Both are very similar and have a lot of parallels, enough that I generally call what humans do "kind of Fourier Transform", but "convolution of roughly sinusoid

Both are very similar and have a lot of parallels, enough that I generally call what humans do "kind of Fourier Transform", but "convolution of roughly sinusoidal wavelets" is definitely more correct. For example, you can explain to someone with not much signal knowledge why a 15kHz square wave sounds exactly like a 15kHz sine wave to humans by looking at the harmonics through a Fourier Transform. I do believe most of the magic happens in the brain though, the cochlea is a super advanced biological microphone, but the brain is responsible for harmonic and rhythmic processing. The brains figures out what is a voice, an instrument, or a percussion. My understanding is that it stores short-term temporal information needed to make sense of realtime information: a note alone might be perceived differently depending on the harmonic and rhythmic context ("wrong note").