The most mind-blowing concept in music (Harmonic Series)

Andrew Huang does a good job of explaining harmonics and overtones[0]. You only need to watch until about the 4 minute mark (from the timestamp) to get an explanation of harmonics and what the sonograms represent. The short of it is that most natural sounds product a root tone plus a varying amount of related tones above it. Our ears hear the root tone, and the other tones above it are what give the sound its uniqueness. That's why a guitar, a clarinet and 3 singers can produce the same note while sounding distinct. Birds seem to produce a natural sound without a lot of the related tones above it. Their sound is, relatively speaking, much purer than most other natural sounds. That's very unique. [0]: [VIDEO]

Music producer Andrew Huang does a fantastic job demonstrating the harmonic series concepts in a video from last year: [VIDEO]

The harmonic series is a really neat thing to learn about -- one of those "art is math" kind of moments. This video does a good job of explaining it in a relatively short and simple way, but goes in-depth enough that even people with an understanding of music might learn something: [VIDEO]

Well, a lot of harmonies are built on top of the harmonic series. See [VIDEO] And tuning is all about 'numerical puns', similar to how eg 2^10 ~ 10^3, but for perfect fifths and octaves etc. Of course, our physiology and culture is a bit too complicated and convoluted to understand everything about music from first principles like this. So most of the time you are better off learning (and treating) music as music instead of as applied math or physics.