I have a prepress "Color Process Manual" copyright 2000, used by graphic designers and bought off Amazon that's sheetfed printed. I created a 128RGB gray patch in ProPhotoRGB and noted PS's Info Palette CMYK readings converting this patch to US Sheetfed Coated v2 profile and wrote the numbers down as C40%,M30%,Y30%,K1%.
I located the CMYK combo patch of this gray on my "Color Process Manual" and isolated it with the provided crop viewer and took a picture of it lit under my 5000K daylight flotubes. See below.
I've also included a picture of the CMYK ink purity ramp between two completely different printing companies using their own ink formulation, commercial sheetfed press and coated paper. The Ole No Moire color target was printed on a Komori 300LPI press at Copy Craft in Odessa Texas and the "Color Process Manual" was printed in Hong Kong.
I know the Copy Craft color target was converted to regular US SWOP in PS5 as indicated by the company's online instructions on how to prep files for their presses.
The "Color Process Manual" 24,000 CMYK combo color swatches were printed on a Heidelberg Speedmaster w/direct to plate technology using Japan ink & glossy coated paper with these additional specs...
10% dot gain, 175LPI...
Ink densities: Black 1.8-2.0, Cyan 1.6-1.7, Magenta 1.4-1.5, Yellow 1.3-1.4 AND printed in that order.
From the manual's Photoshop 5 Color Picker screengrabs I'm assuming they converted to default PS 5 US SWOP.
It doesn't seem exact CMYK grayscale numbers are all that necessary. Derive your own conclusions.