Jacob Collier's key-change advice, from a widely shared clip: a diminished chord is 'a four-way crossroads between you and any chord.' The mechanics hold up exactly. A dim7 is stacked minor 3rds — perfectly symmetrical — so it respells four ways, and any of its four tones can act as a leading tone resolving up a half step: four keys from one grip. Same chord, second door: lower any single note by a half step and the dim7 collapses into a real dominant 7th in root position — and the four dominants you can mint this way aim at the same four keys, just with a smoother ride in. Third door: only three distinct dim7 collections exist in all of music, so sliding the hinge one fret in either direction hands you a different four-pack — 3 hinges × 4 exits = all 12 keys, never more than two moves from anywhere. The crossroads image is accurate: stand on the hinge, look four ways, walk.