A phononic band gap is a frequency range where mechanical waves propagation is suppressed in a material. Such materials usually consist of two phases - a matrix with a regular array of inclusions - with a large mismatch of elastic constants. We have developed a single phase phononic band gap material using selective electron beam melting, a powder-based additive manufacturing method. By using only one material instead of two the mechanism is different to the most descriptions in literature. The open cellular geometry was designed by FEM eigenmode analysis of a cubic strut-based unit cell. Additionally, numerical dispersion relations were calculated to determine the band gap position. In a sound transmission experiment using additively manufactured Ti-6Al-4V samples the numerical results were verified. The influence of geometrical parameters on the band gap position was analyzed. It is shown that a combination of different types of unit cells can lead to wider band gaps. Therefore it is possible to design structures with low relative densities that absorb certain sound frequency ranges, e.g. for an application as insulators against vibration or noise.