A tetradic color scheme uses four hues instead of two or three. The usual construction puts them at even quarter turns around the wheel, 0, 90, 180 and 270 degrees, which is why it also goes by square color scheme. The looser version keeps four colors but arranges them as two complementary pairs at an offset other than 90, giving a rectangle rather than a square.
Every guide describes it the same way and warns you off in the same breath. Four colors, evenly spaced, maximum variety, hard to balance, let one dominate. The warning is correct. What none of them do is say where the imbalance actually comes from, and the answer is not a matter of taste. It is measurable, it sits in a specific place, and it is not the place most people look.
I ran every square tetrad on the wheel through the color difference formula this site uses for scoring, all 360 rotations, all six pairwise relationships in each. The average square contains 0.96 pairings under ΔE 40. The average triad contains 0.06. Practically every square tetrad has a weak spot, and practically no triad does. Below are the worked palettes, the numbers, and which base hues escape the problem.
What a tetradic color scheme is
Take the wheel, pick a starting hue, then take three more at 90 degree intervals. Because 90 doubled is 180, the four colors automatically form two complementary pairs: your base with the hue opposite it, and the other two with each other. A square tetrad is two complementary schemes stacked at right angles.
The rectangular variant, sometimes called double complementary, keeps that structure but narrows the offset. Base, base plus 60, base plus 180, base plus 240 is the common recipe. Still two complementary pairs, just closer together, so the palette leans toward the two ends of the wheel it occupies rather than spreading around it.
Set against the rest of the family, the angles run like this: monochromatic is 0 degrees, analogous is a cluster inside 60, complementary is 180, triadic is 120 and 240, split complementary is 150 and 210. Tetradic is the only one that closes a shape with area rather than a line or a triangle, and it is the only one where you have six relationships to manage instead of one or three.
That count is worth sitting with. Two colors give you one relationship. Three give you three. Four give you six. The number of things that can go wrong doubles when you add the fourth color, which is the real reason tetradic palettes are hard, and it is arithmetic rather than aesthetics.
Tetradic color palettes with hex codes
Square tetrads at full saturation and brightness, so the hue geometry is the only thing varying. If the notation is unfamiliar, how to read hex color codes covers what the six digits are doing.
- Red base. #ff0000, #80ff00, #00ffff, #8000ff. Red, chartreuse, cyan, violet. Six pairs run ΔE 36 to 111, mean 68.
- Orange base. #ff8000, #00ff00, #0080ff, #ff00ff. Orange, green, azure, magenta. Pairs run ΔE 36 to 111, mean 65.
- Yellow base. #ffff00, #00ff80, #0000ff, #ff0080. Yellow, spring green, blue, rose. Pairs run ΔE 28 to 103, mean 71.
- Green base. #00ff00, #0080ff, #ff00ff, #ff8000. The orange palette re-rotated, so identical numbers.
- Best balanced. #ff4d00, #33ff00, #00b3ff, #cc00ff, from base hue 18. Pairs run ΔE 49 to 112, mean 68, the tightest ratio of any square on the wheel.
And two rectangles at offset 60, for comparison:
- Red base rectangle. #ff0000, #ffff00, #00ffff, #0000ff. Red, yellow, cyan, blue. Pairs run ΔE 42 to 103, mean 67, which is better balanced than any square built on red.
- Spring green rectangle. #00ffbb, #0044ff, #ff0044, #ffbb00, from base hue 164. Pairs run ΔE 44 to 87, mean 61, a ratio of 1.98. This is the most balanced four-color set in the entire sweep.
Note what just happened. The best rectangle beats the best square. That is not what the guides imply, and it comes up again below.
The measurement: where the weak pairing lives
For every base hue from 0 to 359 I built the square tetrad, measured all six pairwise CIEDE2000 distances, and recorded the spread. ΔE is the standard perceptual measure of how different two colors look, the same formula behind the scoring on this site, explained in what CIEDE2000 actually is. Roughly, ΔE 1 is the smallest difference a trained eye catches in lab conditions, ΔE 40 is where two colors stop being confusable at a glance, ΔE 100 is about as far apart as sRGB goes.
- Mean distance across all six pairs, averaged over the wheel: ΔE 68.1.
- Weakest pair in a square, averaged over the wheel: ΔE 34.6.
- Weakest pair in a triad, same measure: ΔE 50.0.
- Average ratio of strongest to weakest pair inside one square: 3.28 to 1.
- Worst case, at base hue 341: weakest pair ΔE 24.9, strongest ΔE 108. A ratio of 4.33.
The mean is the number that misleads. A square tetrad averages ΔE 68 across its six pairs and a triad averages ΔE 69 across its three. On that measure the fourth color buys you nothing at all. What it buys you is a weak pairing: in 328 of 360 rotations, the square contains a pair closer together than anything in the triad built on the same base hue.
So the honest summary of the square tetrad is not more variety. It is the same average variety, spread more thinly, with a soft spot added. That matches how the scheme feels to use, and I have not seen it stated as a number anywhere.
The weak spot is always in one of two places
The four 90 degree steps in a square are geometrically identical and perceptually are not. Measuring a single 90 degree step across the wheel, the mean is ΔE 56 and the range runs from 24.9 to 82.3. Where the small values sit is the useful part.
- Steps starting anywhere in hue 49 to 89 fall under ΔE 35. This is yellow through chartreuse into green.
- Steps starting in hue 212 to 231 also fall under ΔE 35. This is azure into blue.
- The weakest step anywhere is hue 71 to hue 161, ΔE 24.9. A yellow green and a spring green, which sit a quarter turn apart in HSV and look like neighbours.
- The strongest step is around hue 3 to 93, ΔE 82. Red to chartreuse.
Because a square covers four quarters at once, it always lands one of its legs in the yellow-to-green band and one in the azure-to-blue band. There is no rotation that avoids both. That is the structural reason the scheme cannot be balanced by choosing a nicer base hue: the wheel has two soft regions a quarter turn apart from each other, and a square is exactly a quarter turn wide.
Both soft regions have the same cause, which is that HSV hue is a coordinate in a cube, not a perceptual angle. Green occupies a huge stretch of HSV hue for very little perceptual movement, because human vision devotes most of its discrimination to the yellow-green region and rather little to the difference between one green and another green. Blue does the same thing at the other end for a different reason: the blue primary contributes about 7 percent of white's luminance, so everything near it is dark and dark colors compress.
The two complementary pairs are not equal partners
A square tetrad is sold as two complementary pairs, which invites you to treat them as interchangeable, one for the main contrast and one for the accents. Measured, they are rarely close.
- Average gap between the two complementary pairs in a square: ΔE 33.6.
- Worst case, base hue 24: pair one ΔE 53.0, pair two ΔE 111.7. One pair does slightly over twice the work of the other.
- That palette is #ff6600, #1aff00, #0099ff, #e600ff. The orange and azure opposition is the weak one, the green and magenta opposition is the strong one.
This has a direct practical consequence. If you are picking which pair carries your primary contrast, headline against background, button against page, the geometry does not tell you and the guides do not either. Measure both oppositions and use the stronger one. In the example above, choosing wrong halves your available contrast while leaving the palette technically identical.
Square versus rectangle, settled numerically
I swept the rectangle offset from 15 degrees to 90 in 5 degree steps, averaging over all 360 rotations at each offset. The result is cleaner than expected.
- Mean pairwise ΔE barely moves: 63.9 at offset 15, 68.1 at offset 90. About 7 percent, across the entire range of the parameter.
- The weakest pair moves enormously: ΔE 7.7 at offset 15, ΔE 34.6 at offset 90. Four and a half times.
- Strongest-to-weakest ratio falls monotonically from 26.3 at offset 15 to 3.28 at offset 90.
So the offset is not a variety dial. It is a weakest-link dial. Changing it hardly affects how much perceptual ground the palette covers overall and almost entirely decides how close its two closest members sit. A rectangle at offset 20 is a complementary pair with two near-duplicates bolted on, ΔE 10 apart, which will read as a rendering artifact rather than a decision.
On average, then, the square wins, since offset 90 is the balanced end of the sweep. But averages hide the interesting case. Per base hue, the best rectangle at offset 60 has a ratio of 1.98, from base hue 164, while the best square anywhere on the wheel has 2.30, from base hue 18. The worst rectangle at offset 60 has a ratio of 9.60. Choosing the base hue well matters more than choosing square over rectangle, and it matters more for a rectangle than for a square.
Does letting one color dominate actually fix it?
The standard advice for tetradic palettes is a dominance rule, often given as 60-30-10 or some variant: pick one color to carry the layout and mute the others. It is repeated everywhere and never quantified, so I tested the version that is easy to measure. Keep the base at full saturation, drop the three accents, and see what happens to balance.
- All four at saturation 100: ratio 3.28, mean ΔE 68.
- Accents at 80: ratio 3.09, mean ΔE 66.
- Accents at 60: ratio 2.95, mean ΔE 60.
- Accents at 40: ratio 3.00, mean ΔE 52.
- Accents at 25: ratio 3.32, mean ΔE 44.
The advice works, mildly, and it has a floor. Balance improves by about 10 percent as the accents come down to saturation 60, then gets worse again below that, because heavily desaturated accents start converging on each other and on gray. Meanwhile the palette's total spread is dropping the whole way, ΔE 68 down to 44.
Saturation 60 for the accents is the measured sweet spot, and it is worth being clear about what it costs. You trade 12 percent of your total perceptual range for 10 percent better balance. That is a reasonable trade if the imbalance is the thing bothering you, and it is not a fix. The geometry problem is a hue problem and desaturation is not a hue tool.
What this means if you are trying to see color accurately
There is a version of all this for anyone training their eye rather than building a palette. Because HSV hue and perceptual hue disagree, equal moves in the picker are not equal moves in appearance, and the disagreement is large enough to change how a mistake scores.
Running four base hues through this site's scoring curve, a 90 degree hue error costs wildly different amounts depending on where you are:
- From red, off by 90 degrees is ΔE 81.5, scoring 1.3 out of 10.
- From yellow, off by the same 90 degrees is ΔE 27.7, scoring 4.4.
- From blue, off by 90 is ΔE 38.6, scoring 3.2.
- From yellow, off by 180 degrees is ΔE 103, scoring 0.9. The full reversal costs three and a half times what the quarter turn does.
The same quarter turn is worth 1.3 from one starting point and 4.4 from another. If you have ever felt that some rounds punish you harder than others for what feels like the same size of mistake, that is not a feeling. The yellow and green region is forgiving because it is perceptually compressed, and the reds and magentas are unforgiving because they are not. Getting good at this game partly means learning where on the wheel you can afford to be sloppy, and training your eye for color goes into the drills.
How tetradic compares to the rest of the family
All measured the same way, averaged over 360 rotations, at full saturation and brightness:
- Complementary pair, 180 degrees: ΔE 91.9.
- Triadic, mean of three pairs: ΔE 69.1. Weakest pair ΔE 50.
- Square tetrad, mean of six pairs: ΔE 68.1. Weakest pair ΔE 34.6.
- Rectangle at offset 60, mean of six: ΔE 67.3. Weakest pair ΔE 30.5.
- Split complementary, gap between the two accents: ΔE 40.9.
- Monochromatic, whole five-swatch palette end to end: ΔE 52.8.
The pattern down that list is that every color you add past two lowers the average and lowers the floor faster. Two colors is the maximum contrast arrangement and there is nothing to balance. Three is nearly as wide with a comfortable floor. Four is no wider than three and the floor drops by a third. Which is why a tetradic palette rewards restraint in a way a triadic one does not: the fourth color is not earning average spread, so it has to earn its place some other way, by carrying a distinct job in the layout.
The short version
A tetradic scheme is four hues, normally at 0, 90, 180 and 270 degrees, which makes it two complementary pairs at right angles. Measured across the wheel it averages ΔE 68 over its six pairs, the same as a triad averages over its three, while its weakest pair drops from ΔE 50 to 35. Practically every square contains one pairing under ΔE 40 and practically no triad does, and the weak leg always lands in either yellow-to-green or azure-to-blue because those are the two compressed regions of the wheel. Measure both complementary oppositions before deciding which carries your contrast, since they differ by ΔE 34 on average. If you mute the accents, stop at saturation 60. If you want the most balanced four-color set available, it is a rectangle at offset 60 from base hue 164, not a square at all.
Then play a few rounds and pay attention to what a yellow-green target does to your score. It will be kinder than you deserve.