to light up TWO of its sub-pixels. Eg: to make a pixel Yellow the device needs to turn both the red and green sub-pixels up to maximum intensity. On the other hand, to generate a primary colour the device only lights up ONE sub-pixel. Eg: to make a pixel Blue the device needs to turn just the blue sub-pixel up to maximum intensity.
   
   Two sub-pixels at full means twice the intensity, which is one reason why yellow, cyan and magenta are brighter than red, green and blue on your computer display device. Colour in the real world of course is not composed of RGB pixels but a bewildering array of quantised wave packets at discrete points across the entire visible spectrum. Nevertheless, Yellow is still perceived as brighter than Blue.
2. The human eye is most sensitive to green and least sensitive to blue.
   
   If you examine a graph of the human eye's sensitivity to wavelength you will see that green is the most sensitive, with red not too far behind and blue a LONG way back. The effect of this on the colour wheel is that not only is blue very dark, the hues around it are also dark. Similarly: the hues around green are bright.
   
   In fact, the entire spectrum between the two darkest hues, (blue and red), is obviously darker than the other segments. Likewise, the entire spectrum between the two brightest hues, (green and red), is obviously brighter than the other segments. Finally as one might expect, the segment between the brightest and darkest hues, (green and blue), is of medium intensity.

The entire imbalance of tone around the wheel can be explained by a combination of these two considerations.

Before any adjustment can be made it must be understood that the "primary exemplar" (ie the colour at 100% intensity and 100% saturation), for a given hue, as far as possible must remain at full intensity and full saturation. It can be moved inward or outward a ring, but if it can be avoided it should not be desaturated or attenuated. This is to preserve the purity of the hue and to present it in its best light.

You will notice that very bright colours such as Yellow and Chartreuse are at least as bright as colours in an outer ring in a darker segment, such as Musk. Similarly very dark colours, such as Blue are at least as dark as colours in an inner ring in a brighter segment, such as Prickly Pear.

Bearing this in mind, the first thing to be done in adjusting for tone is move the most out-of-balance primary exemplars inward or outward a ring.

When you move a primary exemplar in or out you must remove a colour from one side and create a new one for the other side. When you move OUT you delete a desaturated one and create a saturated one. This is good, as it makes a more pure and colourful wheel. Conversely when you move inward you delete a saturated colour and create a desaturated one. This is less desirable...

The OUTWARD movement happens with Yellow, which moves from ring 3 to 4. In fact, due to the brightness of the yellows, greens and cyans, this outward ring jumping happens to all the primary exemplars from Turmeric through to Cyan! In order to smooth the transition from Red on the 3rd ring to Yellow on the 4th, Turmeric is desaturated slightly¹.

Conversely, Blue, whose hue appears so much darker than others, is moved IN one ring. This means that for the blue hue there are 3 unsaturated colours instead of 1 or 2. Since unsaturated lose a little "punch" Light Blue is less strong than its neighbours Azure and Violet.

Once the primary exemplars have been relocated it is fairly simple adjust the other colours in order to get a steady transition of shading through each hue and a reasonably constant tone throughout each ring.

Note that it is NOT possible to get a truly constant tone around each ring without desaturating or attenuating many of the primary exemplars, as those on a given ring are of considerably varying intensity. It MAY be possible to get an even tone on the other rings but that would throw out the steady variation of tone in a given hue.

The clearest illustration of the problem of adjusting the tone of primary exemplars is Yellow. To bring it into line tonally with its neighbours you need to attenuate it by around 15% but since it no longer looks yellow with even a 10% darkening, this is clearly out of the question. There is not such a problem with other hues but they DO lose punch when darkened or desaturated. The other problem with weakening primary exemplars is that a colour from the screen gamut is no longer there on the wheel...

You can see from the tone-adjusted wheels below that the tone is now much more uniform around each ring compared with the wheel at the start of this section. HOWEVER you will note that blue is still clearly the darkest hue and yellow the lightest. I tried moving these yet another ring, but they looked wrong there. The fact is that the human eye expects blue to be dark and yellow to be bright, so although they are still tonally out of balance I decided to leave them there.

Finally I should mention that the grey scale conversion does not entirely reflect the tones that we see. Perhaps this is a problem with Adobe Photoshop²'s conversion algorithm or perhaps it is some other artifact, in any event grey scale must be taken with a grain of salt and should not be followed precisely, (at least not this conversion). In particular Red and Green and all the purples seem much brighter in colour than depicted in the monochrome conversion.

Step 4 - 12 hues corrected for hue & tone (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Comment
Ham	0°	20%	100%	Additive primary
Pale Raspberry	0°	50%	100%	Additive primary
Red	0°	100%	100%	Additive primary
Dark Red	0°	100%	65%	Additive primary
Maroon	0°	100%	45%	Additive primary
Buff	40°	32%	100%	Secondary
Turmeric	40°	85%	100%	Secondary
Yellow Ochre	40°	100%	85%	Secondary
Tan	40°	100%	60%	Secondary
Milk Chocolate	40°	100%	35%	Secondary
Butter	60°	35%	100%	Subtractive primary
Yellow	60°	100%	100%	Subtractive primary
Wasabi	60°	100%	75%	Subtractive primary
Olive	60°	100%	52%	Subtractive primary
Olive Drab	60°	100%	23%	Subtractive primary
Avocado Flesh	80°	35%	100%	Secondary
Chartreuse	80°	100%	100%	Secondary
Celery	80°	100%	80%	Secondary
Sage	80°	100%	57%	Secondary
Oak Leaf	80°	100%	27%	Secondary
Green Hellebore	120°	40%	100%	Additive primary
Granny Smith	120°	100%	100%	Additive primary
Green	120°	100%	75%	Additive primary
Green Grass	120°	100%	64%	Additive primary
Zucchini	120°	100%	31%	Additive primary
Variscite	160°	42%	100%	Secondary
Chrysolite	160°	100%	100%	Secondary
Light Emerald	160°	100%	74%	Secondary
Emerald	160°	100%	58%	Secondary
Brunswick Green	160°	100%	32%	Secondary
Blue Spruce Light	180°	42%	100%	Subtractive primary
Cyan	180°	100%	100%	Subtractive primary
Dark Cyan	180°	100%	75%	Subtractive primary
Blue Spruce Dark	180°	100%	55%	Subtractive primary
Pthalo Green	180°	100%	29%	Subtractive primary
Powder Blue	200°	36%	100%	Secondary
Light Azure	200°	55%	95%	Secondary
Azure	200°	100%	100%	Secondary
Cobalt Blue	200°	100%	65%	Secondary
Prussian Blue	200°	100%	38%	Secondary
Forget-Me-Not	240°	26%	100%	Additive primary
Corn Flower	240°	45%	100%	Additive primary
Light Blue	240°	75%	100%	Additive primary
Blue	240°	100%	100%	Additive primary
Dark Blue	240°	100%	50%	Additive primary
Mauve	280°	25%	100%	Secondary
Kunzite	280°	50%	100%	Secondary
Violet	280°	100%	100%	Secondary
Dark Violet	280°	100%	70%	Secondary
Spectral Violet	280°	100%	45%	Secondary
Extra Light Magenta	300°	25%	100%	Subtractive primary
Light Magenta	300°	50%	100%	Subtractive primary
Magenta	300°	100%	100%	Subtractive primary
Dark Magenta	300°	100%	65%	Subtractive primary
Purple	300°	100%	40%	Subtractive primary
Light Pink	320°	25%	100%	Secondary
Pink	320°	50%	100%	Secondary
Dark Pink	320°	100%	100%	Secondary
Prickly Pear	320°	100%	70%	Secondary
Elderberry	320°	100%	44%	Secondary

Step 5 - Correct for the Abney Effect

The Abney Effect is the apparent dominance of the subtractive primaries (yellow, cyan & magenta) in tinted colours, (ie colours that have white added to them). This means that: Tints of emerald or azure will appear pulled towards cyan. Tints of chartreuse or turmeric will appear pulled towards yellow. Tints of pink or violet will appear pulled towards magenta. The more white you add the stronger the pull. Even the additive primaries are not entirely immune to this effect with light blue pulled towards purple, light red pulled towards pink and light green pulled towards emerald.

This is the most subjective correction of the entire exercise. There is no way to make a correction for this psychological effect other than by eye. You can refer to the literature of experiments done on the Abney Effect³ but their data is not of much use for this job since their results vary significantly and very dry, muddy and abstruse they are also.

To make these corrections it is necessary first to correct the additive primaries: They must be subjectively of constant hue. To my eye the unsaturated reds were a little too pink and needed to be moved toward yellow and the unsaturated green was a little too cyan in hue so it also needed to be moved toward yellow. Blue had three unsaturated tones and they appeared to be moved a little towards purple so I moved them back a little towards cyan. In all cases the outer ring exemplar moved about 10°. To my eyes at least, the subtractive primaries do not exhibit a hue change.

Adjusting for the Abney effect is complicated because not only is the effect different for each hue but the effect increases with the amount of desaturation. When you move a colour in hue its tone will change. When you correct the tone change its hue will then change. Tricky...

The hardest part comes next when you need to adjust the secondaries to exhibit not only a constant hue but that hue must appear to be halfway between its two primary neighbours, not only that but the rings must appear to step up a consistent amount in tone.

In order to judge the halfway point between two hues the 3 colours in question must all be of the same tone... but that is often impossible when one is dealing with primary exemplars... unless we break the rule and desaturate or attenuate them... And so it is that various primary exemplars, in reluctant contravention of the purity rule detailed above, were attenuated or desaturated. Specifically these are: Turmeric 85% saturated, Cyan 85% intensity, Azure 85% intensity, Violet 75% saturated, Magenta 70% intensity, Dark Pink 95% intensity. Three of these were due to the extreme brightness of Magenta. If it were possible to attenuate Yellow no doubt there would have been more alterations around that.

Step 5 - 12 hues corrected for tone, hue contraction and Abney Effect (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Comment
Ham	10°	20%	100%	Additive primary
Pale Raspberry	10°	50%	100%	Additive primary
Red	0°	100%	100%	Additive primary
Dark Red	0°	100%	64%	Additive primary
Maroon	0°	100%	40%	Additive primary
Buff	30°	32%	100%	Secondary
Turmeric	40°	85%	100%	Secondary
Yellow Ochre	40°	100%	85%	Secondary
Tan	40°	100%	60%	Secondary
Milk Chocolate	40°	100%	32%	Secondary
Butter	60°	35%	100%	Subtractive primary
Yellow	60°	100%	100%	Subtractive primary
Wasabi	60°	100%	70%	Subtractive primary
Olive	60°	100%	52%	Subtractive primary
Olive Drab	60°	100%	27%	Subtractive primary
Avocado Flesh	90°	35%	100%	Secondary
Chartreuse	80°	100%	100%	Secondary
Celery	80°	100%	75%	Secondary
Sage	80°	100%	57%	Secondary
Oak Leaf	80°	100%	27%	Secondary
Green Hellebore	110°	38%	100%	Additive primary
Granny Smith	120°	100%	100%	Additive primary
Green	120°	100%	75%	Additive primary
Green Grass	120°	100%	60%	Additive primary
Zucchini	120°	100%	31%	Additive primary
Variscite	140°	36%	100%	Secondary
Chrysolite	157°	100%	100%	Secondary
Light Emerald	160°	100%	70%	Secondary
Emerald	160°	100%	58%	Secondary
Brunswick Green	160°	100%	30%	Secondary
Blue Spruce Light	180°	40%	100%	Subtractive primary
Cyan	180°	100%	85%	Subtractive primary
Dark Cyan	180°	100%	67%	Subtractive primary
Blue Spruce Dark	180°	100%	55%	Subtractive primary
Pthalo Green	180°	100%	29%	Subtractive primary
Powder Blue	210°	35%	100%	Secondary
Light Azure	210°	57%	100%	Secondary
Azure	200°	100%	85%	Secondary
Cobalt Blue	200°	100%	60%	Secondary
Prussian Blue	200°	100%	36%	Secondary
Forget-Me-Not	230°	30%	100%	Additive primary
Corn Flower	230°	47%	100%	Additive primary
Light Blue	235°	70%	100%	Additive primary
Blue	240°	100%	100%	Additive primary
Dark Blue	240°	100%	45%	Additive primary
Mauve	265°	27%	100%	Secondary
Kunzite	265°	50%	100%	Secondary
Violet	264°	75%	100%	Secondary
Dark Violet	280°	100%	60%	Secondary
Spectral Violet	280°	100%	43%	Secondary
Extra Light Magenta	300°	27%	100%	Subtractive primary
Light Magenta	300°	50%	100%	Subtractive primary
Magenta	300°	100%	70%	Subtractive primary
Dark Magenta	300°	100%	55%	Subtractive primary
Purple	300°	100%	40%	Subtractive primary
Light Pink	334°	25%	100%	Secondary
Pink	331°	46%	100%	Secondary
Dark Pink	324°	100%	95%	Secondary
Prickly Pear	320°	100%	62%	Secondary
Elderberry	320°	100%	42%	Secondary

Step 6 - Add An Additional 12 Tertiary Hues

The 12 hue wheel is attractive and useful and provides a half decent colour vocabulary, but the gaps between colours are still too great. To get a comprehensive colour vocabulary you need to do the same thing with 24 hues. The 12 new hues slot in to the gaps between the hues on the 12 hue wheel. They also need to be corrected for hue contraction, Abney effect and tone but will tend to fall roughly halfway between their neighbours on each side of them on their ring.

With much painstaking effort I produced a 24 hue wheel that did all this.

Step 6 - 24 hues corrected for tone, hue contraction and Abney Effect (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Comment
Ham	10°	27%	100%	Additive primary
Pale Raspberry	10°	50%	100%	Additive primary
Red	0°	100%	100%	Additive primary
Dark Red	0°	100%	64%	Additive primary
Maroon	0°	100%	40%	Additive primary
Parmesan Cheese	26°	30%	100%	Tertiary
Peanut Butter	26°	60%	100%	Tertiary
Orange	30°	100%	100%	Tertiary
Brown	30°	100%	65%	Tertiary
Dark Brown	30°	100%	37%	Tertiary
Buff	35°	35%	100%	Secondary
Turmeric	40°	82%	100%	Secondary
Yellow Ochre	40°	100%	85%	Secondary
Tan	40°	100%	60%	Secondary
Milk Chocolate	40°	100%	32%	Secondary
Wheat Ear	45°	37%	100%	Tertiary
Yellow Cheese	50°	100%	100%	Tertiary
Olive Oil	50°	100%	80%	Tertiary
Cane Toad	50°	100%	55%	Tertiary
Cow Dung	50°	100%	28%	Tertiary
Butter	60°	35%	100%	Subtractive primary
Yellow	60°	100%	100%	Subtractive primary
Wasabi	60°	100%	75%	Subtractive primary
Olive	60°	100%	52%	Subtractive primary
Olive Drab	60°	100%	27%	Subtractive primary
Champagne	73°	35%	100%	Tertiary
Golden Delicious	68°	100%	100%	Tertiary
Green Grape	68°	100%	78%	Tertiary
Light Kelp	68°	100%	52%	Tertiary
Dark Kelp	68°	100%	26%	Tertiary
Avocado Flesh	87°	35%	100%	Secondary
Chartreuse	80°	100%	100%	Secondary
Celery	80°	100%	80%	Secondary
Sage	80°	100%	57%	Secondary
Oak Leaf	80°	100%	27%	Secondary
Green Cabbage	97°	38%	100%	Tertiary
Green Pea	87°	100%	100%	Tertiary
Basil	87°	100%	77%	Tertiary
Spinach	87°	100%	57%	Tertiary
Rhubarb Leaf	87°	100%	29%	Tertiary
Green Hellebore	110°	38%	100%	Additive primary
Granny Smith	120°	100%	100%	Additive primary
Green	120°	100%	72%	Additive primary
Green Grass	120°	100%	60%	Additive primary
Zucchini	120°	100%	31%	Additive primary
Celadon	127°	36%	100%	Tertiary
Chayote	147°	100%	100%	Tertiary
Clover	147°	100%	71%	Tertiary
Shaded Fern	147°	100%	60%	Tertiary
Cucumber	147°	100%	31%	Tertiary
Variscite	140°	36%	100%	Secondary
Chrysolite	157°	100%	100%	Secondary
Light Emerald	160°	100%	70%	Secondary
Emerald	160°	100%	58%	Secondary
Brunswick Green	160°	100%	30%	Secondary
Blue Agave	150°	38%	100%	Tertiary
Verdigris	164°	100%	100%	Tertiary
Shallow Green Sea	172°	100%	70%	Tertiary
Broccoli	172°	100%	57%	Tertiary
Malachite	172°	100%	30%	Tertiary
Blue Spruce Light	175°	40%	100%	Subtractive primary
Cyan	176°	100%	85%	Subtractive primary
Dark Cyan	180°	100%	67%	Subtractive primary
Blue Spruce Dark	180°	100%	55%	Subtractive primary
Pthalo Green	180°	100%	29%	Subtractive primary
Uranus	195°	36%	100%	Tertiary
Turquoise	188°	100%	90%	Tertiary
Blue Topaz	190°	100%	72%	Tertiary
Sea Green	190°	100%	60%	Tertiary
Dark Sea Green	190°	100%	31%	Tertiary
Powder Blue	215°	32%	100%	Secondary
Light Azure	215°	55%	100%	Secondary
Azure	195°	100%	82%	Secondary
Cobalt Blue	200°	100%	60%	Secondary
Prussian Blue	200°	100%	36%	Secondary
Pale Sky Blue	227°	31%	100%	Tertiary
Sky Blue	227°	50%	100%	Tertiary
Delphinium Blue	227°	61%	100%	Tertiary
Royal Blue	214°	100%	65%	Tertiary
Dark Royal Blue	214°	100%	40%	Tertiary
Forget-Me-Not	234°	28%	100%	Additive primary
Corn Flower	234°	45%	100%	Additive primary
Light Blue	235°	60%	100%	Additive primary
Blue	240°	100%	100%	Additive primary
Dark Blue	240°	100%	48%	Additive primary
Rose De France	255°	30%	100%	Tertiary
Lavender	255°	47%	100%	Tertiary
Dark Lavender	258°	62%	100%	Tertiary
Han Purple	267°	100%	65%	Tertiary
Dioxazine	267°	100%	45%	Tertiary
Mauve	270°	29%	100%	Secondary
Kunzite	270°	47%	100%	Secondary
Violet	270°	70%	100%	Secondary
Dark Violet	280°	100%	63%	Secondary
Spectral Violet	280°	100%	43%	Secondary
Lilac	278°	30%	100%	Tertiary
Rose Of Sharon	278°	47%	100%	Tertiary
Purple Daisy	280°	100%	96%	Tertiary
Aniline	290°	100%	63%	Tertiary
Amethyst	290°	100%	42%	Tertiary
Extra Light Magenta	300°	28%	100%	Subtractive primary
Light Magenta	300°	50%	100%	Subtractive primary
Magenta	300°	100%	72%	Subtractive primary
Dark Magenta	300°	100%	58%	Subtractive primary
Purple	300°	100%	40%	Subtractive primary
Dog Rose	330°	25%	100%	Tertiary
Purple Loosestrife	325°	47%	100%	Tertiary
Shocking Pink	313°	100%	85%	Tertiary
Purple Bougainvillea	310°	100%	65%	Tertiary
Purple Bean	310°	100%	42%	Tertiary
Light Pink	338°	25%	100%	Secondary
Pink	335°	48%	100%	Secondary
Dark Pink	325°	100%	95%	Secondary
Prickly Pear	320°	100%	62%	Secondary
Elderberry	320°	100%	42%	Secondary
Baby Pink	356°	23%	100%	Tertiary
Pink Hydrangea	346°	46%	100%	Tertiary
Dragon Fruit	335°	100%	100%	Tertiary
Chinese Strawberry	333°	100%	65%	Tertiary
Red Plum	333°	100%	44%	Tertiary

Step 7 - Reinstate the full brightness and final adjustments

After step 6 I felt unhappy. I had weakened my beloved colours to make them fit into a uniform system and they had lost their impact. I couldn't live with this result so I decided to return them to their previous glory whatever the cost!

Cyan, Magenta, Chrysolite and various others were returned to their proper colour and I knew I had done the right thing. Theory should never be allowed to over-rule the truth!

There is a jump up from 3 to ring 4 between Orange & Turmeric and thanks to the great brightness of Green the primary exemplars stay on ring 4 all the way to Azure after which there is a step down to Delphinium. The darkness of Blue pulls the primary exemplar immediately down to ring 2 on the next spoke to Blue and it stays there for one more spoke at Han Purple before jumping up to ring 3 at Violet. The brightness of Magenta pulls the primary exemplar up to ring 2 again for Rose Of Sharon where it stays for 2 more spokes to Pink after which it returns to ring 3 at Beauty Berry where it stays through to Orange.

Reinstating these colours meant the moving of surrounding colours as well, so it is that there are numerous small alterations from the previous step...

I also moved a number of spokes a little to get a more even feeling of distance between the hues. Specifically I moved the Pinks and Anilines closer to Magenta and Green Peas closer to Yellow. These movements also necessitated further small alterations.

Because there were only 12 spokes in the wheel when I adjusted for the Abney effect I didn't see some of the problems that became apparent once I increased the hues to 24. In particular celadon and variscite as the lightest tints were the most obviously affected and their hues had to be moved away from cyan. This meant that they no longer embodied the colour that bore their name. I reused "celadon" as a colour name in its new hue of "emerald" but variscite no longer fitted and had to be discarded. New exemplars "Iceberg Lettuce" and "Horned Spurge" were added.

Step 7 - 24 hues corrected for tone, hue contraction and Abney Effect with primary exemplars at full intensity (click to enlarge)

Colour Name	Hue Angle	Satu- ration	Inten- sity	Red	Green	Blue	Comment
Chicken Breast	10°	30%	100%	255	191	178	Additive primary
Pale Raspberry	10°	52%	100%	255	144	122	Additive primary
Red	0°	100%	100%	255	0	0	Additive primary, primary exemplar
Dark Red	0°	100%	63%	161	0	0	Additive primary
Maroon	0°	100%	40%	102	0	0	Additive primary
Parmesan Cheese	30°	35%	100%	255	210	166	Tertiary
Peanut Butter	30°	60%	100%	255	178	102	Tertiary
Orange	30°	100%	100%	255	128	0	Tertiary, primary exemplar
Brown	30°	100%	65%	166	83	0	Tertiary
Dark Brown	30°	100%	37%	95	47	0	Tertiary
Buff	39°	35%	100%	255	224	166	Secondary
Turmeric	44°	100%	100%	255	187	0	Secondary, primary exemplar
Yellow Ochre	44°	100%	85%	217	159	0	Secondary
Tan	44°	100%	60%	153	112	0	Secondary
Milk Chocolate	44°	100%	32%	82	60	0	Secondary
Wheat Ear	45°	35%	100%	255	233	166	Tertiary
Yellow Cheese	50°	100%	100%	255	212	0	Tertiary, primary exemplar
Olive Oil	50°	100%	80%	204	170	0	Tertiary
Cane Toad	50°	100%	55%	140	116	0	Tertiary
Cow Dung	50°	100%	28%	71	60	0	Tertiary
Butter	60°	35%	100%	255	255	166	Subtractive primary
Yellow	60°	100%	100%	255	255	0	Subtractive primary, primary exemplar
Wasabi	60°	100%	77%	196	196	0	Subtractive primary
Olive	60°	100%	54%	138	138	0	Subtractive primary
Olive Drab	60°	100%	27%	69	69	0	Subtractive primary
Champagne	73°	35%	100%	236	255	166	Tertiary
Golden Delicious	65°	100%	100%	221	255	0	Tertiary, primary exemplar
Green Grape	65°	100%	78%	182	199	0	Tertiary
Light Kelp	65°	100%	52%	122	133	0	Tertiary
Dark Kelp	65°	100%	26%	60	66	0	Tertiary
Avocado Flesh	82°	38%	100%	219	255	158	Secondary
Chartreuse	76°	100%	100%	187	255	0	Secondary, primary exemplar
Celery	76°	100%	80%	150	204	0	Secondary
Sage	76°	100%	57%	106	145	0	Secondary
Oak Leaf	76°	100%	27%	51	69	0	Secondary
Green Cabbage	90°	38%	100%	207	255	158	Tertiary
Green Pea	83°	100%	100%	157	255	0	Tertiary, primary exemplar
Basil	83°	100%	77%	121	196	0	Tertiary
Spinach	83°	100%	60%	94	153	0	Tertiary
Rhubarb Leaf	83°	100%	29%	46	74	0	Tertiary
Green Hellebore	110°	36%	100%	178	255	163	Additive primary
Granny Smith	120°	100%	100%	0	255	0	Additive primary, primary exemplar
Green	120°	100%	75%	0	191	0	Additive primary
Green Grass	120°	100%	60%	0	153	0	Additive primary
Zucchini	120°	100%	31%	0	79	0	Additive primary
Horned Spurge	125°	34%	100%	168	255	175	Tertiary
Iceberg Lettuce	147°	100%	100%	0	255	115	Tertiary, primary exemplar
Clover	147°	100%	71%	0	181	81	Tertiary
Shaded Fern	147°	100%	60%	0	153	69	Tertiary
Cucumber	147°	100%	31%	0	79	36	Tertiary
Celadon	139°	33%	100%	171	255	198	Secondary
Chrysolite	158°	100%	100%	0	255	161	Secondary, primary exemplar
Light Emerald	160°	100%	70%	0	178	119	Secondary
Emerald	160°	100%	58%	0	148	99	Secondary
Brunswick Green	160°	100%	30%	0	76	51	Secondary
Aquamarine	152°	31%	100%	176	255	218	Tertiary
Verdigris	166°	100%	100%	0	255	196	Tertiary, primary exemplar
Shallow Sea Green	172°	100%	72%	0	184	159	Tertiary
Broccoli	172°	100%	57%	0	145	126	Tertiary
Malachite	172°	100%	30%	0	76	66	Tertiary
Blue Spruce Light	180°	31%	100%	176	255	255	Subtractive primary
Cyan	180°	100%	100%	0	255	255	Subtractive primary, primary exemplar
Dark Cyan	178°	100%	70%	0	178	178	Subtractive primary
Blue Spruce Dark	180°	100%	55%	0	140	140	Subtractive primary
Pthalo Green	180°	100%	29%	0	74	74	Subtractive primary
Uranus	200°	36%	100%	163	224	255	Tertiary
Turquoise	194°	100%	100%	0	195	255	Tertiary, primary exemplar
Blue Topaz	190°	100%	72%	0	153	184	Tertiary
Sea Green	190°	100%	60%	0	127	153	Tertiary
Dark Sea Green	190°	100%	31%	0	66	79	Tertiary
Powder Blue	210°	41%	100%	150	203	255	Secondary
Azure	200°	100%	100%	0	170	255	Secondary, primary exemplar
Dark Azure	200°	100%	70%	0	119	178	Secondary
Cobalt Blue	200°	100%	53%	0	90	135	Secondary
Prussian Blue	200°	100%	34%	0	57	87	Secondary
Pale Sky Blue	220°	35%	100%	166	195	255	Tertiary
Sky Blue	220°	55%	100%	115	162	255	Tertiary
Delphinium Blue	214°	100%	100%	0	110	255	Tertiary, primary exemplar
Royal Blue	214°	100%	60%	0	66	153	Tertiary
Dark Royal Blue	214°	100%	40%	0	44	102	Tertiary
Forget-Me-Not	235°	30%	100%	179	185	255	Additive primary
Corn Flower	235°	48%	100%	133	143	255	Additive primary
Light Blue	240°	65%	100%	89	89	255	Additive primary
Blue	240°	100%	100%	0	0	255	Additive primary, primary exemplar
Dark Blue	240°	100%	48%	0	0	122	Additive primary
Rose De France	255°	30%	100%	197	178	255	Tertiary
Lavender	255°	48%	100%	165	135	255	Tertiary
Dark Lavender	256°	68%	100%	128	82	255	Tertiary
Han Purple	264°	100%	100%	102	0	255	Tertiary, primary exemplar
Dioxazine	264°	100%	45%	46	0	115	Tertiary
Mauve	268°	36%	100%	206	163	255	Secondary
Kunzite	268°	58%	100%	176	107	255	Secondary
Violet	273°	100%	100%	140	0	255	Secondary, primary exemplar
Dark Violet	280°	100%	61%	103	0	156	Secondary
Spectral Violet	280°	100%	43%	72	0	110	Secondary
Lilac	284°	36%	100%	230	163	255	Tertiary
Rose Of Sharon	286°	100%	100%	196	0	255	Tertiary, primary exemplar
Purple Daisy	290°	100%	73%	155	0	186	Tertiary
Aniline	290°	100%	59%	124	0	150	Tertiary
Amethyst	290°	100%	40%	86	0	102	Tertiary
Light Magenta	300°	27%	100%	255	186	255	Subtractive primary
Magenta	300°	100%	100%	255	0	255	Subtractive primary, primary exemplar
Dark Magenta	300°	100%	67%	171	0	171	Subtractive primary
Light Purple	300°	100%	54%	138	0	138	Subtractive primary
Purple	300°	100%	33%	84	0	84	Subtractive primary
Light Pink	321°	32%	100%	255	173	226	Tertiary
Pink	316°	100%	100%	255	0	187	Tertiary, primary exemplar
Dark Pink	310°	100%	71%	181	0	152	Tertiary
Purple Bougainvillea	310°	100%	55%	140	0	117	Tertiary
Purple Bean	310°	100%	35%	89	0	75	Tertiary
Pink Cherry Blossom	338°	28%	100%	255	191	214	Secondary
Pink Hydrangea	334°	45%	100%	255	140	190	Secondary
Beauty Berry	324°	100%	100%	255	0	153	Secondary, primary exemplar
Prickly Pear	320°	100%	62%	158	0	106	Secondary
Elderberry	320°	100%	40%	102	0	68	Secondary
Baby Pink	352°	25%	100%	255	191	200	Tertiary
Rhodochrosite	348°	44%	100%	255	143	165	Tertiary
Dragon Fruit	333°	100%	100%	255	0	115	Tertiary, primary exemplar
Chinese Strawberry	333°	100%	65%	166	0	75	Tertiary
Red Plum	333°	100%	44%	112	0	51	Tertiary

Conclusion

This subjectively corrected 124 colour wheel is the Martian Colour Wheel on display here. Note that since there are in fact an infinite number of colours this subset misses a great many. However, such esoteric nit-picking is of little point since any colour you may want will have a close equivalent here. There are exceptions to this however, since I have not provided the very deep tone for each hue, nor have I provided any dark tone unsaturated colours, such as asphalt, clay, tree bark etc.

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1. I realise that this is disobeying the strong directive I gave previously, but there was no way to make the transition look smooth otherwise. I figured that one small break of the rule over the entire colour wheel was acceptable.
2. The graphic design tool that I used to create these colour wheels.
3. "The Abney Effect: Chromaticity Coordinates Of Unique And Other Constant Hues" by Burns, Eisner, Pokorny & Smith 1982 amongst others.