1. The Two Rings: The outer ring is distance by sound (semitones). The inner ring is distance by harmony (perfect fifths). Hover over any note to see the bridge connecting them.
2. The Geometry (The Math): Music is just dividing the number 12. Triangles divide it by 4 (Major Thirds). Squares divide it by 3 (Minor Thirds). These shapes act as "wormholes" to instantly travel between distant keys.
3. The Scale Lens (The Rules): Traditional music lives within a 7-note scale (Red). Turn it on to see the boundaries of a key.
4. The Secret: Turn on a Scale (Red) and a Geometry (Orange). Watch the geometry step outside the red rules. That is how John Coltrane broke the rules using math. Hit "Giant Steps Cycle" to hear the wormhole in action.
Further Exploration
To dive deeper into the mathematics of John Coltrane's system and the "Tone Circle":