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This paper introduces an approach based on transition potentials for inelastic scattering to understand the underlying physics of electron magnetic circular dichroism (EMCD). The transition potentials are sufficiently localized to permit atomic-scale EMCD. Two-beam and three-beam systematic row cases are discussed in detail in terms of transition potentials for conventional transmission electron microscopy, and the basic symmetries which arise in the three-beam case are confirmed experimentally. Atomic-scale EMCD in scanning transmission electron microscopy (STEM), using both a standard STEM probe and vortex beams, is discussed.