The mode of the incommensurate modulation in the b direction of the Bil,Sr~(Ca& Y )Cu2 20, (0.05 &x &0.75) system is investigated by means of electron diffraction and high-resolution lattice imaging. The change of period of the long-period structure with x is found to be basically due to the mixing ratio of domains of two modulation periods with b =4. 5bp and 5bp or 4.5bp and 4bp, thus creating periods of b=4.75bp-4. 0bp. The fundamental orthorhombic lattice has dimensions of a =b = bp (0.54 nm) and c =cp (3.1 nm). The change of the mixing mode from one to the other mentioned above occurs just in the yttrium concentration range, 0.45 & x & 0.65, which also corresponds to the superconductor (metallic)-to-semiconductor transition boundary. The mixing modes of the domains are directly recorded as a contrast modulation with half periods, 4.5bp/2 and 5bp/2 or 4.5bp/2 and 4bp/2 in high-resolution lattice images. These images are reproduced well by a multislice computer-simulation technique.