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Here we would like to discuss the light transmission modulation by the one-dimensional polymeric quasi-multilayer which is formed according to substitutional generalized Octonacci with PMMA and PS as the constituent materials. In particular, we will present some theoretical findings using the well-known transfer matrix method. PBG inter-band spacing and depth can be managed by choosing the appropriate generation number. The number of PBGs is the same while increasing in the generation number and are shifted symmetrically towards the designed frequency. It also reveals the aroused forbidden frequency band can be manipulated by changing the applied hydrostatic pressure and the thickness of the constituent polymeric materials. The increase in pressure shows a blue shift in the PBGs while the increase in thickness of the polymeric material provides a redshift to PBGs. The proposed structure could be another possible system for optical device design specially multi-band tunable optical reflectors.