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Based on the theory describing traveling waves on three-dimensional (3-D) periodic arrays of two sets of magnetodielectric spheres arbitrarily arranged on a simple tetragonal lattice, dispersion diagrams of seven different arrangements of the spheres are analyzed for three combinations of sphere types: I) dielectric spheres with equal permittivity but different radius; II) dielectric spheres with equal radius but different permittivity; and III) one set of spheres is purely dielectric while the other set is magnetic. Results show that the maximum bandwidths of the DNG region provided by different spheres arrangements for spheres combinations I-III are, respectively, 0.21%, 0.069%, and 7.403%. Compared to results reported in previous literature, analysis of these possible arrangements of the spheres shows similar narrow double-negative (DNG) bandwidths for spheres combinations I and II, and wider DNG bandwidths for spheres combination III. Although purely dielectric materials with relative permittivity much greater than one are readily available, the usefulness of purely dielectric DNG metamaterials still depends on whether the narrow bandwidths achievable are acceptable for the particular applications. Since purely magnetic materials with relative permeability much greater than one above 1 GHz are not currently available, the practicality of fabricating DNG metamaterials using arrays with spheres combination III is questionable for radio frequency (RF) applications, at least at present, despite the fact that this combination yields much wider DNG bandwidths than those of spheres combinations I and II.