All four open ratifications are decided, and the draft is corrected at both
places where it would have misled the agent that reads it next.
The 12-note 5-limit scale is the contiguous lattice block {3^a 5^b | a in
[-1,2], b in [-1,1]}, octave-reduced and assigned in ascending order from the
anchor. The draft called this one "asymmetric" and offered it third; that name
is an artifact of describing it as a 5x3 grid minus three discarded cells.
Generated from its bounds it discards nothing, fills all twelve chromatic
positions exactly once, and states in one sentence -- which is the property
Ruling B exists to get. The name is now banned normatively.
Two of the three candidates fell to computation rather than preference.
"Symmetric scale 2" makes G-D a 40/27 wolf, so a scale the catalog calls
"anchored to C tonic" would have an unusable dominant. And the draft's own
argument for "symmetric scale 1" -- that its D and Bb match C-based
Pythagorean and quarter-comma meantone -- is false: meantone's are 193.157
and 1006.843 cents, each half a syntonic comma away. It can only hold of
circle-of-fifths position, and even then covers 2 notes of 12 while the other
ten shift a comma between systems. Struck at its site and at the head of the
file, with the numbers, so it cannot be quietly reinstated.
The block also wins on merit: 23 pure intervals of 36 against 22 and 21, and
it gains pure Eb major and G minor for the price of Bb minor.
The three ji-static identifiers are one construction at three anchors -- which
the catalog already said, in the same phrase three times, more strongly than
the vallotti/young-ii naming parallel the draft reasoned from.
ji-adaptive-5limit version 1 is the key-anchored static scale, identity
"default-v1" with the version inside the string. Checking the prerequisite
turned up why that is affordable: KeyContext is not defined anywhere and the
spec puts its completion out of scope, but KeySignature { fifths } already
exists, is canonical, and is encoded -- so the anchor is (7 * fifths) mod 12
today, mode-blind exactly as ruled. C, G and D are fifths 0, 1 and 2; the
catalog's three anchors were never arbitrary.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
`req:tuning:builtin-tuning-catalog` MUST-resolves 20 tuning identifiers while
specifying only the six `tet-*`. Ruling B keeps all 20 and pins them by
**construction** rather than by cents table, because published sources agree on
constructions and differ mainly in rounding. This lands the draft of the other
14 as a **non-normative** artifact for review; nothing enters `core_spec.tex`
until the four open ratifications are decided.
Drafting rather than editing was deliberate, and it earned its keep. An agent
writing Werckmeister III from memory into a normative document is the
`NOTEHEAD_ANCHORS` failure exactly: hand-written, authoritative-looking,
unverifiable in-tree, and load-bearing.
**The first draft was well-sourced and wrong.** Ten entries, ten live citations,
zero recalled, zero unknown -- and three of them could not exist. A twelve-fifth
circle must absorb exactly one Pythagorean comma (23.4600 c). Checked:
kirnberger-ii 2 x 1/2 syntonic, "remaining ten pure" -> 21.5063 c
kirnberger-iii 4 x 1/4 syntonic, "remaining eight pure" -> 21.5063 c
Both short by 1.9537 c -- exactly one schisma, the signature of a dropped
schisma-tempered fifth. The draft said of the first, in terms, "This closes the
circle." It does not. And `werckmeister-iii` carried the syntonic-vs-Pythagorean
comma forward as a "genuinely ambiguous" hedge into its summary table, when
closure settles it: only the Pythagorean reading closes, and a well temperament
that does not close is not one.
The supporting reasoning had been *correct* -- the derivation that C-E, G-B and
D-F# come out pure is right. The error was inferring from it that every
remaining fifth is pure. Making those thirds just does not discharge the full
comma. That is precisely the failure a citation count cannot detect and an
invariant catches in one line.
**Corrected and re-verified by recomputation, not by re-reading.** All six
circulating temperaments now close to exactly 23.4600 c; all four
non-circulating residues reproduce independently (`pythagorean` 678.495 c;
meantone 1/4, 1/5, 1/6 wolves 737.637 / 725.809 / 717.923 c). The schisma fifth
is sourced at F#-Db, and Kirnberger III's four fifths are now a direct quotation
rather than a reconstruction.
**The best result is a disagreement.** Recomputing Kirnberger II's thirds from
its own chain, the agent found its new source's prose claims four pure thirds
where the construction yields three -- F-A comes out at 397.067 c, not 386.314.
It reported the conflict instead of deferring to the source or dropping it.
Independently confirmed to the cent.
The count is still 10 verified / 0 recalled / 0 unknown, but `verified` now
means sourced **and** invariant-checked. The number did not move; its meaning
did. A stable metric hiding a changed reality is this session's recurring lesson
in another costume.
`CONTRACT_P13S6_TEMPERAMENTS.md` gains a permanent section, "Check the
arithmetic, not just the source", stating the general principle first so it
transfers: a citation proves the source said it, not that it is right, that you
read it correctly, or that you transcribed it completely. Five obligations --
closure; closure as a decision procedure for vague sources; non-circulating
temperaments must *not* close, with the wolf computed; twelve fifths each
exactly once; recompute every derived claim and treat disagreement as a finding.
Plus the guard that matters most: never adjust a construction to make the
arithmetic work and present it as sourced -- that manufactures a temperament
nobody published. An unresolved entry is the correct output.
Still open, surfaced not decided: the three `ji-static-5limit-*` scales and
`ji-adaptive-5limit`'s algorithm, the latter recommended to follow
`req:pitch:spelling-algorithm`'s versioned-identifier pattern.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Levi Neuwirth