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Theoretical studies, based on three independent techniques, of the band structure of a one-dimensional width-modulated magnonic crystal under a transverse magnetic field are reported. The band diagram is found to display distinct behaviors when the transverse field is either larger or smaller than a critical value. The widths and center positions of bandgaps exhibit unusual non-monotonic and large field-tunability through tilting the direction of magnetization. Some bandgaps can be dynamicallydoi:10.1063/1.4863776 fatcat:kec44qpwgngzdhe6tqfm5lj5be