The ten temperaments tranche 2 left Deferred now resolve, via
TuningResolution::Function with reserved built-in ids. Each is a
[FifthTempering; 12] descriptor over the fixed circle of fifths -- Pure,
NarrowPythagorean(f), WidePythagorean(f), NarrowSyntonic(f), NarrowSchisma, or
Residual (the closing wolf, computed as whatever brings the chain to seven
octaves). One walk places the notes and derives their ratios; the same code path
yields the wolf for the four non-circulating temperaments and full closure for
the six circulating ones. Comma sizes are 1200*log2(exact ratio), never
hardcoded cents. Still no Codec, no wire movement -- canonical bytes unmoved.
The closure invariant is recomputed in code, which is the whole reason this was
its own pass. Six circulating temperaments sum to one Pythagorean comma
(23.460010c); four non-circulating wolves match the ratified residues
(pythagorean 678.495, meantone 737.637/725.809/717.923) within 0.001c.
Verified independently of the agent. Through the public resolver, pythagorean,
kirnberger-ii and kirnberger-iii reproduce the spec's derived-cents tables to
0.01c -- and the Kirnberger tables only close WITH the schisma fifth, so the
match is end-to-end proof the schisma is present and the S6 trap avoided. The
kirnberger-ii/iii D discriminator holds (203.910 vs 193.157), meantone-1/4's
major third is the just 5/4 (386.314c), werckmeister-iii's C# is distinct from
tet-12's. And the closure test is non-vacuous: dropping kirnberger-ii's schisma
fifth myself made it fail -- the S6 defect reproduced as a mutation and caught.
TuningParameters is a documented zero-field marker (no built-in parameterizes
Function, its schema is unspecified); an unknown TuningFunctionId fails closed.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Levi Neuwirth
c68f317e47