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The origin of narrow pseudogaps close to the Fermi energy is examined in two model systems: α-AlMn(Si) and i-AlCuFe (1/1). We show that long-range electronic interferences in the Mn/Fe sub-systems give rise to such narrow spectral features which are highly important for the electronic transport. Besides the ASA-LMTO and the TB-LMTO recursion method we employ a cluster-recursion method within the muffin-tin scattered wave concept which reveals interference results on arbitrary length scales. We conclude that certain properties of quasicrystals are due to the physics in chemically defined sub-systems.