Strong magnetic fields in chemically peculiar A-type (Ap) stars typically suppress low-overtone pressure modes (p modes) but allow high-overtone p modes to be driven. KIC 11296437 is the first star to show both. We obtained and analysed a Subaru spectrum, from which we show that KIC 11296437 has abundances similar to other magnetic Ap stars, and we estimate a mean magnetic field modulus of $2.8pm0.5$ kG. The same spectrum rules out a double-lined spectroscopic binary, and we use other techniques to rule out binarity over a wide parameter space, so the two pulsation types originate in one $delta$ Sct--roAp hybrid pulsator. We construct stellar models depleted in helium and demonstrate that helium settling is second to magnetic damping in suppressing low-overtone p modes in Ap stars. We compute the magnetic damping effect for selected p and g modes, and find that modes with frequencies similar to the fundamental mode are driven for polar field strengths $lesssim4$ kG, while other low-overtone p modes are driven for polar field strengths up to $sim$1.5 kG. We find that the high-order g modes commonly observed in $gamma$ Dor stars are heavily damped by polar fields stronger than 1--4 kG, with the damping being stronger for higher radial orders. We therefore explain the observation that no magnetic Ap stars have been observed as $gamma$ Dor stars. We use our helium-depleted models to calculate the $delta$ Sct instability strip for metallic-lined A (Am) stars, and find that driving from a Rosseland mean opacity bump at $sim$$5times10^4$ K caused by the discontinuous H-ionization edge in bound-free opacity explains the observation of $delta$ Sct pulsations in Am stars.
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