The microstructure of threshold hearing curves and the frequency spectra of evoked otoacoustic emissions both often evince a roughly periodic series of maxima and minima. Current models for the generation of otoacoustic emissions explain the observed spectral regularity by supposing that since the cochlea maps frequency into position the spectral periodicity mirrors a spatial oscillation in the mechanics of the organ of Corti. In this view emissions are generated when forward-traveling waves reflect from periodic corrugations in the mechanics, suggesting that the amplitude of the cochlear waves at the stapes--should manifest pronounced maxima and minima with a corresponding periodicity. This paper describes measurements of stimulus-frequency emissions, establishes their analyticity properties, and uses them to explore the spatial distribution of mechanical inhomogeneities (emission "generators") in the human cochlea. The approximate form and frequency dependence of the cochlear traveling-wave ratio are determined noninvasively. The amplitude of the empirical traveling-wave ratio is a slowly varying, nonperiodic function of frequency, suggesting that the distribution of inhomogeneities is uncorrelated with the periodicity found in the threshold microstructure. The observed periodicities arise predominantly from the cyclic variation in relative phase between the forward- and backward-traveling waves at the stapes.