This paper explores the relationship between two kinds of linear MHD disturbances, namely interchange and ideal magnetohydrodynamic (MHD) ballooning. We consider the limit of zero ionospheric conductance (see Appendix A). In that case, the square of the frequency ω 2 is real. If ω 2 > 0, it represents a wave, and ω 2 < 0, it represents a instability. In this paper, we are mostly concerned with waves. For simplicity, we consider even waves with k ‖ ∼ 0 propagating in the meridional xz plane (An even wave is one in which the perpendicular displacement is symmetric about the equatorial plane.). We define k ‖ := 2π/λ, where λ is the wavelength of the thin filament mode. Our (x, y, z)-coordinates are the geocentric solar magnetospheric (GSM) coordinate system. We consider waves in thin magnetic filaments, which have been studied in various geometries [e.g., solar corona (Parker, 1981); and magnetosphere (Chen & Wolf, 1999;Toffoletto et al., 2020;Wolf et al., 2012)]. These structures are infinitesimally thin in the y-direction and also in the xz plane perpendicular to the magnetic field. They slide through the magnetospheric background without friction. In a uniform medium, there are three MHD wave modes (fast, intermediate, and slow). The fast modes do not propagate in thin filaments (Chen & Wolf, 1999). We