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The effect of total circumference on the terahertz transmission response of coaxial H-shaped annular aperture arrays punctured in a thin metal film on a silicon substrate is investigated. Unexpectedly, the resonance frequencies are not sensitive to the details of the shape for the coaxial annular aperture, but intensely depend on the total circumference in a unit cell. Furthermore, a clear inverse proportion relationship between the resonance frequencies and the total circumference is revealed and confirmed experimentally, which is interpreted by the standing-wave plasmonic resonance mechanism. This characteristic paves an avenue to the quick and accurate construction of the desired operating frequencies for filtering, biosensing, and ultrafast switching applications.