The high-field and zero-field behavior of the linearized magnetic excitations (harmonic magons) in a one-dimensional +/-J Heisenberg spin glass are studied. In the high-field limit-a field strong enough to ensure complete alignment of the ground state-the density of states (DOS), the inverse localization length (ILL), and the dynamic structure factor are calculated over the interval -4J < E - H < 4J (H is applied field) by employing the coherent-exchange approximation (CEA), negative-eigenvalue counting, and matrix diagonalization. In the low-energy regime (0.001 < E - H < 0.1 J), the CEA closely approximates the exact results reproducing, in particular, the anomalous power-law behavior of the DOS rho(E) approximately (E - H)1/3 and the ILL 1/L(E) approximately (E - H)2/3 for the symmetric distribution of the exchange interactions (concentration c = 0.5). In zero field, the DOS and the ILL are calculated using negative-eigenvalue counting for 0 < E < 4J and 0.0001 < E < 0.01 J. For c = 0.5, a connection is established between the zero-field and the high-field limits, and for other concentrations, a phenomenological approach is developed in the low-energy regime where it is found that rho(E) = f(c)E-1/3 and 1/L(E) = g(c)E2/3.