We study the spin excitations in the frustrated coplanar 120-degree ground state of the triangular-lattice Heisenberg antiferromagnet and demonstrate that they carry a magnetic moment perpendicular to the plane in which the spins order, despite the ground-state sublattice moments having no out-of-plane component. The symmetry of the momentum dependence of the magnetic moment and energy of the magnons renders the system an odd-parity f-wave magnet. Extending this model to a stack of antiferromagnetically coupled triangular layers provides a realization of magnons in a three-dimensional f-wave antialtermagnet. We show that nonlinear thermal transport effects of magnons, such as Edelstein and spin-splitter effects, provide clear experimental signatures of magnons in f-wave antialtermagnets.