Equal temperament

If an octave doubles the frequency and holds twelve equal half steps, each half step must multiply the frequency by the twelfth root of two (≈ 1.0595). Do it twelve times and you land on exactly ×2 — the octave. This system is called 12-tone equal temperament (12-TET).

The formula for any note is f = 440 × 2^((n−69)/12), where n is the MIDI number and 69 is the A above middle C. Feed in n = 60 and you get middle C ≈ 261.6 Hz. Every frequency in this app comes from that one line of math.