  We investigate the optical transmission spectra for $s$-polarized (TE) and
$p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a
quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and
\textit{metamaterials}, organized by following the Octonacci sequence.
Maxwell's equations and the transfer-matrix technique are used to derive the
transmission spectra for the propagation of normaly and obliquely incident
optical fields. We assume Drude-Lorentz-type dispersive response for the
dielectric permittivity and magnetic permeability of the metamaterials. For
normally incident waves, we observe that the spectra does not have self-similar
behavior or mirror symmetry and it also features the absence of optical band
gap. Also for normally incident waves, we show regions of full transmittance
when the incident angle $\theta_{C} = 0^{\circ}$ in a particular frequency
range.
