It's as if you saw a treestump that looks like a human. Audio neural response is similar to image neural response. Your brain will definitely see a human where the tree is, and your brain will ALSO experience 880Hz and related subfrequencies of audio where the 440Hz is because they look similar.
Difference between similar shapes and similar sounds, the tree requires your full attention, and the 880Hz subfrequency scan/comparison happens more efficiently, briefly and unconsciously, at the same speed that you can differentiate an oak leaf and a fig leaf, nearly instantly.
Sound will cause a complex pathway of neurons to signal to previously connected neurons which will attribute conscious memories and feelings to the sound. The brain has to compare the tone with other known tones, in a tree of neurons through wich the sound travels...
So the first neurons can identify "static pitch / glissando", and "frequency spectrum of tone" ... measure loudness of "880 / 3rd / 4rth partial" = none. You would think "sounds like a perfect sine wave"
So your neurons project a variety of possible imaginary variations onto the nerve signal that your ears receive, and you imagine for a second that the sound is them, just like you can see a tree that looks like a cat, or a person walking and think "it's a person walking" ... "oh it's only a tree" your mind actively experiences other sounds and signals and compares them to incoming data...
You imagine other sounds consciously or subconsciously(it's felt as you becoming tuning awareness of something "what's that?"), so effectively, your brain is comparing the sound to all those other frequencies, but it is not activating full stimulus for them, only sensing if that frequency region is responding to the sound.
with a-lot of the human musical response being interpreted by the vocal interpretation structures of humans which are 10-100 times bigger than animal sound-interpretation regions (for voice communication).