Tuesday, May 19, 2020

Is metamerism a big issue in print? (Part 2)

This is part 2 in a series of blog posts that recap my presentation on metamerism at Color 20. If you were actually looking for the first part, the part where I set up the characters and give the back story, then you should go to the first part.

Ahhh... so you decided to tough this blog post out? Well, good on ya, mate!

Today's post is about the intersection of expanded gamut, spot color replacement, and metamerism. I suspect that this might result in another standing-room-only blog post.

Is metamerism a big deal when you are doing spot color replacement?

Expanded gamut

In kindergarten, I was taught the lie that red, yellow, and blue were the primary colors. I will never forgive my kindergarten teacher for that. That really messed me up when I found out that the real primaries for ink were cyan, magenta, and yellow. There is a big long story about that, but for now, I will just pass the explanation along to Stephen Westland and Stephen Westland and David Briggs and David Briggs. Good articles, all of them.

And then I got even more confused when people kept talking about black ink. Why do you need black ink, if you can get all the color with just CMY? (I mean, I thought the whole idea of primaries is to give you all possible colors?) Well, there are many reasons for using black, but one of them is that you can't get all the colors with just CMY. One notable color that you can't get is black.

And guess what? Even with CMY and K, you can't get all the colors. If you want more colors, you need to add more primaries. Expanded gamut printing uses color beyond CMYK, typically orange, green, and violet, to get more of the entire range of visible colors.

(Interesting fact: Generally we would call this CMYKOGV printing, but that's a really silly order for the letters. Maybe it should be CVMOYGK?)

Spot color replacement

I know that some of you are thinking that spot color replacement is what you do to get your Dalmatian ready for St. Pat's Day. Nope. Good guess though. (To get your Dalmatian ready for St. Pat's Day, I would recommend giving him a long reddish-brown, silky coat.)

My dog Spot is not looking excited about the St. Patty's Day festivities

Historically, there has been a distinction made between process colors and spot colors. Process colors are CMYK and are used in packaging for image content. Each pixel of the printed image gets some build of those four inks. Spot colors are specialty inks that are mixed to the desired color and are printed in, well, certain spots of the printed package. The spot color inks don't usually get overprinted with other inks, and are generally not used in imagery.

This is not an endorsement. They do go well with a wasabi mustard, though.

The package above uses (maybe) a total of eight inks -- cyan, magenta, yellow, and black for the image and spot colors of dark blue, light blue, black, and green. (And there is probably a white to cover the metallic (mylar) surface. White is not referred to as a spot color, but rather a flood coat. I think this is an egregious abuse of the English language.) Each of these inks gets its own print unit.

The next print run will likely require a different set of spot colors. This leads to an expense, since the old spot color inks needs to be cleaned out between print runs. There would be an economic advantage to printing those spot color with an equivalent combination of process color inks. But if we augment those process inks with a few extra colors of inks, typically orange or red, green, and violet or blue, then nearly all spot colors can be emulated with this augmented set of inks. No need to clean up after each print run!

So, there is an economic advantage, but it comes with a hidden cost: metamerism. If one package printed with CMYK+spots should land on the shelf next to one printed with CMYKOGV, then the best we can hope for is a metameric match. Perhaps there is an excellent match under D50, but can you find a store that has good D50 lighting?

That leads us to the question of the day....

Is the degree of metamerism enough to worry about?

Disclaimer #1: I suspect that many of the people who have implemented spot color replacement have gone through the exercise of evaluating the degree of metamerism for the spot colors that are important to them. I don't intend to minimize this or necessarily replace this worthwhile test. My goal here is to help set expectations in general.

Disclaimer #2: If you are bringing a new design into production, metamerism probably isn't an issue for you, beyond perhaps needing to explain to the brand owner why the color of the package didn't match the Pantone book in the designer's living room. If you are switching production of an existing pretzel pouch to spot color replacement, and expect a short period of co-mingling on the store shelves, I leave it to you to decide on the importance of the transition period and weigh the cost of that against savings.

Those who read the previous blog will recall this image of a set of metameric sextuplets, all of which are perfect matches to my version of Pantone 147C under D50/2.

In the delivery room, with D50 lighting, these appeared to be identical sextuplets

The spectra look quite different, but when it comes down to it, is there a large metameric difference?

The following table is stolen from my Color 20 presentation. It shows the CIEDE2000 color difference between Pantone 147C and the emulated version under D65/10. This should give an appreciation for the magnitude of metamerism. The spectra look a lot different, but they still match under one illuminant, and are not a bad match under another.

Not so bad? John shrugs his shoulders. I would be cautious about trying to read much into this table. There are many combinations of CMYKOGV that could yield a given color. The software that I wrote to create the matches did not put a whole lot of thought into which one of those combinations to use. I don't claim that it yielded builds similar to any commercial spot color replacement software, Mileage may vary. This package sold by weight, not volume. Contents may have settled during shipping. Blah blah blah.

Here is another set of metameric sextuplets from my database. In this one, for whatever reason, the spectra are all a reasonably good match. We see some larger disparities around 400 nm, but these are less significant to the eye.

And another set that appear to vary about as much as the first one.

Here are the color differences.

What to make of this table? Once again John shrugs. There are bigger numbers and smaller numbers. The intent here is not to focus on one specific case, but rather to look at the data in aggregate. The database has plenty of aggregate to offer, with 3,604 metameric spectra. Here is the big picture.

I love cumulative probability density functions of color difference data

How to interpret this? John shrugs his shoulders and makes woogly eyes. I have blogged before about this sort of Cumulative Probability Density Function plot, and again here. I show below one very reasonable way to look at this data. The plot can be used to determine the percentage of color differences that are below a certain point.

I arbitrarily set 2.0 ΔE00 as a tolerance. This is a typical tolerance for print under D50/2. From that alone, it seems like a reasonable starting point. But, one may argue that this is a secondary requirement in the eyes of the print buyer. (I want it to match under D50/2, and could you also make sure the match isn't horrible under D65/10?) So maybe this is too wide?

Arguing the other side, there are two contributors that we want to consider. The first is the normal process variation, for which we may set a tolerance of 2.0 ΔE00. The second contributor is the color difference due to metamerism. These two contributors combine in the final analysis. If we allow for 2.0 ΔE00tolerance of normal process variation under D50/2, and we allow for a 2.0 ΔE00 color relative change due to metamerism, then we could see something like 4.0 ΔE00 color change when they happen together.

Now for the math stuff. They two sources of variation could cancel each other out. IT could be that by fluke, the sample is 2.0 ΔE00 off from the target under D50/2, but matches perfectly under D65/10. Generally speaking us folks in the stats world use "sum in quadrature" to describe how tolerances stack up on each other. A 2.0 DE00 variation and a 2.0 ΔE00 variation (statistically speaking) add up to sqrt ((2.0)^2 + (2.0)^2) = about 2.8 ΔE00.

So, is this a big issue for spot color replacement?

Based on this analysis, I can say this: 

If you replace a traditional spot color with another set of pigments,
and you get a perfect match under D50/2,
then you have an 8 in 9 chance of having an acceptable match under D65/10.

I make the assumption here that the normal process variation is less than 2.0 ΔE00, and that a 3.0 ΔE00 variation under D65/10 is considered acceptable. In the next blog post in this series, I will look at other illuminants. 

Tolerance for metameric index

I had a question from Rachel after my previous post regarding reasonable tolerances for the metameric index. I pause to define metameric index in this context. The graph and table I show above fit one definition of metameric index: the color difference that you see between two perfect metamers under one illuminant when you view under a second illuminant.

From my graph, I can say that 2.0 ΔE00 is a reasonable tolerance for metameric index for D65/10. Eight of nine times you can hit that. If you pay a bit of attention to metamerism when you decide on how to render an EG color, you can do better, In the next blog post in this series, I will look at other illuminants. Hint: the change from D50/2 to D65/10 is not huge...

I hope that this leads to some good argument among the folks who like to argue about standards.

Wednesday, May 13, 2020

Is metamerism a big issue in print? (Part 1)

In January 2020, I spoke that the Printing Industry of America Color Conference. This colorful event is sponsored every year by the PIA in gorgeous San Diego where the weather is always gorgeous. Next year, I understand that the colorful event that is always in San Diego will occur in gorgeous La Jolla, and it will be hosted by the as-yet unnamed organization that is the combination of PIA and SGIA.

The talk I delivered to a standing-room-only crowd was on metamerism. Based on the fact that one or two of them looked up from the cell phones a few times, I would say that the talk went over quite well. This series of blog posts will recap those exciting moments.

Metamerism - when objects are the same color under one light,
but differ under another 

Now, at the conference I didn't just state my position on whether I was fer metamerism or agin it... I went right up to it and measured it. I considered several practical issues and sought to determine just how big an issue metamerism really is. And since you are part of the elite group that is reading this blog post, you have the opportunity to read a summary of my presentation.

In Part 1 of this series of blog posts, I describe the metameric database that I used to quantify metamerism. The blog post you are currently reading, by the way, is Part 1. So, when I finally get done with this introduction, I will talk about the metameric database.

In Part 2, I use this database to answer one practical question: If I switch from printing spot colors with pre-formulated inks to printing them with expanded gamut builds of CMYKOGV, will metamerism deliver a sucker punch to me in the gut?

In Part 3, I look at the magnitude of metamerism that I see when I go from D50 to a variety of popular illuminants that were standardized in CIE 15.2, and have been used for years. This leads us to a surprising conclusion about how well the Color Rendering Index works. Stay tuned!

After Part 3, I move on to Part 4. In this section I swap out the standard illuminants for a plethora of white LED illuminants. (Or is it a plethorum? I dunno.) I measured a whole pile of white LEDs and answered a pressing question: do white LEDs pose a big problem for us when it comes to metamerism?

Finally, and rather unexpectedly, I present Part 5 of these series of blog posts. In this blog post I find out how serious a problem viewing booth metamerism is. What is viewing booth metamerism? Get this: the D50 in your viewing booth is merely an approximation to the D50 in your spectro. As a result, your spectro may disagree with your eye as to whether a proof and press sheet match. Should you lie awake at night worrying about this?!?!?

Metameric Encyclopedia for the Graphic Arts

I decided that I would need a database of metameric pairs in order answer the questions that I posed. Now, John the Busy Guy Who Doesn't Have Time for Frivolous Tasks would probably have been too busy to take the time for a frivolous task like creating more than a handful of metameric pairs. But, the presentation at Color 20 was given by John the Math Guy, and I am never too busy for any sort of frivolity. I heard a rumor that there might be a world record waiting to be broken, so I took it upon myself to make a collection of metameric spectra that would make an acid trip with Jim Morrison seem like a Whiter Shade of Pale.

My metameric database (on the left) compared with the competitor's (on the right)

I started with spectral measurements of a Pantone book. These are real spectral from ink formulated as they might be formulated in any printing plant in the world. Then I brought in a characterization data set from flexographic printing. For each of the Pantone colors, I searched through the flexo data to find a close CIELAB match. If I found a flexo color that was reasonably close, I mathematically adjusted it so that it was a perfect match under D50/2.

(For the non-printing-geeks out there... Characterization data is a set of measurements of printing with a zillion or so combinations of the inks in a press. On a four-color press, the characterization data typically includes about 1,600 patches. For expanded gamut printing, it might be several times that many.)

(For the geeks out there... the mathematical adjustment was done through principal components. I determined the singular value decomposition of the full flexo data set and used the first three vectors as a basis. I then found the linear combination of the basis vectors to add to the actual spectrum so that the adjusted flexo spectrum was a perfect metameric match. I discarded any spectra with values outside the range of real printing. You know, simple obvious stuff.)

(For the those concerned about social justice and stuff out there... No spectra were hurt in the filming of this blog post or the presentation. The spectra that I arrived at were realistic and perfect metameric matches.)

I mentioned flexo. A bit more detail there. This is data that I received from Liam O'Hara, who has been a friend for many years is now a colleague of mine at Clemson. The data was an expanded gamut characterization data set. So I was investigating spot color replacement with expanded gamut. But I saw the opportunity to have even more fun with the data. I broke it into two subsets; one subset had only CMYK, and the other subset had at least one of the extraquaternary inks (that is, orange, green, or violet).

Thus, for each (or I should say, most) of the Pantone colors, I had

1) The spectrum of how a flexo press with a particular CMYK inkset might render a perfect colorimetric match to that Pantone color, and

2) The spectrum of how a flexo press with a particular CMYKOGV inkset might render a perfect colorimetric match to that Pantone color, with the caveat that the build must include at least one of O, G, and V. 

Some Pantone color were out of gamut, so they did not make it into MEGA. Some were in gamut for the expanded gamut printing, so a metameric pair was added to the database. And for some of the Pantone colors, I had not just a pair of metamers, but a set of metameric triplets! How awesome is that!?!?!

Enter the Indigo 7900

Did I stop there? Of course not. I was going for the world record!

I just happened to have data from another friend, one who happens to not be a colleague of mine at Clemson, since he doesn't teach at Clemson. He actually teaches at Ryerson, so we work at different schools together. Abhay Sharma recently pitted one piece of expanded gamut software against another in a study of the capabilities of expanded gamut software. When Abhay wasn't looking, I grabbed a copy of the expanded gamut characterization data for an Indigo 7900. Please don't tell him I have that data.

And I went through the same procedure with this data so that I potentially had two additional metameric matches for each Pantone color. We're talking the birth of metameric quintuplets! (I hope everyone is as excited as I am.)

And one more!

No. I didn't stop there! I had one more database up my sleeve. But first a little background.

Let's face it. The Pantone Formulation Guide has a few problems. The first problem, which is obvious to anyone who has casually looked through the book is the haphazard ordering and numbering. Below, I show seven pages from the swatchbook. The first and the fourth start with 256 and 263 at the top. The pages with 2563 and 2567 have been shoehorned in between. These four pages are consecutive. Much later in the book, we find consecutive pages 511, 5115, and 518, which are in more or less the same color family. In between, we have a bunch of blues and greens and yellows and grays. Just for convenience, the colors in the latter set are upside-down. The darkest, richest colors are at the top instead of the bottom.

Just to be clear, I'm not blaming Pantone for this. The hodge-podge numbering system was inevitable. The books have grown through the ages and there has been an understandable unwillingness to change the numbers on existing colors. 

Another issue with the swatch book is that the pages, when fanned out, don't have a nice, smooth flow. That is aesthetically unnerving, but from a practical sense it means that the colors are not equally spaced perceptually. And it makes you wonder whether there are holes -- colors that have been missed entirely.

I have blogged previously about how a swatch book could be ordered more uniformly. Albert Munsell created such a book in the early 1900's. Much more recently, Phil Kenyon wrote some software that organizes paint company swatch books. So it can be done. (Well... you have to somehow map 3D color space into two dimensions...)

Yet another problem with the Pantone book is that the recipes in the book don't work. Paula Gurney (recently retired from Ink Systems) explained to me that this is because the formulators of the book didn't impose a standard ink film thickness for all the recipes.

And then there's the base ink reflex blue. Printers don't like reflex blue. It takes longer to dry than the other inks, and it has this property called bronzing. It takes on a coppery tone viewed at a shallow angle. It would be good to not use that as one of the base inks.

Much to their credit, Pantone tackled all these problems and introduced a very good solution in 2007. It was called the GOE System. It was beautiful. You may have noticed the use of the past-tense in both the previous sentences? Yeah. It was a great idea, so naturally it didn't take off in the market. It was discontinued in 2013.

But I managed to find a GOE book at a garage sale and chased my spectrophotometer after it. So, I have a file on my computer with spectral measurements of a GOE book. I applied the same technique to this data. This added another set of plausible metameric matches to my database.

MEGA database

I show below a set of metameric sextuplets from the database. These six spectra have exactly the same CIELAB values under D50/2. Since the spectra are all different, one could expect that the CIELAB values would not match under a different illuminant.

Identical sextuplets, under D50/2

I don't know how many of you have spent an evening with a set of metameric twins, but I gotta tell you, a night on the town with metameric sextuplets is a bucket list event!

As an aside, some of you may have been wondering if Pantone 147 (in the diagram above) is the ugliest color in the world. It's close, but not quite. That honor goes to Pantone 448. There was actual research into this. The idea was to find a color that would best "unsell" a product. The product in mind? Cigarettes, in Australia.

And speaking of world records, how many metamers are in my database? An awesome 3,604. Are you listening Guinness? The old record might have been a few dozen, so that's a record that will stand for a while. At least until I announce Metameric Encyclopedia for the Graphic Arts II.

This is an ongoing effort of mine. Over the next few blogs, I will describe some of the uses that I have put this database to. Any other ideas? Contact me!

Wednesday, May 6, 2020

An Easter egg in the film "Die Another Day"

Ok... so let me make this clear from the start. I am not a film buff, nor do I claim any more than superficial expertise in film. If you want the honest truth (as opposed to my usual dishonest truth), I will likely need to look up the title of this movie again before I finish blogging about it.

Another thing to clear up at the start -- this is not my usual blog post subject matter. Normally I go on ad nauseum about color and math and physics and other boring stuff. Not today. Prepare to not learn any science.

For those who are unfamiliar with the term "Easter egg" when applied to film, this is something innocuous put in a film just as a joke. If you would like an example, I would suggest having a look at the scene in the movie Airplane that starts at 0:00:00, and ends at 1:25:00 in the sequel Airplane 2.

The topic of this blog post is an Easter egg in the James Bond movie "Die Another Day".

To set the time stamp on the movie, the Easter egg occurs between when a) Bond uses the secret code word delectados to elicit the help of some guy, and when b) Halle Barry makes a breathtaking exit from the ocean.

An egregious image of Halle Barry being viewed through Bond's binoculars

If I were a true film aficionado, I would point out the similarity of the outfit worn by Barry to that worn by Ursula Andress in her coming out of the water scene from an earlier Bond flick, Dr. No. I might also take this time to comment on the cinematography in those two scenes, comparing it to Bo Derek running on the beach in the movie 10. Blah blah blah ... Daryl Hannah in Splash ... Phoebe Cates' pool scene... blah blah A Fish Called Wanda ... blah blah ... the primeval attraction ... subliminal reference back to one million years of evolution at the water side ... Descent of Woman...

But I can't even recall the scene from A Fish where Jamie Lee Curtis came out of a pool wearing a bikini. So I will skip all that.

Getting back to the Easter egg in Die Another Day... In the unforgettable scene just before Halle Barry emerges from the water, James borrows a pair of binoculars so he can pose as a bird watcher and get a look at the island. At this point, I had to pause the film to clean up the martini that I snorted out my nose and to explain to my wife what tickled my funny bone. I'll explain it to you as well, but first I rewind the film a bit.

I remembered that while he was in the delectado guy's office, Bond had idly picked up a book to look at, just before he picked up the pair of binoculars. I went back to see what the book was. As I suspected, it was a bird guide. I had a hunch about the author of this book. I was hoping to see the name of the author of the book, but I couldn't make it out. I think they did that on purpose to hide the Easter egg for all but the most diligent of Easter egg hunters.

But since I had already guessed who the author was, I knew what to google for. Here is a better shot of the book Birds of the West Indies:

You can probably just make out the author's name: James Bond! Yes. James Bond picked up a book by James Bond.

Now for the reveal. The real James Bond was an ornithologist. Ian Fleming (who wrote the books about James Bond the spy) was an avid bird-watcher who lived in Jamaica, so he knew of the bird book. Fleming was looking for a name for his character and felt that the name James Bond had just the right sound. Short and masculine. That's why I laughed when James Bond introduced himself to Halle Barry's character as an ornithologist. And since I knew where Fleming got the name from, I knew to look back to see if the book was an inside joke hidden in the previous scene.

The real James Bond
By Jerry Freilich - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=9724104

When Ian Fleming was contacted by the wife of the ornithologist about the theft of her husband's name, Fleming gave permission for the real James Bond to use the name Ian Fleming. "Perhaps one day he will discover some particularly horrible species of bird which he would like to christen in an insulting fashion."

Thanks to my buddy Mike for recommending the movie.

Tuesday, December 24, 2019

What is the most accurate color wheel?

I received a question the other day. This happens to me all the time. Just a thought here... Maybe I would get fewer questions if I pretended to be ignorant rather than all this pretending to be an expert? I will have to talk with an image consultant about that.

Here is the latest example of things that people want to know.

I have a question for you. I understand that there are different color wheels for different subjects. ... I haven't noticed before...there seems to be two "main" color wheels, but which one is the most accurate?

With the wheels that have 12 colors there seems to be two that come up - one with a red-orange and no magenta, or one with a magenta and no red-orange.

Which one is more accurate? Or are they both accurate but for different reasons?



I have a lot to say on this topic -- enough that I will break it up into two blog posts. In this blog post, I will look at various color wheels, with a eye toward the underlying theory. In the subsequent blog post, I will look at the more general question of the utility of color wheels in general.

Red, blue, and yellow primaries

Here is a color wheel that does not have magenta. This beautiful little color wheel with 72 spokes dates back to a book by Michel Eugene Chevreul in 1839. He was a chemist involved in the dyeing of carpet. His work on color perception came out of trying to understand why dyeing did not always turn out as one expected. This color wheel was his first step in understanding color.

This is kinda pretty, but the left-hand side of this color wheel is a bit dark for my taste. It could be that the colors faded -- after all, this book was made in 1839 afterall. Or it could be that the creation of the color plates suffered from the fact that a good magenta pigment wasn't invented until 1858.

The image below (on the left) is a black and white version of Chevreul's color wheel, with color words for each of the 12 basic colors. Each of these 12 colors are subdivided into 6 steps to make a total of 72 colors in the wheel. At the right, I show my colorized interpretation.

I drew a little triangle inside my rendition to make a point. The colors red, blue, and yellow are all explicitly called out, and are conspicuously 120 degrees apart. The Chevreul color circle is based on the artists' primaries, red, blue, and yellow.

This color wheel satisfies Ashley's first criteria: "one with a red-orange and no magenta". RO is red-orange, and VR (violet-red) appears maybe somewhere around where magenta might be. Perhaps if the color name magenta existed at this time, it may have been incorporated into the color wheel, but I haven't had the opportunity to query M. Chevreul on the topic.

Red, green, blue primaries

My computer monitor doesn't use the artist's primaries. For some silly reason, it uses red, green, and blue. (Note to self: I need to contact those people who design computer monitors and televisions and screens for cell phones and tablets. They need to learn about the artist's primaries, because clearly that would be a much better way for them to encode color.)

I did a little playing in PowerPoint (my graphics design program of choice) and came up with my own  twelve step program... err, twelve step color wheel. I hope that everyone reading this takes a moment to step back and say "ohhhhhhh...." in appreciation of my epic artistic skills.

The Seymourian twelve-step RGB color wheel

For those interested in the details, the red, green, and blue anchor points are (255, 0, 0), (0, 255, 0), and (0, 0, 255). The halfway points between them are yellow (255, 255, 0), cyan (0, 255, 255), and magenta (255, 0, 255). I filled in the points between using HSL coordinates. The hue of HSL goes through steps of 21.3333 from 0 to 235.

This color wheel fits Ashley's second criteria: "one with a magenta and no red-orange". The magenta is at the very bottom, and there is red, and there is orange, but no steps in between.

Cyan, magenta, and yellow primaries

I have a little bonus for those involved in my twelve step program: a color wheel that is specially designed for anyone involved in printing. Here we see that the basic colors are cyan, magenta, and yellow. Please note carefully that the cyan-magenta-yellow color wheel bears no resemblance at all to the red-green-blue color wheel. None whatsoever. Completely different.

The Seymourian twelve-step RGB color wheel

That last line was just a tiny bit of sarcasm. I said that as a way to highlight the fact that these really are the same color wheel. Both are based on RGB color theory, which is a simplification of scientific color theory. This is a fascinating and illuminating topic, and one which is worth a whole blog post to itself.

Oh... I should mention one thing here. Cyan, magenta, and yellow don't do so well at getting all colors. Early printers found it was a good idea to add black. Oh yeah, one more thing... When you print magenta over cyan, you don't really get blue. It's usually more of a purple. And when you print yellow over magenta, it's not a good red. It's a little too orange.

As a result... lately there has been a lot of kerfuffle about expanded gamut printing, where you print with CMYK, but then add in orange, green, and violet inks to extend the range of colors that you can get. Or sometimes you use red instead of orange, or blue instead of violet.

The artists' primaries

Allow me for the moment to revisit the concept of artists' primaries on which the Chevreul color wheel is based. I was taught in kindergarten that:

1) Red, blue, and yellow are the primary colors.
2) You can make all the colors by mixing appropriate amounts of these three primaries.
3) Red plus blue is purple. Red plus yellow is orange. Blue plus yellow is green.

The first is more of a definition than anything that you can test. But the second and third are testable. The second is hard to test, but I tested the third one during lab period in kindergarten. An actual image of the results of my experiments has not survived, but a rough approximation is shown below.

Artists conception of the artists' color wheel

I recall presenting my disappointing results to Mrs. Reidhouse, who was the main lecturer in my kindergarten class. I also vividly recall trying to explain to her that the lack of saturation in the pairwise mixtures was predictable using the Kubelka-Munk equation. But I don't recall her offering a cogent counter argument in support of the artists' primaries theory of color. I do recall being told that it was nap time, though.  

I was trying to articulate to her a basic postulate of paint mixing: Mixing pigments will usually lead to a loss in richness (chroma) of color. In other words, you can't get a rich, vivid green by mixing yellow and blue. You can't get a rich purple by mixing red and blue.

If you find yourself disagreeing with this, then I suggest you visit an art supply store. If Rule 2 were correct, then you would generally see beginner paint sets with five different paints: red, blue, yellow, white, and black paints. Maybe you would see sets with more colors premixed, but if you look at the ingredients, you would only see those five basic pigments. There would be no need for any others.

This set contains 12 of the most popular colors in 2 oz (59 ml) tubes, including Burnt Umber, Burnt Sienna, Raw Sienna, Yellow Oxide, Naphthol Crimson, Cadmium Orange, Phthalo Green, Yellow Medium Azo, Cadmium Red Light, Ultramarine Blue, Titanium White, and Mars Black.

Still not convinced? Then take a trip to the hardware store and ask to see their paint mixing equipment. Count the canisters... do they mix all the colors of paint with five pigments, or are the dispensing devices "Available as either 12, 14, or 16 canister turntables"?

Here's another suggestion for those not yet convinced. I put together a little a do-it-yourself guide to printing with the artists' primaries instead of CMY. Visit my blog post, print out the supplied images, and see what kind of results you would get if HP supplied you with red, blue, and yellow ink cartridges.

In order to get a full range of colors, you need to start with a variety of pure pigments that cover the full range of colors. The theory of the artists' primaries is just plain wrong. 

Red, yellow, green, blue, and purple primaries

Albert Munsell was a smart guy when it came to color. As proof, there was once an upstart wannabe color guru who was so bold as to refer to Munsell as the Father of Color Science. Munsell devised a color wheel that he actually manufactured with paints. (Before I go on, I need to say that his color wheel, was just part of the Munsell color space.)

Munsell started with five primatries. There were an additional five secondaries squished between those five primaries, and each of those ten hues had ten levels in between. Munsell's color wheel thus had a total of 100 different hues.

My rendition of the Munsell color wheel

I want to share a bit about how he created his physical actualization of the color wheel. I share because this is interesting and not well known. Part of this is reverse engineering and presumption on my part. If I have errors in this, I would be happy to recant.

Munsell started with five primaries: red, yellow, green, blue, and purple. With the exception of purple, he had pigments for each of these that he felt truly exemplified the colors. He had to mix two pigments together to get purple, but I mean, how could he avoid purple?

Next he used a creature known as a Maxwell disk to find complements to each of his first five primaries. This spinning disk would have a portion colored with one of his primaries, like red, and another portion colored with a potential shade for the compliment. The complement of red he called "BG" or "peacock blue". He would adjust the pigments mixed for the second pigment until he attained a gray color when the disk was spun.

The ten basic colors in the Munsell color space are listed below. The primaries are in bold type, which coincidentally all have single letter Munsell hue names. Note that Munsell made these with 8 different pigments.

Munsell hue
Color name
Venetian red
Orange cadmium
Raw sienna
Grass green
Emerald green and raw sienna
Emerald green
Peacock blue
Viridian and cobalt
Purple madder and cobalt
Purple madder

(From Albert Munsell, A Color Notation, 1919. Pigments are from paragraph 104, pps. 66 – 67; common color names are from paragraph 58, page 35. I received an email from Robin Myers which recounted the formulations for the ten basic colors that were used in the 1st, 2nd, 4th, 5th, 6th, and 7th editions. The only change over that time was that in the first two editions, 5BG was made with viridian as the only pigment, and later editions mixed this with cobalt. I appreciate having the help of experts like Robin to make sure that my blog posts are precise!)

Red, yellow, green, and blue primaries

A quick review...

The Chevreul color wheel and its derivatives is based on the dubious assumption that red, blue, and yellow paints can be mixed to make all colors. The RGB color wheel is based on the primaries RGB that work well for computer monitors and televisions and cell phones and tablets, and have always worked well in coordinating my underwear. The CMY color wheel is based on the colors of inks that seem to work well, but you almost always want to at least add black. Then you have the color wheel based on Munsell's color space, which in turn was based on a set of paint pigments that Albert Munsell decided upon back in the early 1900's.

These color wheels are all based on the color capabilities of physical stuff. Which is a bit odd, since "color" is largely a function of the spectral response of the cones in the eye, and the brain's processing of the signals from the cone.  It would seem that a color wheel would best be based on what goes on inside the human head, doncha think?

Ewald Hering proposed the idea of color opponents in 1892. His theory was that we sense an object as being reddish or greenish, but never both. There is a continuum of red to green where every color falls. Similarly, there is a continuum from blue to yellow. All color are perceived as somewhere on this continuum. Finally, there is a third such continuum between white and black. This general idea has been borne out with what we have learned about how the cones in the eye and the neurons leading to the brain work together to create color perception.

This idea was incorporated into the color wheel of the Natural Color System (NCS) shown below. This system was developed by Anders Hard and first described in 1966. The rendition below shows 40 steps. The NCS color system is perhaps not as well known as the Munsell color system, but both companies are in existence today, both selling books of colors.

This idea of color opponents (red vs green, blue vs yellow, and white vs black) can also be seen in the design of CIELAB, shown below.

Image from XRite website

I won't say much about CIELAB in this blog post, partly because I am getting tired of typing and suspect that most everyone is getting tired of reading. But, I think I can get away with not talking about the CIELAB color wheel, since I don't recall ever seeing a color wheel that was explicitly built on CIELAB. I say this not to diminish anything about CIELAB.

So, what's the answer?

Which one is more accurate?

The color wheel based on the artists' primaries is not bad, but it is based on a flawed proposition about the primaries.

The RGB color wheel works well for colors on a computer screen. The CMY color wheel works marginally well for printed colors. The two together are compatible, which makes them a very good conceptual model.

The color wheels based on the Munsell and the NCS color systems both have a great deal of research built into them, and accurate physical renditions of each can be purchased. They are both a bit of money, but they exist. And  I would call either of these accurate.

I will leave this discussion for the time being. But beware, I will have more to say..

Tuesday, September 17, 2019

Music soothes the savage Lactobacillus helveticus

I'm sure you saw the news item. The one about how exposing cheese to different types of music during its formative years can give cheese distinctive flavors? It was determined that hip hop music is best, that is, if you like a cheese with a fruity flavor.

It's a compelling thought. On the one hand, it's silly and ridiculous since bacteria don't have ears (like corn does). And even if the bacteria did have ears, does a wheel of cheese have enough sentience to distinguish between The Magic Flute and Stairway to Heaven? I mean, if I have a good hangover going on, I would be hard pressed to tell the difference!

On the other hand, sound is energy. Pick the right range of frequencies, and it can be translated into heat, which (I assume) could change the flavor of the cheese. Sound is also mechanical energy. If you hit the right frequencies, you presumably could set up standing waves that encourage some sort of structure to the cheese. Or maybe there are polymers in cheese that are long enough to have resonant frequencies in the audible range?

I dunno. Maybe cheese is just smarter than we give it credit for. After all, just look at how intelligent Wisconsinites look with cheesehead hats! (Due to the family friendly nature of this blog, I have decided not to include pictures of fans wearing the classy cheesehead bra. Google it if you are interested. It really is a thing.)

The general idea of the experiment

The cheese maker Käsehaus K3 in Burgdorf, Switzerland placed nine wheels of Emmental cheese in nine separate crates for aging. The wheels were exposed to various sounds over the next six and a half months. One wheel got 24/7 of Led Zeppelin. Another got Mozart. Still others got hip-hop, ambient, and techno. Three cheeses had to suffer with a rather constant tone. Finally, one cheese got peace and quiet. This was called the control group.

After six months in these boxes, judges did a random blind assessment of the cheeses to assess whatever it is that official cheese assessors assess. From the images below, it would appear that olfaction is 80% of it. The assessments were repeated, and the results were consistent. Here is a quote from the Reuters article: "Beat Wampfler, the cheesemaker behind the project, said the cheeses were tested twice by the jury and both times the results were more or less the same."

Photos of the judging from the Käsehaus K3 website

What the media has to say

Many news outlets have covered this groundbreaking experiment. Here is a sampling of the reports of the findings.

From NPR: "[The  professional food technologists] concluded the cheese wheels exposed to music had a milder flavor compared with the control cheese. The group also determined the cheese that was played hip-hop had "a discernibly stronger smell and stronger, fruitier taste than the other test samples"

From Smithsonian: "The experts said A Tribe Called Quest’s [hip-hop] cheese was “remarkably fruity, both in smell and taste, and significantly different from the other samples.

The best music to age cheese by

From Reuters: "“The differences were very clear, in term of texture, taste, the appearance, there was really something very different.”"

Well. That certainly sounds conclusive.

Digging a bit deeper

Before I continue, let me say this. I love this work. It's offbeat (no pun intended) and innovative. It opens the way for a better understanding of how things work. It rests in the cracks between science and craft.

On the other hand, I hate to be a spoilsport, but I am skeptical. Hip-hop?!?!?! Really?  I'm not so much a fan of hip-hop, and I like cheese. A good cheese should have the same taste in music as I do. This all creates cognitive dissonance in my little brain.

So, I swam upstream to read a more first-hand-ish version of the results. Here is the original press release, and here is a website version of the experiment.

They did some good things, by which I mean, they used some Science. Here is one thing: "The milk was produced by the same farmer and was processed in the same kettle on the same day of production."

I have already mentioned another thing that they did right. They repeated the assessments and concluded that they were in agreement, that is, the differences weren't just because of the variability in the humans smelling the cheeses. I couldn't find the actual assessment data, but I will assume that they applied the right stats on the assessments to verify that the judges agreed. (That might not be a good assumption, of course. Statistics is a slippery subject.)


All that said, here is a quote from the original press release.

In general, it can be confirmed that the discernible sensory differences detected during the
screening process were minimal. The conclusion that these differences did indeed confirm the
hypothesis, namely that they can clearly be traced back to the influence of music, is conceivable,
but not compelling.

This is common statistics-speak. I will translate for the non-statistician. They started with the hypothesis that music can affect the maturation of cheese and set out to either prove or disprove it.

My professor for Stats 101 +/- 2.7

One possible outcome would be that the judges all said the cheeses smelled and tasted the same. The conclusion would be that, at least for this particular combination of cheese type, music selection, and means for delivering the music, the music has no effect on the cheeses.

Another possible outcome would be that the judges may have agreed that there is a difference between at least some of the cheeses. Upon hearing this, the conclusion from a typical layperson might be "Aha! Music causes cheese to age differently!!" The comments in the articles from NPR, Smithsonian, and Reuters all promote this conclusion. It makes for good headlines.

But a statistician is more careful with the analysis of the results. The faithful statistician is open minded to other possible interpretations of the data. A statistician concludes that the experiment does not disprove the hypothesis that music influences cheese flavor. While English majors abhor this double negative construct, but it is key to critical thinking to see the difference between "does not disprove" and "proves".

The statistician recognizes that "music affects the aging cheese" is one possible explanation for the outcome, but there could be other explanations. Here are some alternate explanations, some more plausible than others.

1) There are several pictures where the wheel of cheese has a placard that identifies the type of music that it listened to. Did the judges see the placard? (This is unlikely. The website says that they followed ISO 13299, which precludes any presentation of the samples that might identify individual cheeses.)

2) I noticed from the pictures that all the judges appear to be together in the same room. Is there a possibility that one judge picked up non-verbal cues from another judge?

3) Quoting from the original press release: "the discernible sensory differences ... were minimal". Hmmm... Maybe the differences were due to subtle differences in the way each cheese was processed? One of the cheeses was probably poured into a mold first, and another was poured last. Some of the cheeses were aged closer to the ceiling, and some closer to the floor -- there is likely a small difference in temperature. Some were closer to the door, which might open the door to more airborne bacteria. Perhaps one cheese received a little more personal attention (and/or bacteria) when workers did their routine inspection?

I don't claim to understand the potential causes of variability in the manufacture of cheese, and I am certainly not casting aspersions on the folks at Käsehaus K3. I just know that there are causes of variability in all manufacturing, however small or large.

4) Were the results analyzed for statistical significance? I say this because people are not good with statistics. Without rigorous statistics, we almost invariably jump to conclusions. Statistics is a tool that forces us to make sure those conclusions are valid. I did not see any detailed description of the statistics that the researchers applied to the assessments, so either the analysis of consensus was minimal or they recognized that the audience would be bored with it, since people are not good with statistics.

5) Were the results analyzed for statistical significance? I say this because the website lists only eight judges. Don't get me wrong. I commend them for putting this level of effort into the experiment. But, consider the fact that a rigorous poll or pharmaceutical test will survey thousands of people in order to provide statistically valid conclusions. But, don't get me wrong. I'm not saying "those darn cheesemakers really should have hired a thousand cheese testers." I am saying that we need to review the data in light of the statistical significance due to the limited number of judges.

6) Were the results analyzed for statistical significance? I say this because they have included a control cheese which didn't listen to any music. If you are testing whether music affects the flavor of cheese, the "obvious" statistical test would be to determine the variation of the eight cheeses that listened to music, and then test for whether the control cheese is within this variation.

Who understands this tripe, anyway!?!?!?

But, quoting from the website: "Thus, the reference sample was comparatively most pronounced in odor, as well as in taste, whereby here also the sample sinus 2 (medium frequency) was perceived as intensively." The control for this experiment was within the natural variation of the rest of the cheeses, so the hypothesis "sound has an effect on cheese" seems to be not supported by this experiment.

My favorite alternate explanation

There is normal variation in all manufacturing processes. The experimenters were careful to make sure that the milk came from the same farm and that the milk was all processed the same way. I am sure that K3 has a standardized practice for making cheese. Good on them. But even in the tightest of manufacturing facilities, there is variation.

That means that some of the cheeses will naturally taste spicier than others, while some will be fruitier -- even if the music was completely feckless. One of the cheeses will be the fruitiest. It could have been the cheese that listened to ambient music, or it could have been the Mozarted cheese. If by random chance the cheese that listened to techno music was the fruitiest, then the articles would all be talking about the effect of techno, rather than the effect of hip-hop.

My favorite alternate explanation is that through normal and random variation, one cheese will be chosen as the fruitiest, regardless of whether there is any effect of music on cheese aging.


Every good research paper ends with a statement like "clearly further research is required to keep the researchers employed". I say that with tongue-in-cheek, but refinement and replication are at the very core of Science.

I was heartened to read this from the original press release: "More extensive testing is required in order to determine whether there is a link between exposing cheese wheels to music as they mature and discernible sensory differences."

The press release goes on to say that tighter controls and more sampling are required. From my previous comments, you could gather that I agree. I would add that rigorous statistics is always a good thing.

I would suggest another experiment: put all the mp3 players on pause, and repeat the 9 cheese experiment. Use this data to better understand the natural process variation.

Tuesday, September 10, 2019

Why are Bermuda onions called "red" onions?

Quora often provides me with suggestions for blog posts. I read a question today that filled me with such indignation that I had to answer it, and had to post this to my blog as well.

Question: Why are 'red onions' called so when they're clearly purple in color?

Bermuda and Spain

Oh! The injustice!! I get angry with misplaced apostrophes, and livid when someone gets all floofy in the spelling of there/their/thay're/thare. But this is more than just word injustice -- this is about color. Anyone who knows me knows that color and beer are the most sacred things in my life.which is as close to being sacred to me as beer is.

But I digress. There is actually a very reasonable answer to this question, and oddly enough, it's one that doesn't require me to call anyone stupid.

In 1969, two linguistic researchers [1] asked a whole lot of people from around the world to name colors in their native language. Altogether, they surveyed a few thousand people, speaking 110 different languages. Based on an analysis of their data, they proposed the theory that languages follow a distinct pattern in the development of color names.

Primitive languages start with analogs of white and black with everything that is a light color being called white (or their word for white), and everything that is a dark color being called their word for black.

Red is the next color that is added, with a single word standing for red, yellow, orange, pink, etc. The next step after red is either to create a new word to separate yellow from red, or to distinguish a collection of greens and blues from white and black.

Ultimately, the language evolves to 11 basic color names: white, black, gray, red, orange, yellow, green, blue, violet/purple, pink, and brown. Some languages (namely Japanese, Russian, and Italian) have further broken the blue category into sky blue and navy blue.

Yes, I understand that my rendition of orange is not so good

Hang on, John. In English, we have sky blue and navy blue. Why aren't these considered basic color names? 

That's a fair question. In English, we distinguish between the two versions of blue by adding the modifiers sky and navy. But, we have a lot of other modifiers that could be applied to blue to arrive at the colors cadet blue, cobalt blue, greenish blue, midnight blue, Pacific blue, pale blue, purplish blue, robin's egg blue, steel blue, and turquoise blue. None of these are basic color names because they are just modifiers of the basic name blue. Chromolinguists also have a requirement that basic color names must also be monolexic, meaning they must be one word.

Getting back to the theory of Berlin and Kay, here is the original sequence, taken from a subsequent paper by one of the same authors [2]:

Original B&K evolutionary sequence of color term development

If this is all true, then it explains the use of red applied to Bermuda onions and also to cabbage which happens to have lots of anthocyanin, both of which are actually purple. At the time when it became necessary to distinguish between Spanish onions and Bermuda onions, the word purple was not commonly used in the language. In the diagram above, the language was in Stage VI. Red was the common term that signified either purple or red, so red was the name given.

The terms red onion and red cabbage stuck, in much the same way as the anachronistic phrases "hit return", "dial your phone number" and "tape a TV show".

Here are some more examples of vestigial chomo-misnomers: What color are your blue jeans?

[1] Berlin, B., Kay, P.: Basic Color Terms: Their Universality and Evolution. University of California Press, Berkeley/Los Angeles (1969)

[2] Kay, Paul, and Richard S. Cook, World Color Survey, Encyclopedia of Color Science and Technology, Springer Science+Business Media New York 2015