arts

Music Theory & Sound

The mathematical structures behind music — from the circle of fifths to polyrhythms, tuning systems, and the physics of harmony.

music theoryharmonycircle of fifthschord progressionsrhythmtuningscales

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.

5 interactive simulations

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Chord Progression & Harmony Simulator

Build and analyze chord progressions using Roman numeral analysis — explore voice leading, harmonic tension, and resolution in real time

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Circle of Fifths Explorer

Navigate the circle of fifths to visualize key signatures, relative majors and minors, and the 3:2 frequency ratio that structures all of Western harmony

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Polyrhythm & Time Signature Simulator

Layer two independent rhythmic cycles to create polyrhythms — watch how 3:2, 4:3, and complex ratios generate emergent rhythmic patterns

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Musical Scales & Modes Explorer

Explore the seven diatonic modes from bright Ionian to dark Locrian — visualize interval patterns, semitone positions, and modal color on a keyboard and circle

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Tuning Systems Comparison

Compare equal temperament and just intonation side by side — hear and see the cent differences between pure frequency ratios and the compromises of modern tuning