Hermann von Helmholtz (1863) proposed that perception of pitch corresponds to the vibration of different portions, or places, along the basilar membrane.  Thus, different places have different pitches, like keys on a piano.
Other researchers (Rutherford, 1886) proposed an alternate model called frequency theory, which holds that perception of pitch corresponds to the rate, or frequency, at which the entire basilar membrane vibrates, causing the auditory nerve to fire at different rates for different frequencies. Thus, according to this theory, the brain detects the frequency of a tone by the rate at which the auditory nerve fires.
Like with research in theories of color vision, researchers argued about these two competing theories for almost a century.  It turns out that both are valid– in part.  The two are reconciled by Georg von Bekesy’s (1947) traveling wave theory.  Basically, von Bekesy said that the whole basilar membrane does move as a traveling wave, but the waves peak at particular places, depending on frequency.
Current thinking is that pitch perception depends on both place and frequency coding of vibrations along the basilar membrane.