In the frame of long-wavelength Heisenberg model, a simple magnonic device is designed to obtain possibly transmission stop bands (where the propagation of spin waves is forbidden). This simple device is composed of an infinite one-dimensional mono-mode waveguide (the backbone) along which N(N′) side resonators are grafted at two sites. Contrary to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with this simple structure. This is obtained by combining appropriately the zeros of transmission of the side resonators. Sharp resonant states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for various systems of this kind within the framework of the Green’s function method. The amplitude, the phase, and the phase time of the transmission are discussed as a function of frequency and it is shown that the width of the stop bands is very sensitive to the number of the side resonators. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches.