Similar to the post about clocks, I thought I'd bring to attention that modular arithmetic is also used in music theory! It is a little more tricky to explain then the clocks, but with music modulo 12 is also used. Modular arithmetic is used when a 12 tone equal temperament scale is used. Different octaves and enharmonics can be of the same tone, which is how modular arithmetic ties in. For example, pitches in a 2:1 ratio are the same as pitches in a 1:2 ratio. Also, some sharps (like C sharp) are the same as flats (like D flat and C sharp). I played violin for 9 years and knew all this information, but had no idea it related to modular arithmetic.

Modular Arithmetic and Music