A generalized filter structure is introduced that serves as a basis for discussing high-transmission comblike (HTC) optical filters capable of being tuned between reflection peaks having linewidths that are relatively narrow compared with the line spacing. The generalized filter may consist of any structure from a single periodic element to a multiple series of filter elements; identical or similar filter elements may occur two or more times and may be spatially separated, forming optical cavities having one or more optical lengths. Here a cavity is defined as the space between identical or similar filter elements. Special cases of the generalized filter include singularly modulated quarter-wave-stack, sinusoidal (rugate), and Fabry-Perot filters as well as multiple-cavity high-order HTC filters. The individual filter elements of the last-named type have low-to-moderate reflectivity and may have either stepwise constant or sinusoidal refractive-index modulation. Prior calculations of HTC filter spectra used matrix methods; we develop an alternative perturbation approach.