Music Theory for Developers: How Chords Are Built From Math

I started learning guitar during the pandemic. My teacher told me to memorize chord shapes. I memorized about fifteen before I realized I had no idea why those specific finger positions produced those specific sounds. I was memorizing outputs without understanding the function. As a developer, that bothered me deeply. So I learned how chords are actually constructed. Turns out, the entire Western music system is built on a logarithmic frequency scale and simple integer ratios. Chords are not arbitrary -- they are formulas applied to that scale. The chromatic scale is a data structure Western music divides the octave into 12 equally spaced semitones. Starting from C: C C# D D# E F F# G G# A A# B C 0 1 2 3 4 5 6 7 8 9 10 11 12 Each semitone is a frequency multiplied by the twelfth root of 2 (approximately 1.05946). So if A4 is 440 Hz, A#4 is 440 * 1.05946 = 466.16 Hz, and B4 is 493.88 Hz. After 12 steps, you reach 440 * 2 = 880 Hz -- exactly one octave up. This is a modular arithmetic sy