Auditory Equivalent to 'Observation'

The word you're theoretically looking for is audition in its original sense

1. a. The action of hearing or listening.

It's the abstract noun describing the latinate action of hearing, similar to what you think is going on with observation. That said, very few people use audition in that sense these days and Mr Ashworth is right that you're mistaken in your understanding of observation.

II. 5. a. The action or an act of observing, watching, or noticing; the fact or condition of being watched or noticed; notice; perception.

[...]

II. 7. a. The action or an act of observing scientifically; esp. the careful watching and noting of an object or phenomenon in regard to its cause or effect, or of objects or phenomena in regard to their mutual relations (contrasted with experiment). [...]

Very generally speaking, English tends to use the latinate synonyms in its vocabulary for more formal, educated, or professional senses. Observe gets used for paying close attention to something in formal scientific settings but—even though it originated from senses involving following orders or keeping watch over sth—it's now used more broadly with any of the senses.

Having said that, the more common way you'd describe detecting something specific in a song would be noticing it or picking it out. Those aren't specific to hearing either, but like you said most of our sense vocabulary is focused on sight or just applied generally to any sense information.