epiphany/spec/CONTRACT_P13S6_TEMPERAMENTS.md

Contract: P13-S6 — drafting the built-in tuning constructions for review

Repo root /home/jeans/Repos/active/epiphany. The plan is spec/PLAN_PUSH4B_TUNING.md, Ruling B. Read it before starting.

What this is, and why it is a draft

req:tuning:builtin-tuning-catalog makes all 20 built-in tuning identifiers MUST-resolve with normative semantics. Only the six tet-* are actually specified — structurally, by TuningResolution::EqualTemperament. The other 14 are bare names (P13-S6). Ruling B keeps all 20 and pins them by construction rather than by cents table, because published sources agree on the constructions and differ mainly in how they round cents.

You are producing a reviewable draft, not a specification edit. Write spec/DRAFT_P13S6_TEMPERAMENTS.md. Do not edit any .tex file. Promotion into core_spec.tex happens only after human review.

The reason is specific and this project has paid for it: NOTEHEAD_ANCHORS was a table of hand-written glyph metrics that looked authoritative, was wrong in two independent ways, and survived for passes because nothing consumed it. A tuning construction written from memory into a normative document is the same artifact. Confidence is not a source.

The deliverable

For each of the 14 unspecified systems, one entry:

• Identifier exactly as the catalog spells it.
• Construction — the generative rule, stated so an implementer can compute it without further research. For a circulating temperament that means: which fifths are tempered, by what fraction of which comma (syntonic vs Pythagorean — say which; they are different and confusing them is the classic error), and which remain pure. For a JI scale it means the ratio for each of the twelve degrees.
• Wolf / chain placement where the construction does not determine it — pythagorean in particular is a pure 3:2 chain whose twelve-note selection is a choice, and the choice must be stated, not assumed.
• Source — a specific, checkable citation: author, work, date, and where the construction appears. "Common knowledge" is not a source.
• Confidence, explicitly: verified (you can cite it precisely), recalled (you believe it but cannot cite it precisely), or unknown.

A recalled or unknown entry is a useful result and an honest one. A fabricated citation is the worst possible output of this task — worse than leaving the row blank — because it defeats the review that exists to catch it. If you cannot source something, say so in that entry and move on.

The 14: pythagorean; meantone-1/4-comma, meantone-1/6-comma, meantone-1/5-comma; werckmeister-iii, werckmeister-iv; vallotti; kirnberger-ii, kirnberger-iii; young-ii; ji-static-5limit-C, ji-static-5limit-G, ji-static-5limit-D; ji-adaptive-5limit.

Four are open ratifications — surface, do not decide

The plan marks these as needing a human decision. Present the options and their trade-offs; do not pick.

• ji-static-5limit-C / -G / -D. Which 12-note 5-limit scale — the comma choices for the chromatic degrees are genuinely unsettled and more than one selection is defensible. Lay out the main candidates and what each optimizes. Note whether the three differ only by transposition of one scale or are independently chosen.
• ji-adaptive-5limit. Needs a real algorithm, constrained by req:tuning:adaptive-tuning-purity — read that requirement first and state what it permits. The in-house pattern for this shape is req:pitch:spelling-algorithm, which pins SpellingAlgorithmId "default" at version 1 to a named algorithm and errors on any other identifier; recommend the analogous versioned AdaptiveTuningFunctionId, but do not invent the algorithm's content as though it were settled.

Cents tables are derived, never primary

If you include cents, mark them derived from the construction and give the derivation. Do not copy a cents table from a source and present it as the definition — that reintroduces exactly the rounding variance Ruling B exists to avoid. Exact-ratio form is preferred wherever a construction yields rationals; say plainly where it does not (quarter-comma meantone's fifth is 5^{1/4}, and several others are irrational by construction).

Note for context, so you do not over-engineer precision: resolved frequencies never enter canonical bytes (req:determinism:canonical-floating-point lists tuning among the floating-point contexts and bars floating point from anything needing exact identity), and acoustic comparison is governed by ToleranceClass::AcousticCents in epiphany-determinism.

Check the arithmetic, not just the source

A citation proves the source said it. It does not prove it is right, that you read it correctly, or that you transcribed it completely. Sourcing catches fabrication; only an invariant catches a real source misapplied. This section was added after a first draft produced two impossible temperaments and one false ambiguity, every one of them properly cited.

Where the data has an internal invariant, compute it and show the computation in the entry. For tuning constructions the invariants are:

1. Closure. A circulating (wolf-free, twelve-note) temperament's twelve fifths MUST absorb exactly one Pythagorean comma — 531441/524288, 23.4600 cents. Narrowings count positive, widenings negative. State the sum. A construction that does not close is not a well temperament, and if your sum lands 1.9537 cents short you have dropped a schisma-tempered fifth — the difference between the Pythagorean and syntonic commas, and the single most commonly omitted element of these constructions.
2. Closure is also a decision procedure. Where a source is vague about which comma a fraction refers to, closure usually settles it: try both and report which one closes. Do not carry an ambiguity forward that arithmetic resolves — a normative hedge on an answerable question is worse than either answer.
3. Non-circulating temperaments must NOT close. Meantone and Pythagorean have a wolf by construction. Compute the wolf's size — it is the residue — and state it. "Does not close" is a positive claim here, not a gap.
4. Twelve fifths, each exactly once. Enumerate the full circle and classify every fifth as narrowed, widened, or pure. A construction naming eleven or thirteen is wrong on its face; adjacent fifths sharing a note are two distinct fifths.
5. Recompute every derived claim. If a source says a third is pure, derive it from your own chain and confirm. If your derivation disagrees with the source, that is a finding — report it, do not quietly follow either one.

If an invariant fails, say so in the entry and mark it unresolved. Do not adjust the construction to make the arithmetic work and present the result as sourced — that manufactures a temperament nobody published.

Do not

• Edit any .tex, any Rust file, or any other agent's file. Your entire output is one new Markdown file.
• Take values from anywhere in this repository — there are none, and anything you think you found is something else.
• Present a construction you cannot source as though you could.
• Decide any of the four open ratifications.

Report

State how many of the 14 you marked verified, how many recalled, how many unknown. That ratio is the single most useful number in your report, and a low verified count is a finding about the task, not a failure of it.