We analyze published auditory-nerve and otoacoustic measurements in chinchilla to test a network of hypothesized relationships between cochlear tuning, cochlear traveling-wave delay, and stimulus-frequency otoacoustic emissions (SFOAEs). We find that the physiological data generally corroborate the network of relationships, including predictions from filter theory and the coherent-reflection model of OAE generation, at locations throughout the cochlea. The results support the use of otoacoustic emissions as noninvasive probes of cochlear tuning. Developing this application, we find that tuning ratios-defined as the ratio of tuning sharpness to SFOAE phase-gradient delay in periods-have a nearly species-invariant form in cat, guinea pig, and chinchilla. Analysis of the tuning ratios identifies a species-dependent parameter that locates a transition between "apical-like" and "basal-like" behavior involving multiple aspects of cochlear physiology. Approximate invariance of the tuning ratio allows determination of cochlear tuning from SFOAE delays. We quantify the procedure and show that otoacoustic estimates of chinchilla cochlear tuning match direct measures obtained from the auditory nerve. By assuming that invariance of the tuning ratio extends to humans, we derive new otoacoustic estimates of human cochlear tuning that remain mutually consistent with independent behavioral measurements obtained using different rationales, methodologies, and analysis procedures. The results confirm that at any given characteristic frequency (CF) human cochlear tuning appears sharper than that in the other animals studied, but varies similarly with CF. We show, however, that the exceptionality of human tuning can be exaggerated by the ways in which species are conventionally compared, which take no account of evident differences between the base and apex of the cochlea. Finally, our estimates of human tuning suggest that the spatial spread of excitation of a pure tone along the human basilar membrane is comparable to that in other common laboratory animals.