Peaks don't have to necessary align in frequency multiples (harmonics). You could tweak the phase offset between them so that peaks don't align at all and it wi

Peaks don't have to necessary align in frequency multiples (harmonics). You could tweak the phase offset between them so that peaks don't align at all and it will still sound same. Your ear it is sensing and analyzing in frequency domain and not in time domain. I think there is another reason we can identify when frequency ratios are integers in complex sound. This ability gives brain power to "group together" frequencies so it can assign them to the same sound source. This seems like great optimization for computation and bandwidth. It would make sense for hardwired part of brain to make preliminary analysis of sound. For example, you hear an animal sound in a forest. You want to know the direction, want to estimate the size of animal that made the sound, and you'd also want a small 'fingerprint' of a sound, so you can recall from memories if you heard it before. This has to happen as quickly because you might be bombarded with multiple sounds per second. All of them are sounding over each other, so your ear & brain had to develop ability to group them into separate sources and analyze them independently. Most sound sources are coherent, which means they will contain integer multiples of some base frequencies. This goes for picked string, struck anvil, howling wind, but also for sounds made by animal throat. When a bird sings it can be approximated with handful of sine waves whose pitches slide up and down in sync. Therefore it makes sense for ear to communicate only the spectral analysis to brain, and discard other sensed data. So integer ratios are good indication that heard frequency components can be grouped together and assigned to single source of sound. Music exploits this mechanism by playing same or related pitches across different instruments.