We will report some new conceptual interpretation on a simple functional relation attached to the modular Gaussian curvature on noncommutative two-tori discovered by Connes and Moscovici. The main result is a cyclic module like category whose objects consisting of symbols of the rearrangement operators and the generators of the morphisms are derived from basic operations that occurred in the variational calculus behind the curvature computation. I will also make comparisons with Hopf-cyclic theory to explain why some modifications have to be made to the standard cyclic theory to deal with variation. The talk is based on the recent preprint .