A brand colour is an ink

A brand’s colour is usually written down as a number in a catalogue, and the number identifies a jar. Somebody mixed pigments to a formula, and the result is a substance with a reflectance curve — one curve, chosen for itself, and put on the sheet as a fifth ink at full strength.

Asking a four-colour press to produce that colour is a different operation entirely, and most of the time it is not possible.

The claim #

A single-pigment ink is the most chromatic thing a surface can be at its lightness, so most named colours are outside a four-colour gamut — and the ones inside it are matched metamerically, which means matched under one light.

Both halves are measured below. The first is a fact about spectra and absorption; the second is the field’s central mechanism arriving at the case where the target is a physical sample rather than another separation.

Why one pigment beats three #

The reason a spot ink is hard to reach is worth deriving, because it is not that the pigments are better.

A colour’s chroma comes from the selectivity of its absorption: a surface that absorbs strongly over a narrow band and reflects everything else is highly saturated, and one that absorbs a little everywhere is not. A single pigment can be highly selective by construction — it has one absorption band, and everything outside that band is returned.

A three-ink build cannot. To reach a given hue it must combine inks whose bands overlap, and each ink brings its unwanted absorptions with it — magenta’s band in the blue-violet is 68 per cent as strong as the band it exists to have. Every ink added to reach a hue subtracts a little more light from everywhere, so a build is always duller than a pigment at the same lightness, and the gap widens as the target saturates.

So the exclusion is structural. A press with three chromatic inks cannot reach a colour that a single pigment reaches, in the same way that three fixed primaries cannot reach a monochromatic stimulus — and it is the same argument, one field over, about the corners of a chromaticity diagram.

What was measured #

A family of 156 spot inks was constructed rather than quoted: a Gaussian absorption band at thirteen centre wavelengths across the visible, four widths from 90 to 240 nanometres, and three peak densities. Each ink is the substrate multiplied by the square of its transmittance, exactly as a process solid is.

For each, the closest possible four-colour build was found — a coarse lattice search followed by coordinate descent on ΔE00, which is what a separation program does with an out-of-gamut colour, since the problem is a minimisation rather than a solve.

15 of 156 are reachable at all, taking reachable to mean the best build lands within one ΔE00 under D50. The other 141 are outside the press’s gamut, and the worst is 16.2 ΔE00 from the closest thing four inks can make.

Of the fifteen that are reachable, the median drift under illuminant A is 3.77 ΔE00, and none is below 3.6.

A perfect match under the specification’s illuminant and a four-unit drift under a domestic lamp. That is not a failure of the build; it is what the build is. Three inks arranged to make three integrals come out right have no way to make the eighty-one values they were computed from come out right, and nothing about better presses or better matching software changes it.

The reachable inks and the drifting inks are the same inks #

The two halves of the claim are presented as separate findings — most named colours are out of gamut, and the ones inside it are metamers — and the table says they are one finding with two faces.

Read the four rows by width. The reachable inks are 240, 190, 190 and 140 nanometres wide, and the family contains a fourth width class at 90 nanometres which never appears among them. Read the same rows by drift: 3.68, 3.77, 3.95, 4.46, rising monotonically as the width falls. The broadest ink is the easiest to reach and drifts least; the narrowest reachable one is the hardest to reach and drifts most.

That is one mechanism seen twice. A narrow absorption band is what makes an ink saturated, what puts it outside a four-ink gamut, and what makes the metameric black between it and its build large. Selectivity buys chroma, chroma costs reachability, and the leftover spectral difference is what a second illuminant reveals. There is no separate story about drift.

Which means the two failure modes are not alternatives with a safe region between them. The natural reading of fifteen of a hundred and fifty-six are reachable is that those fifteen are the comfortable cases and the rest are the problem. The drift column says otherwise: the median of the fifteen is 3.77 and none is below 3.6. A distribution of drifts that stops at 3.6 rather than tailing towards zero is a distribution with no comfortable members in it.

The reason is that an ink drifting near zero would have to be one whose build is nearly a spectral match — which means an ink with almost no selectivity, which means a dull colour, which means a colour nobody would choose as a brand colour. The catalogue is a catalogue of saturated things by construction, so the reachable tail of it is not the middle of the gamut but the inside edge of its boundary, and the inside edge of a boundary is exactly where a build has spent everything it has and the residual spectral difference is largest.

So the honest summary is one sentence rather than two. A named ink is either outside what four colours can reach, or just inside it and matched by a build that comes apart by about four units under an ordinary lamp. The four-unit figure is not the price of being close to the edge; it is the price of being reachable at all, and the spread across the four reachable rows shown is only twenty-one per cent — a much narrower band than the sixteen-fold range of failure among the unreachable ones.

That has a practical form worth more than either half alone. A designer told that their brand colour “converts well” has been told the worse of two facts about it. A colour that converts badly will be visibly wrong on the first proof and will be argued about; a colour that converts well will pass every check under the standard illuminant and disagree with its own packaging on a shelf. The second is the failure that survives quality control, and it is the one that comes with the reassuring answer.

Why the fifth ink exists #

All of which is the commercial case for printing a named colour as a named colour: a fifth unit on the press, carrying the actual jar of pigment.

It costs a plate, a unit, a wash-up and a make-ready, and it is bought routinely for packaging, where a brand colour appears on every surface and where a shelf full of the product makes any variation obvious. The alternative — a sixth and seventh chromatic ink chosen to widen the gamut generally — buys a corner of the space rather than a specific colour, and the two strategies solve different problems.

The catalogue systems exist to make the transaction possible: a number identifies a formula, a formula identifies a mixture of base pigments, and any printer in the world can mix it. What travels is the recipe, not the colour — which is the same insight colour order systems are built on, applied to manufacture rather than to description.

The hex code on the brand guidelines #

Every brand document also gives the colour as an RGB triple, for the website, and usually as a CMYK build, for the print, and lists them beside the ink number as though the three were the same thing said three ways.

They are three different objects. A hex code identifies three numbers whose meaning depends on a space, a transfer function, a white point and a display; a CMYK build identifies four ink coverages on an unstated press and paper; the ink number identifies a substance. The first two are device instructions and the third is a specification of a colour.

The practical consequence is visible on any brand’s own materials. The website’s colour is right on some screens; the printed build is a metamer of the ink that agrees with it under the standard illuminant and not on a shelf; and the spot-printed carton is the actual colour. The three are compared by an art director in a room, and the room is the fourth variable.

What “matching” is being promised #

It is worth being precise about what a build promises, because the word match does two jobs in this subject and they are not compatible.

A colorimetric match is an agreement between three integrals under a stated light and a stated observer. It is what a build achieves, when it achieves anything, and it is a genuine and useful thing: two patches that match colorimetrically will look identical to a standard observer under that light, side by side, in that surround.

A spectral match is an agreement between the curves themselves. It is what a spot ink gives, trivially, since the ink is the specification — and it holds under every illuminant, every observer, and every geometry, because there is nothing left to disagree about.

The catalogue’s CMYK equivalent is a colorimetric match. The ink is a spectral one. A brand asking for consistency across print, packaging and signage is asking for the second and being sold the first, and the drift measured above is the size of the difference.

There is a third case worth naming because it is the one people actually experience: an approximate colorimetric match, where the build is several units away even under the standard illuminant because the colour is out of gamut. That is 141 of the 156 inks here, and no amount of care at the press improves it.

One more ink and one look at the process set itself say what the four-colour build is being made out of.

Observers, as well as lights #

One further consequence, and it belongs to this site more than to the trade.

A metameric match is a match for the observer whose matching functions were used to compute it, and observers differ from one another by more than the two CIE standards differ. Two people looking at a brand’s carton beside its spot-printed sign, under one light, can genuinely disagree about whether they match — not as a matter of judgement, but because the pair is metameric and their cone fundamentals are not identical.

This is observer metamerism, and it is the reason a match that survives an instrument and a viewing booth can still be rejected by a client. The instrument used the 1931 functions; the client did not.

A spot ink is immune to all of it. Two identical spectra match for every observer, which is a much stronger property than any build can offer and is the real content of specifying a substance.

Where this model stops #

The spot inks here are single Gaussian absorbers and real ones are mixtures. A catalogue formula is typically two to four base pigments, so its curve has more structure than one band and is usually a little duller — which means the 10 per cent reachable figure is a lower bound on what a real catalogue offers. Published figures for the coated version of the best-known catalogue put roughly half of it outside a four-colour gamut, which is the right order and comes from the same mechanism.

The build is optimised for ΔE00 under D50 and nothing else. A real separation program will often optimise something else — a hue-preserving match, or a match under two illuminants at once, which trades a little accuracy under the first for a lot under the second. That option exists and is rarely used, and it is the fix the previous rung recommends.

Ink film thickness is fixed here. A press running a spot colour can adjust film thickness, which moves the colour along a curve of its own; that is how a pressman hits a target, and it is one more degree of freedom this model does not carry.

And nothing here is about consistency. The reason brands specify inks is as much about variation between runs as about gamut: an ink is mixed to a formula and is the same every time, while a four-colour build inherits every drift in four units. That is a quality-control argument and it does not appear in any of the numbers above.

A denser spot ink under the proofing illuminant is the case a brand guideline actually specifies, and the build’s shortfall there is the number that matters.

What the catalogue’s own conversion says #

Every matching system publishes a four-colour equivalent for every ink, and it is worth being clear about what that table is.

It is not a claim that the build matches. It is the closest available build, computed for a stated printing condition, published because a designer will need something to put in the file when the job is four-colour. The catalogues say so, in the front matter that nobody reads, and their own printed guides show the ink and its build side by side on the same page — which is the most honest possible presentation and is routinely mistaken for a demonstration that the two agree.

The measurement in this essay is the same table computed rather than printed, and its shape is the one the guides show: a minority of the entries are close, most are approximations, and the closeness is a property of where the colour sits rather than of how carefully the conversion was done.

Reading the three process inks as absorbance rather than reflectance is what shows where each one’s unwanted absorption is.

The generalisation #

A specification given as a substance and a specification given as coordinates are different in kind, and converting between them is a projection that loses the difference.

The pattern is everywhere once noticed. A paint is specified by formula and reproduced by measurement. A dye lot is specified by recipe and checked by colorimetry. A camera’s raw file is a set of coordinates in a space nobody standardised, and turning it into a colour requires a matrix that is a claim about a sample set.

In each case the coordinate version is convenient, portable and lossy, and the loss is invisible until a second measurement is made — a second illuminant, a second observer, a second geometry. The substance carries information the coordinates do not, and a system built entirely on coordinates has no place to put it.

The corollary for anybody specifying a colour is short: name the thing if it can be named. A pigment number, a spectral curve, a physical standard — anything that fixes a spectrum rather than an integral — survives changes of light, observer and medium that three numbers do not.

Who found it, and when #

Mixed inks are as old as printing, and the modern arrangement — a numbered catalogue with published formulae, so that a designer and a printer in different countries can name the same colour — dates from 1963, when Pantone published its first matching system with ten base inks.

The insight it commercialised was not chemical but organisational: make the specification a recipe rather than a description. Colour order systems like Munsell had been describing colours since 1905; what a matching system adds is that the description can be manufactured.

The four-colour conversion tables came later and have always been the awkward part of the system. Every catalogue publishes a CMYK equivalent for each ink, and every catalogue notes that the equivalent is approximate; the number of inks for which the approximation is good is the measurement this essay makes, and the honest version of it is that most named colours exist precisely because they are outside what process printing reaches.

Where the ladder goes next #

This rung sits on the separation is not unique, which supplies the metamerism, and on a hex code is not a colour, which is the same confusion between a specification and a device instruction, one field down.

Beside it, the lamp in the shop decides is where the drift measured here has its consequences, and where a two-illuminant specification is proposed.

Above, the fifth ink buys a corner takes the other route out of the same problem: instead of a named ink for one colour, an extra chromatic ink for a whole region — and measures what each additional unit is worth.