The Kβ x-ray spectra of the elements from Ca to Ge have been systematically investigated using a high-resolution antiparallel double-crystal x-ray spectrometer. Each Kβ1,3 natural linewidth has been corrected using the instrumental function of this type of x-ray spectrometer, and the spin doublet energies have been obtained from the peak position values in Kβ1,3 x-ray spectra. For all studied elements the corrected Kβ1 x-ray lines FWHM increase linearly as a function of Z. However, for Kβ3 x-ray lines this dependence is generally not linear in the case of 3d elements but increases from Sc to Co elements. It has been found that the contributions of satellite lines are considered to be [KM] shake processes. Our theoretically predicted synthetic spectra of Ca, Mn, Cu, and Zn are in very good agreement with our high-resolution measurements, except in the case of Mn, due to the open-shell valence configuration effect (more than 7000 transitions for diagram lines and more than 100000 transitions for satellite lines) and the influence of the complicated structure of the metallic Mn.