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I believe Zettt has nailed an answer (nice one Zettt). I want to extend this to a bigger picture. There may be an algorithm but I don't know of it specifically as an equation. This is all about mixing sound tracks like you are a great chef cooking up an unbelievable dish. Start with the finest ingredients, in this case sounds you have already recorded that ...

A digital signal always has a maximum level. If summing two tracks to one signal drives the level above this point, it will clip. Most DAW tools I know of don't have any kind of fix for this. They will happily let you drive a signal to clipping, and leave the decisions of how to deal with this to you. There are a few standard techniques for getting around ...

Shazam (and various others) do this for entire songs. This paper describes how: Beforehand, Shazam fingerprints a comprehensive catalog of music, and stores the fingerprints in a database. A user “tags” a song they hear, which fingerprints a 10 second sample of audio. The Shazam app uploads the fingerprint to Shazam’s service, which runs a search for a ...

Compression codecs and methods are also based extensively in the field of Psychoacoustics. For this, I thoroughly recommend the books available from the Focal Press, such as this one

This is not authoritative at all but here is my best guess. It does a simple frequency analysis to see what notes are present. Each key as 7 notes that can be present and 5 that cannot. As soon as it detects a note that is not in a key, it can rule that key out. Then, the keys of C and A minor (for example) have the same notes so the answer it has so far ...