The cerebral, pared-down asceticism of the two versions of Treatise on the Veil reflects Twomblys abrupt change of course in the late 1960s. In March 1964, an exhibition of his Nine Discourses on Commodus paintings had been given a scathing reception by the New York art world. Twomblys baroque Mediterranean paintings were then considered out of step with the hard edges, clean lines and smooth surfaces of Minimalism. By the middle of the decade, however, Twombly was making a series of paintings on a black ground that explored and adapted some of the techniques associated with Minimal art: the denial of surface ornamentation or exaggerated brushstrokes, the repetition of regular geometric forms and a fascination with the grid structure.
Each of the six panels of the first version of Treatise on the Veil features a rectangle annotated with measurements, corresponding to the actual spatial proportions of the rectilinear form. This first version is formed by six interlinked instalments or parts, while Treatise on the Veil (Second Version) is made from one long unified picture plane. The initial inspiration for the works apparently came from a photograph by Eadweard Muybridge that shows a bride in motion. Another influence may have been The Veil of Orpheus from the ballet Orpheus 53 by Pierre Henri, in which a cloth torn apart suggests lifting the veil of Eurydice but also the rending to pieces of Orpheus himself.