Hue and chroma arcs are real, plus the Munsell thief

Albert Munsell created the Munsell Color System in 1913. 

Frank Reilly studied with Munsell and began teaching painting, including using Munsell for color mixing, at The Art Students League in 1932. 

The idea that any living painter stole Munsell teachings from any other living painter is absurd on its face. 

Nuff, said on that, I hope. 

Some painters are advocating using a shading series to calculate the linear path of chroma. It always starts at Value -1 and progresses straight to its highest value. So you might have to mix a chroma of 3.2, for instance, and good luck with that. 

It is only rarely that I've observed chroma move in a linear expansion. What I mean is that there is a consistent increase in the chroma of an object, starting from less than zero. 

Confused yet? I am. Still.

What I have observed, over 16 years of painting with Munsell, is that objects not only have chroma that curves as values change, but they also have hues that arc. In other words, while an object might have an objective color that color shifts as light moves across it. 

The photo attached to this post illustrates one common pattern I see. Hue often changes as values rise because there is more light hitting those lighter values. In the illustration the darkest value has a hue of 10R and the lightest is 10YR. 

The chroma starts at its highest possible level at the darkest value, Value 1 @ 4th Chroma, and increases to Chroma 6 for Values 2-6, then curves back towards neutral as more light hits the object. This is just an example, but a very common one, and if you look you can see it all around you.

Update from David Briggs: 
...the straight line shading series (below the first influence of specular reflection) is what I'd expect for a completely opaque object, but once you get translucency, as in flesh, then that can certainly boost in colourfulness the half-lit areas, as Richard's diagram shows, as well as introducing other complications.

It feels mighty fine to get confirmation that the hue and chroma arcs I've been observing for the past 16 years are real. There've been quite a few arguments about this, with multiple painters who advocate the linearity of color. But I am stubborn -- one of my sometimes better qualities -- and if I see something repeat almost always I'll follow my observations and not bow to heavy pressure. 

'Cause you know, attitude check.