"The spacing of the filters in a filter bank used to make an ordinary spectrogram is linear, whereas an auditory filter bank has a spacing that corresponds to the way in which sinusoidal frequency maps onto place on the basilar membrane, a so-called tonotopic map. For frequencies of about 1kHz and above, this mapping is logarithmic."
I read this in an article about how the ear works in processing sound. Can someone explain mathematically how the mapping for frequencies of about 1 kHz and above is logarithmic? Also it would be appreciated if anyone can suggest some literature regarding this topic.