The Frank-Kasper a phase and the dodecagonal quasicrystal (DDQC) have been found in binary mixtures of block copolymers and homopolymers. In this study, the effect of the molecular weight length and weight fraction of added homopolymers on the sigma phase region of the phase diagram in sphere-forming block copolymer/homopolymer blends was investigated by synchrotron small-angle X-ray scattering techniques. In addition, the thermodynamic stability of the DDQC was also investigated in a blend system. The ratio (alpha) between the homopolymer chain length and the block copolymer length is defined as alpha = N-A/N-A,N-block, where N-A and N-A,N-bloc are the chain lengths of the homopolymer and that of the block copolymer of the same constituent, respectively. It was found that the Frank-Kasper a phase could be observed in blended samples with alpha = 0.165 and alpha = 0.821. This indicates that the sigma phase is stable when the chain length of the added homopolymer is smaller than the same constituent chain length of the block copolymer. The region of existence of the a phase in the blend sample with alpha = 0.821 is larger than that in alpha = 0.165. The DDQC emerges prior to the forming of the sigma phase in the case of alpha = 0.821. However, it was revealed that the DDQC is a nonequilibrium state observed only in the heating process. Furthermore, the sigma phase exists at the phase boundary between the body-centered cubic phase and the hexagonally packed cylinders.