Harmonic magnon modes in random-exchange and random-field Heisenberg chains are studied in the large spin limit. In the weak disorder limit, the integrated density of states and inverse localization length for the low energy excitations in random fields is computed using the Coherent Potential Approximation (CPA); in the case of random exchange systems, the corresponding calculation is carried out using the Coherent Exchange Approximation (CAE). These results are compared with numerical and exact perturbation results obtained for various disordered systems and with renormalization group studies made for the same systems. Good agreement is obtained; in particular, the anomalous power-law behavior is reproduced. Developing a phenomenological model, we are able to find the density of states for asymmetric distributions of the exchange interactions. We also present a thermodynamic study of the random exchange model and compare our results with those for the corresponding spin-1/2 chain. Finally, we briefly present our analytical solution of the CPA self consistent equation which eliminates the errors associated with the numerical solution of the equation.