Brown if it is a desaturated yellow (like yellow ochre and some raw umbers), green if it is desaturated and the hue is shifted towards green. I have read that a desaturated yellow looks green but I must believe that if it looks green then it is green and not yellow, for all intent and purposes.

Would you say that a desaturated Yellow makes Brown or Olive Green?

This depends quite a bit on the exact hue and how desaturated you mean… plus of course value plays a part.

All true browns are outside the zone of yellows. Similar dark-valued and low-chroma yellows/orange-yellows are more like Raw Umber which can be loosely called “a brown” but that doesn’t mean it’s actually brown (at least not when the hue is a yellow, some Raw Umbers are brown but that’s because they’re atypically orangey).

The dull yellows that look greenish or olive should really be written as ‘olive green’ IMO, to try to help prevent the impression that they’re truly green; people are confused enough about certain aspects of hue without throwing them curveballs

About yellow, lots of paint program don’t display yellow values correctly it seems.

The top is the yellow. The one under that is what I get if I lower the value in RGB. But if you look at a yellow object like a banana that’s already quite desaturated, the yellow is a sort of brown, not green.
…
That CMYK wheel you linked does it too. That can’t be correct, it’s way too green looking.

Is it?

If you can find a representative photo of a banana that shows what you mean and post it here (or post a link) we can have a look at the colours in detail. Remember that some things are the colour that they are, not the colour they appear to be or should be according to theory or expectation.

I have read that a desaturated yellow [U]looks[/U] green but I must believe that if it looks green then it is green and not yellow, for all intent and purposes.

So by extension if a blue looks violet it’s a violet? What about when a grey looks lavender, is it a lavender, or when a red looks blueish…?

Einion

So by extension if a blue looks violet it’s a violet? What about when a grey looks lavender, is it a lavender, or when a red looks [i]blueish[/i]…? Einion

I did refer to a desaturated yellow. To me, desaturated means lowered chroma but the same hue retained, value could be lower, remain the same, or higher.
To some though, I think desaturated means to mix with white!
Here is what saturation is defined as by wikipedia.
“colorfulness of a color related to it’s own brightness”
and “Saturation is the proportion of pure chromatic color in the total color sensation”.
And then there is the WC Glossary:
“saturation – A similar term to chroma but not exactly synonymous. More correctly it means the amount of colour in relation to its brightness.”
Other sources have other descriptions but none describe a shifting of the hue.

So are the charts presented above really attempting to accurately show desaturation or are they showing lowering of value steps?
In my world (albeit somewhat naive theoretically ) a desaturated yellow would still look yellow and a desaturated greenish yellow would look greenish yellow, for my intent and purposes (ie., usage in paintings).
As for a blue that looks violet, I would classify that as a violet blue.
A desaturated lavender should look lavender and could be greyish.
A neutral grey should not look lavender.
Now a red that looks blueish, I don’t know about that one, I would say that the progression of hues that red must go through to get to blue are as follows, starting with a middle blue, then looking violetish blue, then violet, then violet blue, then blue, but a red that looks blueish I don’t know about that one.

In my world (albeit somewhat naive theoretically ) a desaturated yellow would still look yellow and a desaturated greenish yellow would look greenish yellow, for my intent and purposes (ie., usage in paintings).

I think it depends on whether you’re defining “desaturated” through process or perception. In Photoshop, for example, a hue angle of 60 means nothing more than that you have equal parts of red and green with a smaller part of blue. What it looks like to us is completely irrelevant. Perception agrees with you, but perception is subjective, which is why attempts to define colors in an objective system rely on some objective process for reducing saturation. And those seem to always make a darkened, desaturated yellow look green. It is highly unlikely, however, that the shadows in the banana were desaturated by one of these same processes.

The munsell chart posted doesn’t look like it is as greenish in lower values as they do in the pantone chart. In fact, I don’t think it is very greenish at all.
The pantone chart goes quite green with lower values.

I think that a uniform saturation series should have the same colors such as those on this page as Briggs says, “a single color represented under different amounts of illumination”
Though other factors such as reflected light may influence the color in those shadows, I think it is basically what you are seeing in the banana and chip clamp photos, ie, the same basic color under different amounts of illumination. We know that both the banana and the chip clamp are the same color in their respective shaded areas. However, they are desaturated by the lower illumination in the shadows and note that they don’t look green in spite of the fact that the bananas’ surrounding color is green! The sampled banana shadow area would receive reflected light from the adjoining banana surface which is the same basic color, yellow.
The sampled chip clamp would receive reflected light from that surface which looks to be fairly neutral in color.
If I were painting those bananas (realist, not expressionist), then I would choose a desaturated yellow like ochre or mix a desaturated yellow myself, but I would not select a color from a chart that would give me a decidedly greenish hue when applied.
A uniform saturation chart may have a match that is a more appropriate color.
Excellent examples Goldey!