What is the pre-computer version of Photoshop's blending modes?
I think the origins lie in many places. In photograms and photocompositing, each image component is burned-in over the initially white surface and the edges can be blended by using to umbra of the shadow of the hands or stencil controlling the burn. 

Blending tones is an important technique in drawing with pastels. I think a lot of the blending tools come from the color blending realm, perhaps even more than from the collage and photogram realm. So even things liking mixing paints have their computer analogue, which can then be applied to edges due to the converge of the two sub-topics.