We know that frequencies that follow a base two logarithmic relationship sound as the same tone. This seems to be one of the fundamental principles that underlies music theory. For example, frequencies of 220, 440, 880, 1760, ... all sound as the same tone: 'A'.
f_n = f_0 • 2^n
After searching through several different music theory sources, I have not found a convincing physical or mathematical explanation for this phenomenon. Many sources say that human's perceive pitch on a logarithmic/exponential scale, or that the waves 'line up' in a way that creates a sense of 'sameness' between the two frequencies.
It is certainly clear that humans do perceive pitch in a logarithmic manner. My question: why? There must be a physical reason for why humans perceive frequencies that follow such a well defined mathematical relationship as being of the same tone.