> If you have a 2:1 (octave) relationship between 2 waveforms, then you won't hear the beating as the beat frequency exactly overlaps the frequency of the lower

> If you have a 2:1 (octave) relationship between 2 waveforms, then you won't hear the beating as the beat frequency exactly overlaps the frequency of the lower frequency. If we take a look into a human ear we'll see there an apparatus which physically splits sound into a spectrum of frequencies (a long narrowing tube, sound comes from one end and it creates resonances at different places) and a lot of receptors which placed in such a way that allows them to specialize on different frequencies. I know nothing that would point to an innate ability of this apparatus to feel octave as something special compared with a mix of two random frequencies. So the peculiarity we hear pops up on later stages of sound processing. But why it pops up? Moreover there is an evidence (I have no link, sorry) that the peculiarity of an octave is a cultural thing, not a genetic one. European music teaches us to feel octave as something special. There are tribes not exposed to European music who doesn't feel consonance and dissonance like we do. My hypothesis that a mind picks correlation between a frequency and a double frequency. I mean it is not because of some funny math comparing two sine waves, it is because sounds essentially are not single sines. Two sounds forming an octave are both sums of many sine waves, and there is a huge overlap between sets of frequencies, so they sound similar. And then, when mind trains on this data, it becomes conditioned on a similarity of double frequencies, so it starts think of two sines with frequency ratio of 2:1 as of similar. The similarity is just a correlation. And people who didn't tried to make a music with strings cannot grasp the idea, because natural sounds mostly much more complex than just sum of a several sines with frequencies that are multiples of some base frequency.