“…The presence of longitudinal stratification due to gravity, expansion, or curvature leads to coupling of longitudinal harmonics (e.g., Pascoe et al, 2009;Pascoe and Nakariakov, 2016) and changes to the ratio of their periods (e.g., Andries et al, 2005;McEwan et al, 2006;Safari et al, 2007;Verth and Erdélyi, 2008;Arregui et al, 2013) but does not significantly affect the damping rate due to resonant absorption (Arregui et al, 2005;Dymova and Ruderman, 2006). The period ratio for harmonics has been observed in many studies of large-amplitude oscillations (e.g., Verwichte et al, 2004;De Moortel and Brady, 2007;Van Doorsselaere et al, 2007;Pascoe et al, 2016aPascoe et al, , 2017aDuckenfield et al, 2019) and recently in decayless oscillations (Duckenfield et al, 2018). Figure 1 shows the evolution of the transverse loop density profile at the middle of the coronal loop, i.e., the antinode for the fundamental standing kink mode.…”