The Birthday of John Philip Sousa (1854) – Mathematics of Marches

Sousa wrote 136 marches. A march has a steady 2/4 or 4/4 time, with a ‘trio’ section. The structure is a mathematical form: A‑A‑B‑B‑C‑C‑D‑D (repeat). The tempo is around 120 beats per minute (2 Hz). Sousa’s marches are used in military parades, where the step frequency must match the beat. The mathematics of walking: a person’s natural stride frequency is about 2 Hz, so marches are biomechanically optimised. The ‘Sousa effect’ – a form of synchronisation – is studied in nonlinear dynamics.