Left: hough functions Θ_k,m(cosθ;ν) (Top) and associated latitudinal and azimuthal functions (Middle and Bottom) m = 2, ν = 0 (continuous lines); m = 2, ν = 0.86 (dotted lines); m = −2, ν = 0.86 (dashed lines). Right: (Top) Eigenvalue (Λ) of Laplace’s tidal equation (in the presence of rotation and of magnetic field) in the range relevant for a solar model and the MHD TA . (Bottom) Equivalent horizontal eigenvalue () (see Eq. (85)). (Left) Class I waves with 1 ≤ l ≤ 6, and m = −l + 2 (black continuous line), m = 0 (long blue dashed line), and m = l (dashed red line). (Middle) Class III waves (s = 0, s being defined in Eq. (89)) have negative values of m (m = 0,···   , −5). (Right) Class IV waves (s = −1) have indices m = −1,···   , −6. Waves classes are discussed in Sect. 4.2. (see also Mathis et al. 2008).