The two-digit numbers as the discrete torus (ℤ/10)². Reversal is the reflection (a,b)→(b,a); folding by that reflection yields the dyad orbifold — a Möbius strip whose single edge is the palindromes. Each emirp pair becomes one point.
Bulger's toroidal view of the neo-Riemannian Tonnetz wraps the twelve pitch classes onto a torus whose entire rhetoric is homogeneity: transposition is a rigid rotation, every triad-triangle is equivalent, no point of the surface is privileged. That honesty is exactly right for tonal space, where the structure of interest is the group action itself.
The digit torus is the opposite instrument. The lattice is (ℤ/10)², and the arithmetic lives in the breaking of the torus's symmetry: the live block on the units {1,3,7,9}, the emirp-free cells of digit sum divisible by three, the sum-9 band hosting the reverse-and-subtract attractor (09→81→63→27→45), and the two dead edges killed by multiples of 13 and 31. Carrying and borrowing are the seam-crossings a flat table cannot show.
Where the Tonnetz display stops at the torus, this one passes to the quotient by the reversal reflection — the construction of Tymoczko's two-note chord space, with 10 in place of 12. The result is a Möbius strip: its single boundary edge is the ten palindromes (the reflection's fixed points), its core circle is the five difference-5 pairs, and each digit-sum pencil collapses to a single transversal fibre. Each mirrored pair — 13·31, 17·71, 37·73, 79·97 — becomes one point carrying the memory of its twoness. The bridge between incommensurables is not a span between two places but a change of space in which the two were one all along; and non-orientability is the model's sharpest statement about binary framing — "a number" and "its reversal" can be told apart locally but not labelled globally.
The fold is sounded: each pair enters as a beating dyad and resolves to a unison. The gap button plays the pair-differences 18 : 36 : 54 — forced to be 3-smooth by the digit confinement — as the octave, fifth and twelfth they arithmetically are.
Grading: the topology and the identities are forced; base ten is notational (base-20 gaps are multiples of 38, and not smooth); any strategic reading is imported.