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Lead-based relaxor ferroelectrics are key functional materials indispensable for the production of multilayer ceramic capacitors and piezoelectric transducers. Currently there are strong efforts to develop novel environmentally benign lead-free relaxor materials. The structural origins of the relaxor state and the role of composition modifications in these lead-free materials are still not well understood. In the present contribution, the solid-solution (100-x)(Bi1/2Na1/2)TiO3-xBaTiO3 (BNT-xBT), a prototypic lead-free relaxor is studied by the combination of solid-state nuclear magnetic resonance (NMR) spectroscopy, dielectric measurements and ab-initio density functional theory (DFT). For the first time it is shown that the peculiar composition dependence of the EFG distribution width (ΔQISwidth) correlates strongly to the dispersion in dielectric permittivity, a fingerprint of the relaxor state. Significant disorder is found in the local structure of BNT-xBT, as indicated by the analysis of the electric field gradient (EFG) in 23Na 3QMAS NMR spectra. Aided by DFT calculations, this disorder is attributed to a continuous unimodal distribution of octahedral tilting. These results contrast strongly to the previously proposed coexistence of two octahedral tilt systems in BNT-xBT. Based on these results, we propose that considerable octahedral tilt disorder may be a general feature of these oxides and essential for their relaxor properties.