Music is mathematics made audible. Every chord, scale, and rhythm follows precise numerical relationships — the same ratios Pythagoras discovered vibrating on a string 2,500 years ago. Western harmony is built on frequency ratios like 3:2 (the perfect fifth) and 2:1 (the octave), while rhythm subdivides time into nested patterns of stunning complexity.
These simulations let you explore the hidden structure of music. Trace the circle of fifths to understand key signatures. Build chord progressions that follow voice-leading rules. Layer polyrhythms to discover emergent patterns. Compare how equal temperament and just intonation shape the sound of intervals.