Every six-note scale the 2011 drawing rule allows — no two of its semitones adjacent — is here: 282 scales, joined wherever one note moves by a single semitone. 840 connections, one connected world.
Place each scale by how its notes balance around the circle. The horizontal position is the first Fourier coefficient, so evenly-spread scales gather at the axis and chromatically-clustered ones push to the rim; turning a scale up a semitone turns the whole picture by 30°. The height is the sixth coefficient — how many notes sit on the even semitones against the odd — so the two wholetone scales stand alone at the poles, and moving any note one semitone always changes the height by exactly one step. Distances here are honest: the shortest path between two scales along the edges is exactly the smallest total voice-leading motion between them.
A handful of scales share an exact position — symmetry forces them to — and those are nudged apart and drawn with a ring. That is a compromise the mathematics cannot avoid, so the page marks it rather than hiding it.
Six of these scales are already on the torus as hubs: the two wholetone collections at the poles, and the four augmented collections. Every other scale lists which of the 48 parent scales — or which diminished collection — contains it. And remarkably, that accounts for everything: every one of the 282 hexatonics either is a torus hub or lives inside a torus scale or hub. The 48 magenta scales belong to the diminished collections alone, the torus's other symmetric world. There is no hexatonic outside the torus's reach.
Click a scale and its figure is drawn from the notes: the polygon on the twelve-hour clock, semitone edges red. The tension spikes lens redraws it under the 2011 rule, each semitone corner replaced by its spike — the same figures the torus panel draws, for the same reason. The tritones lens draws the tritone diameters dotted through the centre. When you jump to a neighbour the moving note slides along the rim; with spikes on, the rule figure is redrawn live as it goes, so spikes grow, travel and shrink with the motion.
The 2011 rule — a scale is drawable when no two of its semitones sit adjacent — comes from the same kitchen-table diagrams as the torus. Applied to six-note scales it admits exactly these 282, and the structure they form has been verified computationally from every angle: the counts, the connections, the Fourier geometry, the voice-leading distances. This page is the hexatonic sibling of the Harmonic DNA Torus, built to the same design, and will in time join it as a second tab.