We examine how the qualitative structure of the Doppler peaks in the angular power spectrum of the cosmic microwave anisotropy depends on the fundamental nature of the perturbations which produced them. The formalism of Hu and Sugiyama is extended to treat models with cosmic defects. We discuss how perturbations can be ``active'' or ``passive'' and ``incoherent'' or ``coherent'', and show how causality and scale invariance play rather different roles in these various cases. We find that the existence of secondary Doppler peaks and the rough placing of the primary peak unambiguously reflect these basic properties.