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High-order plasma shaping (mainly elongation and shift, as opposed tolow-order toroidicity) is shown, under certain conditions, to open gaps in thecoupled shear-Alfv\'{e}n and acoustic continua at frequencies significantlyabove the values predicted by previous theories. Global eigenmodes in thesegaps, which lie between those of geodesic acoustic modes (GAMs) andtoroidicity-induced Alfv\'{e}n eigenmodes (TAEs), are found unstable to hot-ionpopulations typical of tokamak operation, whilst their fundamental resonanceswith circulating particles are shown to take place at velocities near thegeometric mean of the Alfv\'{e}n and sound speeds. Therefore, such eigenmodesare expected to be observed near the predicted frequencies at operatingtokamaks, playing a still unexplored role in magnetohydrodynamic spectroscopyas well as in the stability of next-step fusion experiments.

High-order geodesic coupling of shear-Alfv\'{e}n and acoustic continua in tokamaks