The Birthday of Ludwig van Beethoven (1770) – Mathematics of Music

Beethoven’s music is mathematically structured: sonata form (exposition, development, recapitulation) is a kind of symmetry. His use of fugue (counterpoint) is a set of rules applied to a theme. The frequency ratios in chords (just intonation vs equal temperament) involve logarithms. Beethoven’s late string quartets explore complex rhythmic structures (5/4, 6/8). The ‘Beethoven code’ – a supposed mathematical cipher in his music – is a myth, but the real mathematics of his composition is rich. Music is mathematics for the ear.