On systematically investigating the electromagnetic response of periodic split-ring resonator (SRR) metamaterials as a function of the size-to-wavelength ($a/\lambda$) ratio, we find that the stop bands due to the geometric resonances of the SRR weaken with increasing ($a/\lambda$) ratio, and are eventually replaced by stop bands due to Bragg scattering. Our study traces the behaviour of SRR-based metamaterials as the resonance frequency increases and the wavelength of the radiation finally becomes comparable to the size of the unit cell of the metamaterial. In the intermediate stages, the dispersion of the SRR metamaterial can still be described as due to a localized magnetic resonances while Bragg scattering finally becomes the dominant phenomenon as $a/\lambda \sim 1/2$.