1,365 slivers on two cyclic coordinates — placement (twelve substance stations, wrapping) and shape (116 transposition classes, wrapping) — with all 20,736 resonance codes folded within as substrate. Material is absolute. Affect is relational. And 21 slivers refuse the map entirely.
The torus is not a clean product. 116 shapes × 12 placements would be 1,392; the codex holds 1,365 because four symmetric classes fold — the twin-tritone lattices, the diminished sevenths, and the doubled tritones occupy short orbits. Those folded classes are exactly the 21 slivers whose centroid does not exist: the torus folds precisely where placement fails, so the unresolved render on the axis — the one place on a torus that has shape but no station. The Perfects are the opposite kind of singular: a unison's centroid is exactly its station — the twelve pure points of the placement circle, each holding precisely two corridors.
This disk is a view, not the codex — radius is voice-leading distance from the vantage you chose, and it silently redraws for every player who re-attunes. Set the vantage to 5667, deep in the F♯ marches, and watch Origin: Prime slide toward the hostile rim. The hatched wedge holds the 21 unresolved slivers at their true wave radius: their distance is real, their bearing is not.
| Tier | Distinct notes | Slivers | Codes within | Grip (interval classes) | Corridors | Habitability | Tolerance range (from 0479) |
|---|---|---|---|---|---|---|---|
| Common | 4 | 495 | 24 | 2 – 6 | 8 | sustains attunement | −0.406 … +1.500 |
| Uncommon | 3 | 660 | 12 | 1 – 3 | 6 | sustains attunement | −0.531 … +1.625 |
| Rare | 2 | 180 | 4 – 6 | exactly 1 | 4 | wilderness | −0.625 … +1.750 |
| Abyssal | 2 · tritone | 18 | 4 – 6 | exactly 1 | 4 | wilderness | −0.031 … +1.156 |
| Perfect | 1 | 12 | 1 | 0 | 2 | wilderness | −0.625 … +1.750 |
Grip is why the ladder exists. Attunement needs interval structure to lock onto; a unison is amplitude, not harmony — its interval vector is all zeros, so there is literally nothing to grip. Habitability is derived, not decreed, and it degrades smoothly: 1,155 slivers sustain attunement (84.6%); 210 are wilderness (15.4%). The verse physically narrows as it refines — 8 → 6 → 4 → 2 — and every Perfect is a two-corridor chokepoint by construction. And rarity carries zero information about hostility: every tier's mean tolerance to Origin is +0.458, identical to three decimals. Rare and Perfect span the widest tolerance range in the verse — the wilderness holds both the friendliest and the cruellest places you can stand. Abyssal spans the narrowest: tritone slivers are never the scariest places, only the wrongest.
Twenty-one slivers have a resultant vector of exactly zero: their four voices cancel, their centroid is mathematically undefined, and they hold no position on the Organic↔Synthetic axis at all — matter that will not resolve into any substance. They are the fixed points of the torus's rotational symmetry, the singular points where any centroid-based projection must fail. The first issue of this exhibit rendered them at fabricated angles; that error hid the most structurally interesting objects in the verse. Their strangeness is intrinsic, where hostility is merely relational.
| Wave | New | Cumulative | % of verse | Arrivals |
|---|
The release order is computed from 0479 and only from 0479 — the one projection that is canon, because everyone starts there. Waves 5–7 deliver 708 slivers — 52% of the verse; the throttle modulates rate, never order. Gold bars mark the launch set.
A sliver's substance never changes. How it feels depends entirely on who stands in it — the same monolith is one player's poison and another's homeland. Two intrinsic axes fix the material: Organic ↔ Synthetic from placement (twelve substances at twelve stations, closed cycle — station 11 is adjacent to station 0, matter refined to its synthetic extreme comes back around to growing), and Accreted ↔ Refined from distinct-count — Common is encrusted and layered, Perfect is seamless and unified. Rarity reads as simplicity, not ornament. That inverts the usual convention, and it is ratified deliberately. Affect is then computed from two independent relational scalars — tolerance and kinship:
Kinship is attunement history, not current attunement. Everyone starts at 0479, so Origin sits permanently in every player's field — which is why Origin stays legible forever while ceasing to be home: kinship holds, tolerance drifts, and Origin slides from bucolic into weird as the player settles elsewhere. Familiarity and belonging are different things; home migrates outward with the frontier, and Origin becomes distant rather than forgotten. Accretion is literal: the strata on a character's body are their attunement history — a many-bridged generalist reads more of the verse and looks like a junk heap; a specialist finds most of the verse hostile and is refined to a narrow band. Breadth versus depth, legible at a glance. Hue is not load-bearing: placement drives material grammar, distinct-count drives silhouette, affect drives lighting and atmosphere — colour belongs entirely to player expression. Acceptance test: convert any gameplay-critical frame to greyscale; if the player can no longer read it, the frame is wrong.