Open a Munsell book to the pale red page and find the chips labelled 7.5RP 9/2 and 10RP 9/2. They sit next to each other. The notation says they are one hue step apart, one unit of the system that was built so that one unit always means the same amount of difference. Convert both to CIELAB and measure the gap and it comes to 0.66 CIEDE2000, roughly a quarter of the smallest difference a careful observer can find under good light. They are printed as two colors and they arrive as one.
That is not a printing fault. It is what the geometry of the system forces. Albert Munsell wanted a color solid where a step of hue, a step of value and a step of chroma were all worth the same to the eye, and he assembled it by looking at painted chips and moving them around until the spacing felt even. I wanted to know how close he got, so I took the official renotation data, converted every chip to a modern color space, and measured all 7,249 pairs of neighbours in the solid.
The short answer is that he got one axis almost exactly right and the other two are a compromise that breaks in opposite directions.
What the Munsell system actually is
Albert Henry Munsell was a painter and a teacher at the Massachusetts Normal Art School, and his problem was a teaching problem. Color names are useless for instruction. Two students hear crimson and mix two different reds. He wanted notation instead of vocabulary, so from 1898 he worked on a scheme that landed in full in A Color Notation in 1905.
The system splits a color into three independent numbers, written as H V/C.
- Hue. Position around a circle of five principal hues (red, yellow, green, blue, purple) and five intermediates, each split into ten, giving 100 hue steps. The book samples 40 of them, so neighbouring pages are 2.5 hue units apart.
- Value. Lightness on a vertical axis, 0 for ideal black and 10 for ideal white. The real chips run 1 to 9.
- Chroma. Distance out from the neutral grey axis, starting at 0 and counting up in twos for as far as pigment allows. There is no upper bound in principle, which is why the solid is a lumpy tree rather than a sphere.
So 5R 4/14 is a mid dark, very saturated red, and 10YR 5/4 is the sort of dull yellow brown that fills a soil chart. The important claim, the one everything else rests on, is that these are meant to be perceptually equal steps. Munsell called it psychological equispacing. Going from value 4 to value 5 should be the same size of change as going from value 7 to value 8, and the whole point of the arrangement is that a number tells you how different two colors look, not just how they were mixed.
The version everyone uses is not quite Munsell's own. After he died in 1918 the Optical Society of America put a subcommittee on the problem, and in 1943 Newhall, Nickerson and Judd published a revised set of coordinates measured against the 1931 CIE observer. That is the Munsell renotation, and it is the dataset here.
How the measurement works
The renotation gives every chip as xyY under CIE illuminant C, the daylight approximation in use at the time. I used the real.dat file from the Munsell Color Science Laboratory at RIT, which holds 2,734 chips that correspond to physically achievable pigments rather than the extrapolated coordinates in the larger file, some of which sit outside the spectrum locus and are not colors at all.
For each chip I converted xyY to XYZ, adapted from illuminant C to D65 with a Bradford transform, and converted to CIELAB. Differences are CIEDE2000, the current standard for how far apart two colors look. A difference of about 2.3 is the usual threshold where an attentive observer starts to see two colors rather than one. Adjacent means a single step in exactly one direction: one value up, one chroma step of two, or one hue step of 2.5. That gives 2,281 value pairs, 2,374 chroma pairs and 2,594 hue pairs.
One caveat worth stating before the numbers, because it changes how you should read them. This is a 2001 color difference formula grading a 1905 color solid, and both are models fitted to human observers, not truth. Where they disagree, neither one is automatically right. CIEDE2000 in particular contains a term that deliberately discounts differences at high chroma, which is the opposite of what Munsell assumed, so some of the gap below is two committees disagreeing about the definition of a step. What makes the result interesting is that the disagreements are structured. They are not noise. They point in specific directions, at specific parts of the solid, for reasons you can name.
Finding one: the value scale is very nearly perfect
Start with the axis Munsell got right, because it is genuinely impressive. Fit CIE lightness against Munsell value across all 2,734 chips and you get:
L* = 10.165 V + 0.336, with an R squared of 0.99973 and a largest single residual of 2.89.
The CIE defined L* in 1976 by fitting a cube root function to lightness judgements. Munsell arrived at his scale by eye seventy years earlier, and the two agree to within about two units of lightness across the entire range. His value scale is the modern lightness scale divided by ten. If you want a single sentence for what a hand-built perceptual system can achieve, that is it.
The step sizes back it up. A one step change in value measures a median 8.02 CIEDE2000, and the consistency across the solid is the striking part:
- At chroma 2, the median value step is 7.98
- At chroma 4, 7.98
- At chroma 6, 8.00
- At chroma 8, 8.01
- At chroma 10, 8.06
Five different regions of the solid, one number. It drifts up to about 8.8 past chroma 12, and it varies more along the scale itself, from 6.8 for the step out of value 1 up to 10.06 for value 4 to 5 and back down to 6.37 for value 8 to 9, so the middle of the scale is stretched relative to the ends. But of all 2,281 value steps in the book, not one falls below the 2.3 threshold. Every rung of every ladder is visible.
Finding two: the three axes are not worth the same
Here is where the promise starts to come apart. If one step means one step, then a step of value, a step of chroma and a step of hue should all measure about the same. Dorothy Nickerson wrote down the classic weighting in 1936, an index of fading built for judging how far a dyed fabric had drifted, and it is still the standard rule of thumb for turning Munsell coordinates into a difference:
Difference = 0.4 C dH + 6 dV + 3 dC
Put the book's own step sizes into that and something neat falls out. At chroma 6, a value step of 1, a chroma step of 2 and a hue step of 2.5 all come to exactly 6. The rule says the three axes are interchangeable there. Measure the same three steps in CIEDE2000 and they are not:
- Value step: 8.00
- Chroma step: 3.96
- Hue step: 3.30
A step up the value axis is worth about two steps of chroma and about two and a half steps of hue. Across the whole solid the medians are 8.02 against 3.28 against 3.58, so to travel as far as one value step you need to move roughly 4.9 units of chroma. The traditional weighting puts that figure at 2. It is out by a factor of two and a half.
The correlation is worse than the medians suggest. Across all 7,249 steps, the Pearson correlation between what the Nickerson rule predicts and what CIEDE2000 measures is 0.022. That is not a weak relationship, it is the absence of one. The old rule takes only three distinct values here so it was never going to track a continuous measurement closely, but a coefficient of 0.022 means that knowing how many Munsell steps separate two chips tells you essentially nothing about how different they will look. The notation is a good address system and a poor distance function.
My reading of this is that lightness carries far more weight in judgements of difference than the Munsell tradition allowed for. That matches what we measured on this site when we went after the just noticeable difference directly and found the lightness threshold to be the tightest of the three by a wide margin, and it matches the red-green color blindness result where almost everything a dichromat has left to work with turns out to be lightness. People notice light and dark first. Every practical color system ends up rediscovering that.
Finding three: the two horizontal axes fail at opposite ends
The value axis holds up everywhere. The other two do not, and the way they break is a mirror image.
A hue step near the neutral axis is almost nothing. At chroma 2 the median hue step is 1.56 and 82 percent of them sit below the 2.3 threshold. Walk right around the 40 page hue circle at value 8 and chroma 2, and 34 of the 40 steps are invisible. The whole circle spans a set of pale putties that a person would call one color.
Chroma does the reverse. Near the neutral axis a chroma step is large, a median 6.99 for the move from chroma 2 to 4. It then shrinks the whole way out: 3.96 at chroma 6, 2.56 at chroma 12, 1.80 at chroma 20. Past chroma 16, 85 percent of chroma steps fall under the threshold, and from chroma 20 outward essentially all of them do.
Set the two side by side and the pattern is clean. The share of steps that no one can see, by chroma level, hue steps in blue and chroma steps in red:
Across the whole book, 14.8 percent of adjacent chip pairs are closer than a just noticeable difference. None of them are value steps. 23 percent are chroma steps and 20 percent are hue steps, and the two failures barely overlap because they happen at opposite radii.
Why a cylinder cannot be uniform
The hue result has a plain geometric cause. Munsell hue is an angle. A step of 2.5 hue units is a fixed rotation, and the distance you actually travel when you rotate is the angle times the radius. Chroma is the radius. So a hue step at chroma 2 covers a seventh of the ground that the same step covers at chroma 14, and there is no way to number the pages of the book that avoids it. Any polar system inherits this. It is a property of the coordinates, not a mistake in the sampling.
The chroma result is different and more contested. Part of it is real: as colors get more saturated they run out of room, the pigments available get scarcer, and differences genuinely compress near the edges of what a surface can do. But a good part of it is CIEDE2000 itself. The formula divides chroma differences by a term that grows with chroma, so it systematically discounts differences between saturated colors on purpose, because that is what the experimental data it was fitted to demanded. Munsell's chips were spaced by observers doing a different task, judging whether steps looked even rather than whether pairs looked different, and those two questions do not have to give the same answer.
I do not think that undermines the finding so much as sharpen it. Two careful attempts to define an equal step, ninety six years apart, both grounded in real observers, disagree by a factor of nearly five in the chroma direction. That is worth knowing before you treat any color difference number as an absolute. The place they agree is lightness, which is also the place where the answer was easiest to get.
What this means if you actually use a Munsell book
The practical version of all this is short.
- If two neighbouring chips look identical, that is expected. One pair in seven is genuinely below the threshold for a difference. You are not failing the book, the book is finer than vision in those regions.
- Trust the value column. If you are trying to match a sample and you are not sure which of two chips is right, the value judgement is the reliable one. It never collapses anywhere in the solid.
- Near neutral, do not agonise over the hue page. At chroma 2 and 4 the pages either side are usually indistinguishable. Pick either. This is exactly the region a soil chart or a skin tone chart lives in, and it is why two trained people can disagree about the page and both be right.
- At high chroma, the chroma number is finer than your eye. Past chroma 16 you are recording a distinction you cannot verify.
There is one more constraint if you are working on a screen rather than with paper. Of the 2,734 real Munsell chips, only 55.0 percent fall inside the sRGB gamut. Nearly half the book cannot be displayed on an ordinary monitor at all, and any image of a Munsell chart you find online has silently clamped those colors to the edge of what the screen can do. On the 10YR page, chips 5/10 and 5/12 both clamp to the same hex. That is the same wall we ran into measuring RGB against CMYK, from the other side. Every swatch shown on this page is one of the 55 percent that survives the trip to a screen, so the ladders above understate how far the real book reaches.
The part Munsell got right
It would be easy to read 14.8 percent invisible steps as a failure. I think it is the opposite. A painter with no colorimeter, no CIE observer functions and no computer laid out a three dimensional solid by moving chips around on a spinning disc, and the lightness axis he produced matches the one an international standards body derived from experiment seventy years later to within two units out of a hundred. The two axes that misbehave misbehave for a reason that is baked into polar coordinates and could not have been designed away.
What he actually built was not a distance function. It was an address system, and a very good one, which is why soil scientists, dermatologists, beer brewers and archaeologists still use it while the color difference formulas get replaced every twenty years. The notation tells you where a color lives. It was never going to tell you how far away it is.
If you want to feel this rather than read it, the Hue Sort variant asks for the ordering judgement the whole system rests on: a run of colors that has to be put in hue order. It draws its saturation at random, and the honest thing to say having done this measurement is that the round is much harder when the run comes out washed out than when it comes out vivid, for exactly the reason above. The main Color Memory Game asks the harder version, holding a color in your head and reproducing it later, and shades of gray covers what happens to color vocabulary when chroma drops to nearly nothing. For the count of how many colors are actually distinguishable in the first place, there is how many colors you can see.