Wednesday, January 23, 2019

Which way is north in Munsell color space?

I wrote a blog post for Inkjet Insight about the Munsell color space. I don't want to spoil it for anyone, but the post is mostly just a gateway post to one about the CIELAB color space. For the Inkjet Insight post, I had my crayons pose for the aesthetically pleasing picture below. I do expect an Emmy for the picture, but I will try to appear surprised when I get called to the stage.

Happy crayons get together for a crayon picnic

Boy! Did that picture stir up a hornet's nest when I posted a link on LinkedIn! Two of my color scientist friends took umbrage. You may be wondering about my choice of the word "friends". Perhaps I use the term loosely, but Danny and Dave are the closest thing I have to friends, I mean, aside from Truffle and Mozart. And I feed Truffle and Mozart twice a day.

Here's Danny's malicious comment: "It seems that you have ordered the crayons as CIELAB would but not as Munsell does."

Dave's equally viscous comment: "Oops. Danny is right of course.  Unless, ... this is a view from below! To be more CIELABish I actually reverse the hue direction in my hanging Munsell Tree."

The gauntlet has been thrown down!!

I gotta ask you gentlemen, Danny and Dave, which Munsell color system you are referring to?

First, there is nothing inherently in the Munsell notation (7.5PB 4/6) that tells us which color points east (0 degrees) and whether orange is clockwise or counterclockwise of red. The Munsell notation for each color includes one of ten designators (R, YR, Y, GY, G, BG, B, PB, P, or RP) to specify a hue family. Within each hue family, there are ten steps which (oddly enough) are numbered from 1 to 10. Each number is one-step change in hue. Thus, 7.5PB is a unique specification for a hue, without any implied orientation.

Take that, Danny and Dave!

Second, there is a disagreement between Albert Munsell and Albert Munsell about the direction of red. As shown in the image below, his 1915 atlas has red pointing at around 45 degrees clockwise of east.

Page ripped from the Munsell Color Atlas of 1915

But in Munsell's New York Times 1919 bestseller "A Color Notation System" the master shows red pointed due north.

More vandalism, but to Musell's A Color Notation System

Both of these Munsell illustrations show orange as being counterclockwise from red. Pretty much the same as the way my Crayolas arranged themselves, and also, the way that CIELAB is arranged. Since there is no "correct" direction for red to point, I feel justified in pointing red to the east.

How do you like the color of them apples, my Dynamic D-named Duo!?!??  Well, I'm not done yet!

Third, the ASTM disagrees with both of these Munsell orientations. In 1968, the ATSM provided us with a "standard method of specifying a color by the Munsell system" (ASTM D 1535). Note that in the ASTM system, red points to the north. This agrees with the second illustration, but hang on a sec while I expound on some ASTM D 1535 trivia that is likely to come up the next time Danny, Dave and I get together for sushi.

ASTM D 1535 dictates this orientation

ASTM D 1535 also assigned a number for each discrete step of Munsell hue angle, from 1 to 100. Interesting point -- their notion of hue "angle" is in centicircs. I just made that word up. One centicirc is 3.6 degrees. It's about time we went metric and got past this silly Babylonian notion that we should measure arcs by comparing against the size of arc that the Earth makes around the Sun in a day. Approximately a day.

The ASTM adopted the obvious convention that 0 Munsellian centicircs would be at 18 degrees counterclockwise from north. I mean... of course. Well... I need to clarify. No one ever really told me whether "true" red was 0R or 5R. I guess I assumed it was 0R.

Also D 1535 is not explicit, but I think that 0 centicrics is not allowed. That has to be called 100. Kinda like the zero-phobia that says that midnight is 12:00 instead of 0:00. And that the first day of a month is 1, rather than 0.

More importantly, note that contrary to "normal" analytical algebra, Munsellian centicircs increment in the clockwise direction! I'm going to report them to their calculus professor!

But hang on. Here's the big thing. Even more importantly, and contrary to Munsell's two books, in the D 1535 system, orange is clockwise from red. O.M.G.!!

Dave boastfully mentioned his "hanging Munsell Tree". Not to be outdone, I provide a picture of my own hanging Munsell Tree. In my case, the world famous Munsell Color Model is joined by the world famous Munsell Color Model Model, Madelaine. We can see that my tree and Dave's tree both adhere to the "orange is counterclockwise from red" convention.

Wild times at the John the Math Guy household

Since there seems to be some latitude in the orientation of the color wheel in Munsell space, I claim that I am well within my rights to orient Munsell space in such a way as to serve as a stepping stone to CIELAB.

For those of you who are wondering about the significance of all this detailed historical research, let me be clear. It's all about me proving that I am right. Nothing else really matters.

NOTE: I would like to thank Robin Myers for pointing out an egregious error in my initial post. I had stated that the Munsell Color Atlas was published in 1913. Robin sent a photo of a page from his very own copy of the Munsell Atlas that clearly shows the date as 1915. (I am so jealous that he has this copy!) I would make up some excuse for why I got this wrong, but it would either be a total "my dog ate my homework" excuse, or it would make me look bad. So, I will just apologize for any pain and suffering which may have been caused by my ineptitude. I am eternally grateful to Robin for finding this embarrassing error, and would like to publicly offer to buy him a cup of coffee or a glass of the most inexpensive beer that can be found, provided he reciprocates by buying me a drink of similar value.

While John the Math Guy, LLC strives to maintain the highest level of scholarly eptitude in all its blog posts, there will inevitably be lapses into complete failure of logic, due diligence, and clarity of exposition. Any liability for anyone actually taking any of these posts seriously shall be limited to any considerations received directly from the party who has his undies in a bundle about this stuff.