Quarter tube periodic resonators are used to attenuate the acoustic energy of discrete frequencies wherein their sizes can vary from narrow to large. This paper reports acoustical properties of additive manufactured, narrow tube, single and multi-periodic structures, both, theoretically and experimentally. Herein, multi-periodic structures are defined as periodically arranged unit sections of tubes, where each section is composed of periodically repeated unit cells of different sizes and shapes. Structures with hexagonal narrow tubes and octagonal narrow tubes with interfacial gaps are considered for the study, and normal absorption coefficients of these samples are measured by using impedance tube. the theoretical absorption coefficient of these structures is predicted using unit section analysis method and narrow tube theory, where shape dependent viscous and thermal losses are incorporated. Estimated theoretical absorption coefficients are in good agreement with measured results. The result shows that the frequency and amplitude of maximum absorption can be varied by altering the aperture ratio and/or the length of periodic structure. The proposed theoretical method gives an alternative approach for designing and manufacturing periodic narrow tubes for different applications such as absorbing panels, acoustic transducers, and engine filter elements. © 2018 Elsevier Ltd