Original	Lab Saturation	Lab Sat + L channel mask	Munsell faces

How about real life? 

I constructed 3 boxes from Post-It notes and took a 5 (1ev) bracket shot of them.  Here is the 0ev one. Now cameras automatically adjust the image to give an out of camera 'good' photo by increasing the contrast etc.  This means that the original colours I saw will be different in the photo.  Note in the following, I have made an assumption (which may be wrong) that in-camera adjustments are carried out in Normal blend mode, rather than Luminosity mode because that results in a more colourful photo. When Reilly was talking about chroma adjustment, he was referring to the painting real-world image, not a photo rendition of an image.  But then we will be looking at the photo, so that becomes the real-world image!
As I had taken a bracketed set of photos, I was able to stack them up in layers and add a curve adjustment layer to correct the 0ev image back to what was actually taken - because each shot was 1 ev apart and I could use the grey card to deduce the correct luminosity of each stop. Opposite is the curve needed and the Watchers showing the difference between the out-of-camera (surrounds) and real-life (colour inside the clocks).  I had also checked the level of each face using the spot exposure meter and the pink box measured 1/13th, 1/25th and 1/60th, which is roughly 1 stop apart - so that ties in with the curve adjustment levels of 40, 48 & 61 (compared to the photo's 31, 42 & 61).
Nearly all post-processing starts with setting the shadow and highlight points, unless we are after a non-punchy image.  These points are set depending on what we are prepared to loose at both ends of the tones and is therefore unpredictable for each photo. We also tend to correct for white balance at an early stage. Thus we now have a rendition that is likely to be quite different from the real-life image.  It is this image (shown opposite) that I shall experiment with.  Whether things improve with Reilly's approach, or not, will not be a proper test of his idea, just using a single example.
Without knowing how things will evolve, I plan to take two approaches to test the chroma.  One involving the above image and another with a processed version of it, increasing the saturation and maybe the contrast.
So first changing the chroma for the above image.  There is not a whole heap of difference, but it is there and I feel that it makes for a 'better' orange box and changes the flavour of the pink one.  The yellow difference although too small to write home about for the two vertical surfaces, does seem to have changed the horizontal one - but that is all in the beholder's eye, they are the same.
Now let us complete the post-processing (of the image but one above) with extra contrast and colour saturation.
and if we alter it for Munsell chroma. So I think it both cases less chroma won the day.
I did a series of tests on random images by adding a L mask during saturation increase and also following the Reilly formulae.  In the main, images like the example opposite tended not to significantly benefit from either technique, but photos with large contiguous areas in a tonal framework did, like the one below. A Thought Painting in Munsell colours is time consuming, but quite effective.  An alternative to the L mask (and quicker to do during processing) is to create a Layer Set with (say) 5 tone stops (controlled by BlendIfs), each with a different saturation level.  Going from the bottom layer, I find -20, 0, +20, +30 & +40 saturation boosts a good starter.  I can then alter the Opacity of each layer as well as the Layer Set.  If I keep this Set in a small .psd file, then I can quickly copy it to the image I am processing!  Needless (?) to say this is all in the Lab colour space. l

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