Because it is a measure of the similarity of signals in a listener’s left and right ears, the long-term interaural cross-correlation (IACC) function within one-third octave bands provides an estimate of auditory envelopment as well as a guide to the ability to localize a sound. The peak height of the IACC, known as the coherence, is particularly relevant. The IACC can be written mathematically in terms of the amplitudes of spectral components in the left and right ears and in terms of the interaural differences in the component phases. The ensemble-average IACC, as measured with an artificial head in real rooms, can be further analyzed in terms of the amplitudes—their statistical distributions and their interaural correlations—and in terms of the interaural phases—their distributions and correlations with amplitudes. The nature of these statistical relationships depends on the frequency range through the ratio of a characteristic wavelength to the head radius. Analysis of this kind helps solve the long-wavelength problem. In the long-wavelength limit, the IACC must be large, but that does not mean that sound localization is good. [Work supported by the NIDCD Grant DC00181.]