We compute the eigenmodes (seiches) of the barotropic and baroclinic hydrodynamic equations for an idealized fjord having length and depth scales similar to those of Ilulissat Icefjord, Greenland, into which Jakobshavn Isbræ (also known as Sermeq Kujalleq) discharges. The purpose of the computation is to determine the fjord’s seiche behavior when forced by iceberg calving, capsize and melange movement. Poorly constrained bathymetry and stratification details are an acknowledged obstacle. We are, nevertheless, able to make general statements about the spectra of external and internal seiches using numerical simulations of ideal one-dimensional channel geometry. Of particular significance in our computation is the role of weakly coupled ice melange, which we idealize as a simple array of 20 icebergs of uniform dimensions equally spaced within the fjord. We find that the presence of these icebergs acts to (1) slow down the propagation of both external and internal seiches and (2) introduce band gaps where energy propagation (group velocity) vanishes. If energy is introduced into the fjord within the period range covered by a band gap, it will remain trapped as an evanescent oscillatory mode near its source, thus contributing to localized energy dissipation and ice/melange fragmentation.