Push 4b tranche 2b: the ten historical temperaments resolve
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>
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@ -874,3 +874,109 @@ something about them.
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**Requirement counts did not move again.** No `.tex` file was touched, no
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**Requirement counts did not move again.** No `.tex` file was touched, no
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requirement added; the 212/282/282 counts stay put.
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requirement added; the 212/282/282 counts stay put.
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## Push 4b tranche 2b: the ten historical temperaments resolve, built from their constructions
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`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`. The ten `TuningCatalogEntry::Deferred`
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entries tranche 2 left behind now resolve, via the specification's own third
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`TuningResolution` variant, `Function`. Same in-memory discipline as
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tranches 1 and 2: no `Codec`, no wire movement, canonical bytes untouched —
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only `tuning.rs`, `pitch.rs` (one new `catalog_id!`), and `lib.rs`
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(re-exports) changed.
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**`TuningResolution::Function { function: TuningFunctionId, parameters:
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TuningParameters }` lands, plus the `TuningFunctionId` catalog newtype**
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(`pitch.rs`, beside `TuningSystemId`). The ten temperaments are reserved
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built-in ids spelled identically to their `TuningSystemId` (`"pythagorean"`,
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`"werckmeister-iii"`, …); an id with no reserved built-in has no registry
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to fall back on, so `coordinate_ratio`'s `Function` arm returns `None` for
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it — the extension point fails closed, never a guessed frequency.
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`frequency_for_position`'s `divisions` match gains a `Function` arm too:
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since the variant carries no division count of its own, divisions comes
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from the *pitch space*'s chromatic cardinality instead (a new private
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`chromatic_cardinality(&PositionStructure) -> Option<u32>`, 12 for
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`cmn-12`), never from the resolution.
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**`TuningParameters` is a deliberate zero-field marker, exactly like
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`SpellingParameters`.** No built-in parameterizes a `Function` resolution —
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each of the ten temperaments is fixed entirely by its `TuningFunctionId`
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alone — and `core_spec.tex` never gives this type's shape (it calls the
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sibling `AdaptiveTuningParameters` "likewise undefined" for the identical
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reason, `:4083`). The type carries no state and exists only so
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`TuningResolution::Function`'s field list matches the specification's own
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listing.
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**The construction, not the cents table, is what's built.** Each temperament
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is represented as a `Construction = [FifthTempering; 12]`: one
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`FifthTempering` tag per fifth of the fixed circle-of-fifths chain
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`C–G–D–A–E–B–F♯–C♯–G♯–E♭–B♭–F–(C)` (`Pure`, `NarrowPythagorean(fraction)`,
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`WidePythagorean(fraction)`, `NarrowSyntonic(fraction)`, `NarrowSchisma`, or
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— for the four non-circulating temperaments' one closing wolf — `Residual`,
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whose cents are computed as whatever value brings the other eleven arcs'
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sum to exactly seven octaves, never given a fraction of its own). One shared
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`walk_temperament` function walks any construction forward from C,
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accumulating raw (unreduced) cents, then reduces each of the twelve chain
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notes' cumulative cents mod 1200 into its `cmn-12` chromatic degree's ratio.
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The same walk produces the wolf (for the four non-circulating constructions)
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and the full twelve-note closure (for the six circulating ones) without
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separate code paths — reducing mod 1200 is what lets the wolf simply fall
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out where the chain doesn't close, exactly as `core_spec.tex`'s own framing
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puts it ("any assignment of twelve distinct pitch classes must sum to seven
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octaves by construction"). The four comma sizes (`pure_fifth_cents`,
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`pythagorean_comma_cents`, `syntonic_comma_cents`, `schisma_cents`) are each
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`1200·log2(exact ratio)` in `f64` — never a hardcoded rounded cents
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constant — and the schisma is computed independently from `32805/32768`
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rather than derived as `pythagorean − syntonic`, so the closure tests prove
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that identity rather than assume it.
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**The closure invariant, recomputed in code, is what the tests assert.**
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For the six circulating temperaments (`werckmeister-iii`/`-iv`, `vallotti`,
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`kirnberger-ii`/`-iii`, `young-ii`), a test recomputes `12·pure_fifth_cents −
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raw_closure_cents` (the sum of the twelve fifths' deviations from pure) and
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asserts it equals `pythagorean_comma_cents()` (≈23.4600 c) within `1e-9`,
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plus a per-fifth bound (`<15 c` deviation from pure) proving none of the
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twelve is secretly a wolf. Computed values: werckmeister-iii, -iv, vallotti,
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kirnberger-ii, kirnberger-iii, and young-ii each summed to `23.460010…` c
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against the ratified `23.4600` c. For the four non-circulating ones
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(`pythagorean`, the three `meantone-*`), the residual wolf (chain arc 8,
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`G♯–E♭`) is asserted against the spec's ratified value: pythagorean
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678.495 c, computed 678.495 c; meantone-1/4 737.637 c, computed 737.637 c;
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meantone-1/5 725.809 c, computed 725.809 c; meantone-1/6 717.923 c,
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computed 717.923 c — all within `0.001` c.
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**The Kirnberger schisma-fifth trap and the Pythagorean-vs-syntonic comma
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trap were both reproduced as mutations, and both caught.** Dropping
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`kirnberger-ii`'s closing schisma fifth (changing its `F♯–C♯` arc from
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`NarrowSchisma` to `Pure`) landed the closure at 21.506 c — one schisma
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(1.954 c) short of 23.460 c — and only the closure test died. Changing
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`werckmeister-iii`'s comma from Pythagorean to syntonic (`NarrowPythagorean`
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→ `NarrowSyntonic` at the same fraction) landed the closure at 21.506 c
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(`4 × ¼ syntonic`) instead of 23.460 c, exactly the defect the contract
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predicted, and again only the closure test died. Both were reversed by
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undoing the exact substitution, never `git checkout`.
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**Discriminator and resolver-level tests were each mutation-verified too**
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(construction- or dispatch-level mutations, run to red, then reversed):
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swapping the `E`/`B` chromatic-degree slots in the shared
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`CHAIN_CHROMATIC_DEGREE` table killed both `pythagorean`'s E/F♯ test and the
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`meantone-1/4-comma` just-third test; doubling `kirnberger-iii`'s comma
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fraction to match `kirnberger-ii`'s killed the D-value discriminator (and,
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incidentally, the closure test, since the doubled fraction no longer sums to
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one Pythagorean comma either); moving `pythagorean`'s residual arc from
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index 8 to index 7 killed only the non-circulating wolf test; making
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`temperament_ratios`'s wildcard arm return `pythagorean`'s construction
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instead of `None` killed only the fail-closed test; typo-ing the
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`"vallotti"` match arm killed only the "all ten resolve" test; and making
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the resolver's `Function` arm ignore `function` and fall back to 12-TET
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killed both the `werckmeister-iii` C♯-distinctness test and the fail-closed
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test (the latter because an unknown id now also produced a ratio instead of
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`None`). Every mutation was reversed by undoing its exact substitution.
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**Zero golden or digest movement**, confirmed by the full gate: `cargo fmt
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--all --check`, `cargo clippy --workspace --all-targets` (0 warnings),
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`cargo test --workspace` (0 failed across every crate), `RUSTDOCFLAGS="-D
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warnings" cargo doc --workspace --no-deps` (0 warnings, after two
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intra-doc links to the private `temperament_ratios`/`coordinate_ratio`
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were de-linked to plain code spans), `conformance_suite` (8/8), and
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`requirement_labels` (6 passed, counts unchanged at 212/282/282) all pass.
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No `.tex` file was touched and no requirement was added.
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@ -103,7 +103,7 @@ pub use pitch::{
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SpellingDirective, SpellingNominal, SpellingPrecedence, SpellingRenderHints, SpellingRule,
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SpellingDirective, SpellingNominal, SpellingPrecedence, SpellingRenderHints, SpellingRule,
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SpellingRuleSetId, SpellingScope, SpellingSource, SpellingSourceKind, StaffGroupKindRegistryId,
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SpellingRuleSetId, SpellingScope, SpellingSource, SpellingSourceKind, StaffGroupKindRegistryId,
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TieClassRegistryId, TransposeRefusal, TranspositionInterval, TranspositionRegistryId,
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TieClassRegistryId, TransposeRefusal, TranspositionInterval, TranspositionRegistryId,
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TuningReference, TuningSystemId, VoiceSelector,
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TuningFunctionId, TuningReference, TuningSystemId, VoiceSelector,
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};
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};
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pub use pitch_space::{
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pub use pitch_space::{
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@ -151,8 +151,8 @@ pub use tempo::{
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pub use tuning::{
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pub use tuning::{
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built_in_tuning_system, frequency_for_position, resolve_pitch_frequency, resolve_tuning_scope,
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built_in_tuning_system, frequency_for_position, resolve_pitch_frequency, resolve_tuning_scope,
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PositionRatio, ResolvedTuning, TuningCatalogEntry, TuningOverride, TuningResolution,
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PositionRatio, ResolvedTuning, TuningCatalogEntry, TuningOverride, TuningParameters,
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TuningResolutionError, TuningScope, TuningSystem,
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TuningResolution, TuningResolutionError, TuningScope, TuningSystem,
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};
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};
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pub use codec::{CanonicalValue, ScoreDecodeError};
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pub use codec::{CanonicalValue, ScoreDecodeError};
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/// include `tet-12`, `werckmeister-iii`.
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/// include `tet-12`, `werckmeister-iii`.
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TuningSystemId
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TuningSystemId
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);
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);
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catalog_id!(
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/// Identifies a registered tuning function consumed by
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/// [`crate::tuning::TuningResolution::Function`] (Chapter 4
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/// §"Tuning Resolution", `core_spec.tex:3318-3324`: "Procedural
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/// definition: a registered tuning function that computes frequencies
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/// from a reference. Historical temperaments ... live here."). The ten
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/// historical temperaments (Push 4b tranche 2b) are reserved built-in
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/// ids — `"pythagorean"`, `"werckmeister-iii"`, and so on — spelled
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/// identically to their [`TuningSystemId`], since each temperament's
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/// catalog entry and its tuning function share one identifier. An id
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/// with no reserved built-in has no registry to resolve against
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/// (`Function` is an extension point this tranche does not build a
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/// registry for) and fails closed.
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TuningFunctionId
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);
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catalog_id!(
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catalog_id!(
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/// Identifies an accidental registry (Chapter 4 §"Accidental Registries").
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/// Identifies an accidental registry (Chapter 4 §"Accidental Registries").
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AccidentalRegistryId
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AccidentalRegistryId
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//! codec in `codec.rs`), so they stay free to change once a later tranche
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//! codec in `codec.rs`), so they stay free to change once a later tranche
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//! discovers they are wrong.
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//! discovers they are wrong.
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//!
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//!
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//! ## What this tranche resolves, and what it does not
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//! ## What resolves, and what still does not
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//!
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//!
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//! [`TuningResolution`] is a **six**-variant enum in the specification
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//! [`TuningResolution`] is a **six**-variant enum in the specification
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//! (`core_spec.tex:3309`); this tranche defines only the two variants the
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//! (`core_spec.tex:3309`); this module defines three —
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//! built-in catalog below actually constructs —
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//! [`TuningResolution::EqualTemperament`], [`TuningResolution::PerPositionRatios`],
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//! [`TuningResolution::EqualTemperament`] and
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//! and, since Push 4b tranche 2b, [`TuningResolution::Function`] (plus
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//! [`TuningResolution::PerPositionRatios`] — plus [`PositionRatio`]. The
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//! [`PositionRatio`] and the marker [`TuningParameters`]). The other three are
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//! other four are transcribed only when a built-in needs them, so their
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//! transcribed only when a built-in needs them, so their unconstructed payload
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//! unconstructed payload subtrees (`TuningParameters`, `ImportedTuningData`,
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//! subtrees (`ImportedTuningData`, `AdaptiveTuningParameters`, …) never become
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//! `AdaptiveTuningParameters`, …) never become an unconsumed type surface
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//! an unconsumed type surface (the `NOTEHEAD_ANCHORS` failure): `Adaptive`
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//! (the `NOTEHEAD_ANCHORS` failure): `Function` waits on Push 4b tranche 2b,
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//! waits on `HarmonicContext`, which does not exist in Rust and whose
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//! which re-derives the ten historical temperaments from their ratified
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//! completion `core_spec.tex` puts out of scope; `Overlay` and `Imported` wait
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//! constructions; `Adaptive` waits on `HarmonicContext`, which does not exist
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//! on a built-in that needs a split-accidental keyboard or an imported
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//! in Rust and whose completion `core_spec.tex` puts out of scope; `Overlay`
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//! `.scl`/MTS tuning respectively — nothing in the twenty-item catalog
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//! and `Imported` wait on a built-in that needs a split-accidental keyboard
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//! constructs either.
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//! or an imported `.scl`/MTS tuning respectively — nothing in the twenty-item
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//! catalog constructs either.
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//!
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//!
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//! [`built_in_tuning_system`] resolves **nine** of the twenty catalog
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//! [`built_in_tuning_system`] resolves **nineteen** of the twenty catalog
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//! identifiers (`req:tuning:builtin-tuning-catalog`): the six `tet-*` equal
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//! identifiers (`req:tuning:builtin-tuning-catalog`): the six `tet-*` equal
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//! temperaments and the three `ji-static-5limit-*` just-intonation systems.
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//! temperaments, the three `ji-static-5limit-*` just-intonation systems, and,
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//! The ten historical temperaments and `ji-adaptive-5limit` are real catalog
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//! since tranche 2b, the ten historical temperaments (`pythagorean`, the three
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//! entries whose resolution this tranche defers
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//! `meantone-*`, `werckmeister-iii`/`-iv`, `vallotti`, `kirnberger-ii`/`-iii`,
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//! ([`TuningCatalogEntry::Deferred`]) — never a guessed frequency.
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//! `young-ii`) — each built from its ratified fifth-tempering construction
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//! (`core_spec.tex` §"Temperament Constructions", `:3696`-`4011`) by
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//! `temperament_ratios`, never from a pasted cents table. Only
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//! `ji-adaptive-5limit` is still a real catalog entry whose resolution this
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//! module defers ([`TuningCatalogEntry::Deferred`]) — never a guessed
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//! frequency — because it needs `HarmonicContext`, which does not exist in
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//! Rust.
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//!
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//!
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//! ## The compatibility check, narrowed the same way tranche 1 narrowed it
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//! ## The compatibility check, narrowed the same way tranche 1 narrowed it
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//!
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//!
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use crate::graph::{Score, ScoreTuningContext};
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use crate::graph::{Score, ScoreTuningContext};
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use crate::ids::{RegionId, StaffId, VoiceId};
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use crate::ids::{RegionId, StaffId, VoiceId};
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use crate::pitch::{
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use crate::pitch::{
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AcousticRealization, Pitch, PitchSpaceId, PitchSpacePosition, ReferencePitch, TuningReference,
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AcousticRealization, Pitch, PitchSpaceId, PitchSpacePosition, ReferencePitch, TuningFunctionId,
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TuningSystemId, VoiceSelector,
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TuningReference, TuningSystemId, VoiceSelector,
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};
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};
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use crate::pitch_space::{built_in_position_structure, JiRatio, PositionStructure};
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use crate::pitch_space::{built_in_position_structure, JiRatio, PositionStructure};
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use crate::time::TimeAnchor;
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use crate::time::TimeAnchor;
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pub ratio: JiRatio,
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pub ratio: JiRatio,
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}
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}
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/// Placeholder for [`TuningResolution::Function`]'s parameter schema
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/// (`core_spec.tex:3318-3324`). The specification never gives this type's
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/// shape — Chapter 4's own forward-reference list (`:4083`) singles out the
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/// sibling `AdaptiveTuningParameters` as "likewise undefined," for the same
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/// reason: no built-in in the twenty-item catalog parameterizes a `Function`
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/// resolution, since each of the ten historical temperaments this module
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/// builds is fixed entirely by its [`TuningFunctionId`] alone. The same
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/// discipline as [`SpellingParameters`](crate::pitch_space::SpellingParameters),
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/// one level down: a documented zero-field marker so
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/// `TuningResolution::Function`'s field list matches the specification's own
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/// listing, carrying no state and inventing no schema.
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#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug, Default)]
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pub struct TuningParameters;
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/// How a tuning system resolves pitch-space positions to frequencies
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/// How a tuning system resolves pitch-space positions to frequencies
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/// (`core_spec.tex:3309-3348`). **Deliberately partial**: the specification
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/// (`core_spec.tex:3309-3348`). **Deliberately partial**: the specification
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/// names six variants; this tranche defines the two the built-in catalog
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/// names six variants; this module defines three. See the module doc for
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/// constructs. See the module doc for which tranche completes each of the
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/// which tranche completes each of the other three.
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/// other four.
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#[derive(Clone, PartialEq, Eq, Debug)]
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#[derive(Clone, PartialEq, Eq, Debug)]
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pub enum TuningResolution {
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pub enum TuningResolution {
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/// N-tone equal temperament: each step is the Nth root of the octave
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/// N-tone equal temperament: each step is the Nth root of the octave
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/// Explicit per-position ratios, each relative to the reference
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/// Explicit per-position ratios, each relative to the reference
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/// position.
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/// position.
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PerPositionRatios(Vec<PositionRatio>),
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PerPositionRatios(Vec<PositionRatio>),
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/// Procedural definition: a registered tuning function that computes
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/// frequencies from a reference (`core_spec.tex:3318-3324`: "Historical
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/// temperaments (Werckmeister, Vallotti, meantone variants) live here").
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||||||
|
/// The ten historical temperaments are reserved built-in
|
||||||
|
/// [`TuningFunctionId`]s, each re-derived from its ratified
|
||||||
|
/// fifth-tempering construction (`core_spec.tex` §"Temperament
|
||||||
|
/// Constructions", `:3696`-`4011`) by `temperament_ratios` rather than
|
||||||
|
/// transcribed from a cents table. No parameter schema exists yet
|
||||||
|
/// ([`TuningParameters`] is a documented marker); an unreserved
|
||||||
|
/// `TuningFunctionId` has no registry to resolve against and fails
|
||||||
|
/// closed (`coordinate_ratio` returns `None`) — `Function` is an
|
||||||
|
/// extension point, not a registry this module builds.
|
||||||
|
Function {
|
||||||
|
function: TuningFunctionId,
|
||||||
|
parameters: TuningParameters,
|
||||||
|
},
|
||||||
}
|
}
|
||||||
|
|
||||||
/// A tuning system: a map from pitch-space positions to frequencies, given a
|
/// A tuning system: a map from pitch-space positions to frequencies, given a
|
||||||
|
|
@ -163,7 +196,7 @@ pub enum TuningCatalogEntry {
|
||||||
/// Looks up a built-in [`TuningSystem`] (Chapter 4 §"Built-in Catalog",
|
/// Looks up a built-in [`TuningSystem`] (Chapter 4 §"Built-in Catalog",
|
||||||
/// `core_spec.tex:3656-3694`, `req:tuning:builtin-tuning-catalog`).
|
/// `core_spec.tex:3656-3694`, `req:tuning:builtin-tuning-catalog`).
|
||||||
///
|
///
|
||||||
/// Nine of the twenty resolve this tranche:
|
/// Nineteen of the twenty resolve:
|
||||||
///
|
///
|
||||||
/// * the six `tet-*` — [`TuningResolution::EqualTemperament`] from the
|
/// * the six `tet-*` — [`TuningResolution::EqualTemperament`] from the
|
||||||
/// identifier's divisions. `tet-12` pairs with `cmn-12` (the default
|
/// identifier's divisions. `tet-12` pairs with `cmn-12` (the default
|
||||||
|
|
@ -175,16 +208,18 @@ pub enum TuningCatalogEntry {
|
||||||
/// computed by `ji_static_5limit_ratios` from the lattice block
|
/// computed by `ji_static_5limit_ratios` from the lattice block
|
||||||
/// (`req:tuning:ji-static-construction`), over `cmn-12`'s twelve chromatic
|
/// (`req:tuning:ji-static-construction`), over `cmn-12`'s twelve chromatic
|
||||||
/// positions (`core_spec.tex:4019-4021`: "assigned in ascending order to
|
/// positions (`core_spec.tex:4019-4021`: "assigned in ascending order to
|
||||||
/// the twelve chromatic positions of `cmn-12`").
|
/// the twelve chromatic positions of `cmn-12`");
|
||||||
///
|
|
||||||
/// The other eleven are real catalog entries whose resolution is deferred,
|
|
||||||
/// not guessed ([`TuningCatalogEntry::Deferred`]):
|
|
||||||
///
|
|
||||||
/// * the ten historical temperaments (`pythagorean`, three `meantone-*`,
|
/// * the ten historical temperaments (`pythagorean`, three `meantone-*`,
|
||||||
/// `werckmeister-iii`/`-iv`, `vallotti`, `kirnberger-ii`/`-iii`,
|
/// `werckmeister-iii`/`-iv`, `vallotti`, `kirnberger-ii`/`-iii`,
|
||||||
/// `young-ii`) — Push 4b tranche 2b re-derives each construction's
|
/// `young-ii`, Push 4b tranche 2b) — [`TuningResolution::Function`], each
|
||||||
/// twelve-fifth closure in code (see `spec/CONTRACT_PUSH4B_RESOLVER.md`'s
|
/// built by `temperament_ratios` from its ratified fifth-tempering
|
||||||
/// closing section);
|
/// construction (`core_spec.tex` §"Temperament Constructions",
|
||||||
|
/// `:3696`-`4011`), over `cmn-12`'s twelve chromatic positions exactly as
|
||||||
|
/// the static-JI systems are.
|
||||||
|
///
|
||||||
|
/// The remaining one is a real catalog entry whose resolution is deferred,
|
||||||
|
/// not guessed ([`TuningCatalogEntry::Deferred`]):
|
||||||
|
///
|
||||||
/// * `ji-adaptive-5limit` — needs `HarmonicContext`
|
/// * `ji-adaptive-5limit` — needs `HarmonicContext`
|
||||||
/// (`req:tuning:adaptive-default-version`), which does not exist in Rust.
|
/// (`req:tuning:adaptive-default-version`), which does not exist in Rust.
|
||||||
///
|
///
|
||||||
|
|
@ -223,8 +258,23 @@ pub fn built_in_tuning_system(id: &TuningSystemId) -> Option<TuningCatalogEntry>
|
||||||
)),
|
)),
|
||||||
})
|
})
|
||||||
}
|
}
|
||||||
const DEFERRED_TEMPERAMENT: &str = "historical temperament; construction re-derivation is \
|
/// A historical temperament's catalog entry: [`TuningResolution::Function`]
|
||||||
Push 4b tranche 2b (spec/CONTRACT_PUSH4B_RESOLVER.md, closing section)";
|
/// naming `name` as its own [`TuningFunctionId`] (item 3 of
|
||||||
|
/// `spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`: "`pitch_space` = `cmn-12`").
|
||||||
|
/// `desc` is transcribed from the built-in catalog table
|
||||||
|
/// (`core_spec.tex:3669-3679`).
|
||||||
|
fn temperament(name: &'static str, desc: &'static str) -> TuningCatalogEntry {
|
||||||
|
TuningCatalogEntry::Resolved(TuningSystem {
|
||||||
|
id: TuningSystemId::new(name),
|
||||||
|
name: name.to_owned(),
|
||||||
|
pitch_space: PitchSpaceId::new("cmn-12"),
|
||||||
|
resolution: TuningResolution::Function {
|
||||||
|
function: TuningFunctionId::new(name),
|
||||||
|
parameters: TuningParameters,
|
||||||
|
},
|
||||||
|
description: Some(desc.to_owned()),
|
||||||
|
})
|
||||||
|
}
|
||||||
const DEFERRED_ADAPTIVE: &str =
|
const DEFERRED_ADAPTIVE: &str =
|
||||||
"adaptive tuning needs HarmonicContext, which does not exist in Rust (out of scope this tranche)";
|
"adaptive tuning needs HarmonicContext, which does not exist in Rust (out of scope this tranche)";
|
||||||
match id.as_str() {
|
match id.as_str() {
|
||||||
|
|
@ -242,9 +292,37 @@ pub fn built_in_tuning_system(id: &TuningSystemId) -> Option<TuningCatalogEntry>
|
||||||
"ji-static-5limit-C" => Some(ji_static("ji-static-5limit-C", 0, "C")),
|
"ji-static-5limit-C" => Some(ji_static("ji-static-5limit-C", 0, "C")),
|
||||||
"ji-static-5limit-G" => Some(ji_static("ji-static-5limit-G", 7, "G")),
|
"ji-static-5limit-G" => Some(ji_static("ji-static-5limit-G", 7, "G")),
|
||||||
"ji-static-5limit-D" => Some(ji_static("ji-static-5limit-D", 2, "D")),
|
"ji-static-5limit-D" => Some(ji_static("ji-static-5limit-D", 2, "D")),
|
||||||
"pythagorean" | "meantone-1/4-comma" | "meantone-1/5-comma" | "meantone-1/6-comma"
|
"pythagorean" => Some(temperament(
|
||||||
| "werckmeister-iii" | "werckmeister-iv" | "vallotti" | "kirnberger-ii"
|
"pythagorean",
|
||||||
| "kirnberger-iii" | "young-ii" => Some(TuningCatalogEntry::Deferred(DEFERRED_TEMPERAMENT)),
|
"Pure-fifth (3:2) Pythagorean tuning.",
|
||||||
|
)),
|
||||||
|
"meantone-1/4-comma" => Some(temperament(
|
||||||
|
"meantone-1/4-comma",
|
||||||
|
"Quarter-comma meantone (pure major thirds).",
|
||||||
|
)),
|
||||||
|
"meantone-1/6-comma" => Some(temperament("meantone-1/6-comma", "Sixth-comma meantone.")),
|
||||||
|
"meantone-1/5-comma" => Some(temperament("meantone-1/5-comma", "Fifth-comma meantone.")),
|
||||||
|
"werckmeister-iii" => Some(temperament(
|
||||||
|
"werckmeister-iii",
|
||||||
|
"Werckmeister III well temperament.",
|
||||||
|
)),
|
||||||
|
"werckmeister-iv" => Some(temperament(
|
||||||
|
"werckmeister-iv",
|
||||||
|
"Werckmeister IV well temperament.",
|
||||||
|
)),
|
||||||
|
"vallotti" => Some(temperament("vallotti", "Vallotti well temperament.")),
|
||||||
|
"kirnberger-ii" => Some(temperament(
|
||||||
|
"kirnberger-ii",
|
||||||
|
"Kirnberger II well temperament.",
|
||||||
|
)),
|
||||||
|
"kirnberger-iii" => Some(temperament(
|
||||||
|
"kirnberger-iii",
|
||||||
|
"Kirnberger III well temperament.",
|
||||||
|
)),
|
||||||
|
"young-ii" => Some(temperament(
|
||||||
|
"young-ii",
|
||||||
|
"Thomas Young's second temperament.",
|
||||||
|
)),
|
||||||
"ji-adaptive-5limit" => Some(TuningCatalogEntry::Deferred(DEFERRED_ADAPTIVE)),
|
"ji-adaptive-5limit" => Some(TuningCatalogEntry::Deferred(DEFERRED_ADAPTIVE)),
|
||||||
_ => None,
|
_ => None,
|
||||||
}
|
}
|
||||||
|
|
@ -323,6 +401,363 @@ fn ji_static_5limit_ratios(anchor_chromatic_degree: i32) -> Vec<PositionRatio> {
|
||||||
.collect()
|
.collect()
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// ===========================================================================
|
||||||
|
// The ten historical temperaments (item 2 of
|
||||||
|
// `spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`): the circle-of-fifths walk and the
|
||||||
|
// ten ratified constructions it is walked over.
|
||||||
|
// ===========================================================================
|
||||||
|
|
||||||
|
/// The pure 3/2 fifth, the Pythagorean comma, the syntonic comma, and the
|
||||||
|
/// schisma, each as `1200 · log2(exact ratio)` — never a hardcoded rounded
|
||||||
|
/// cents value (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 2 and "Do not":
|
||||||
|
/// "Hardcode a rounded comma value"). `f64` throughout is correct here:
|
||||||
|
/// these feed only non-canonical frequencies
|
||||||
|
/// (`req:determinism:canonical-floating-point` binds *stored* canonical
|
||||||
|
/// floats, not values computed and discarded in memory — read and confirmed
|
||||||
|
/// before citing), and several fifths in the walk below (meantone's 1/5- and
|
||||||
|
/// 1/6-comma variants) are irrational by construction, so there is no
|
||||||
|
/// exact-rational alternative to begin with.
|
||||||
|
fn pure_fifth_cents() -> f64 {
|
||||||
|
1200.0 * (3.0_f64 / 2.0).log2()
|
||||||
|
}
|
||||||
|
/// The Pythagorean comma, `531441/524288 ≈ 23.460` c (`core_spec.tex:3713`).
|
||||||
|
fn pythagorean_comma_cents() -> f64 {
|
||||||
|
1200.0 * (531441.0_f64 / 524288.0).log2()
|
||||||
|
}
|
||||||
|
/// The syntonic comma, `81/80 ≈ 21.506` c (`core_spec.tex:3765`).
|
||||||
|
fn syntonic_comma_cents() -> f64 {
|
||||||
|
1200.0 * (81.0_f64 / 80.0).log2()
|
||||||
|
}
|
||||||
|
/// The schisma, `32805/32768 ≈ 1.954` c (`core_spec.tex:3896`) — the
|
||||||
|
/// Pythagorean comma minus the syntonic comma exactly: `syntonic + schisma =
|
||||||
|
/// pythagorean`, which is why a Kirnberger construction's regular
|
||||||
|
/// syntonic-tempered fifths plus its one schisma-tempered closing fifth
|
||||||
|
/// reach exactly one Pythagorean comma of total tempering. Computed here
|
||||||
|
/// directly from `32805/32768`, independently of [`pythagorean_comma_cents`]
|
||||||
|
/// and [`syntonic_comma_cents`], so the closure tests below *prove* that
|
||||||
|
/// identity rather than assume it.
|
||||||
|
fn schisma_cents() -> f64 {
|
||||||
|
1200.0 * (32805.0_f64 / 32768.0).log2()
|
||||||
|
}
|
||||||
|
|
||||||
|
/// How one of the twelve fifths in the circle-of-fifths chain
|
||||||
|
/// `C–G–D–A–E–B–F♯–C♯–G♯–E♭–B♭–F–(C)` is tempered by a historical
|
||||||
|
/// construction (`core_spec.tex` §"Temperament Constructions",
|
||||||
|
/// `:3696`-`4011`). This — which fifths, by what fraction of which comma —
|
||||||
|
/// *is* the construction; the derived cents tables the specification also
|
||||||
|
/// gives are checked against the walk below, never pasted in as data
|
||||||
|
/// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 2).
|
||||||
|
#[derive(Copy, Clone, Debug)]
|
||||||
|
enum FifthTempering {
|
||||||
|
/// The untempered 3/2 ratio.
|
||||||
|
Pure,
|
||||||
|
/// Narrowed by `fraction` of the *Pythagorean* comma (Werckmeister
|
||||||
|
/// III/IV, Vallotti, Young II — the well temperaments).
|
||||||
|
NarrowPythagorean(f64),
|
||||||
|
/// Widened by `fraction` of the Pythagorean comma (Werckmeister IV's two
|
||||||
|
/// wide fifths, `G♯–E♭` and `E♭–B♭`).
|
||||||
|
WidePythagorean(f64),
|
||||||
|
/// Narrowed by `fraction` of the *syntonic* comma (meantone; Kirnberger's
|
||||||
|
/// regular tempered fifths).
|
||||||
|
NarrowSyntonic(f64),
|
||||||
|
/// Narrowed by exactly one schisma — Kirnberger's closing `F♯–D♭` fifth,
|
||||||
|
/// "the single most commonly omitted element of these ... constructions"
|
||||||
|
/// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`'s schisma-fifth trap).
|
||||||
|
NarrowSchisma,
|
||||||
|
/// The closing/residual fifth: given no fraction of its own, but
|
||||||
|
/// whatever cents value brings the twelve-fifth chain to exactly seven
|
||||||
|
/// octaves (8400 c) — the wolf, for the four non-circulating
|
||||||
|
/// constructions (`pythagorean`, the three `meantone-*`).
|
||||||
|
Residual,
|
||||||
|
}
|
||||||
|
|
||||||
|
/// A temperament's construction: the twelve fifths of the circle
|
||||||
|
/// `C–G–D–A–E–B–F♯–C♯–G♯–E♭–B♭–F–(C)`
|
||||||
|
/// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 2), in that fixed arc order —
|
||||||
|
/// index 0 is `C–G`, index 1 is `G–D`, …, index 8 is `G♯–E♭` (the
|
||||||
|
/// conventional wolf/closing position), index 11 is the final `F–C`.
|
||||||
|
type Construction = [FifthTempering; 12];
|
||||||
|
|
||||||
|
/// The `cmn-12` chromatic degree reached after each of the twelve chain
|
||||||
|
/// arcs, in chain order starting from `C` itself: `C`(0), `G`(1), `D`(2),
|
||||||
|
/// `A`(3), `E`(4), `B`(5), `F♯`(6), `C♯`(7), `G♯`(8), `E♭`(9), `B♭`(10),
|
||||||
|
/// `F`(11) — i.e. `CHAIN_CHROMATIC_DEGREE[k]` is chain position `k`'s
|
||||||
|
/// `cmn-12` degree (`C=0, C♯=1, D=2, …, B=11`).
|
||||||
|
const CHAIN_CHROMATIC_DEGREE: [usize; 12] = [0, 7, 2, 9, 4, 11, 6, 1, 8, 3, 10, 5];
|
||||||
|
|
||||||
|
/// The result of walking a construction: the deliverable the closure tests
|
||||||
|
/// below recompute from, never a hardcoded constant
|
||||||
|
/// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`'s "closure invariant, recomputed
|
||||||
|
/// in code").
|
||||||
|
struct TemperamentWalk {
|
||||||
|
/// The twelve ratios relative to `C` (`1/1`), indexed by `cmn-12`
|
||||||
|
/// chromatic degree (`0..12`). The one field production code
|
||||||
|
/// ([`temperament_ratios`]) consumes.
|
||||||
|
ratios: [f64; 12],
|
||||||
|
/// The twelve individual fifths' actual cents, in chain order (index 0
|
||||||
|
/// is `C–G`, …, index 8 is `G♯–E♭`, index 11 is `F–C`) — read only by
|
||||||
|
/// the closure/wolf tests below, hence `#[cfg(test)]`: no production
|
||||||
|
/// code needs a single fifth's cents in isolation.
|
||||||
|
#[cfg(test)]
|
||||||
|
fifth_cents: [f64; 12],
|
||||||
|
/// The *raw* (unreduced) cumulative cents after walking all twelve
|
||||||
|
/// fifths forward from `C` — exactly `8400.0` (seven octaves) if and
|
||||||
|
/// only if the construction closes. Also test-only, for the same reason.
|
||||||
|
#[cfg(test)]
|
||||||
|
raw_closure_cents: f64,
|
||||||
|
}
|
||||||
|
|
||||||
|
/// Walks the circle-of-fifths chain under `construction`
|
||||||
|
/// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 2: "one walk that places the
|
||||||
|
/// twelve notes and derives their ratios"). At most one arc may be
|
||||||
|
/// [`FifthTempering::Residual`] (the four non-circulating constructions);
|
||||||
|
/// its cents are computed as whatever value brings the other eleven
|
||||||
|
/// arcs' sum to seven octaves (`core_spec.tex:3749-3759`'s own framing:
|
||||||
|
/// "any assignment of twelve distinct pitch classes must sum to
|
||||||
|
/// [8400 c] ... by construction").
|
||||||
|
fn walk_temperament(construction: &Construction) -> TemperamentWalk {
|
||||||
|
let pure = pure_fifth_cents();
|
||||||
|
|
||||||
|
// Pass 1: every fixed (non-residual) arc's actual cents, plus the index
|
||||||
|
// of the one residual (wolf) arc, if any.
|
||||||
|
let mut fifth_cents = [0.0f64; 12];
|
||||||
|
let mut residual_index: Option<usize> = None;
|
||||||
|
for (i, tempering) in construction.iter().enumerate() {
|
||||||
|
let deviation = match *tempering {
|
||||||
|
FifthTempering::Pure => 0.0,
|
||||||
|
FifthTempering::NarrowPythagorean(fraction) => fraction * pythagorean_comma_cents(),
|
||||||
|
FifthTempering::WidePythagorean(fraction) => -fraction * pythagorean_comma_cents(),
|
||||||
|
FifthTempering::NarrowSyntonic(fraction) => fraction * syntonic_comma_cents(),
|
||||||
|
FifthTempering::NarrowSchisma => schisma_cents(),
|
||||||
|
FifthTempering::Residual => {
|
||||||
|
debug_assert!(
|
||||||
|
residual_index.is_none(),
|
||||||
|
"a construction may have at most one residual (wolf) fifth"
|
||||||
|
);
|
||||||
|
residual_index = Some(i);
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
fifth_cents[i] = pure - deviation;
|
||||||
|
}
|
||||||
|
// Pass 2: the residual (wolf) arc, if any, closes the chain to exactly
|
||||||
|
// seven octaves.
|
||||||
|
if let Some(i) = residual_index {
|
||||||
|
let sum_of_others: f64 = fifth_cents
|
||||||
|
.iter()
|
||||||
|
.enumerate()
|
||||||
|
.filter(|(j, _)| *j != i)
|
||||||
|
.map(|(_, c)| *c)
|
||||||
|
.sum();
|
||||||
|
fifth_cents[i] = 8400.0 - sum_of_others;
|
||||||
|
}
|
||||||
|
|
||||||
|
// Walk forward from C, accumulating *raw* (unreduced) cents; reducing
|
||||||
|
// only when reading off each chain note's pitch class below is what
|
||||||
|
// lets the wolf (for the non-circulating four) fall out of the same
|
||||||
|
// walk as everything else, rather than needing separate handling.
|
||||||
|
let mut cumulative = [0.0f64; 13];
|
||||||
|
for i in 0..12 {
|
||||||
|
cumulative[i + 1] = cumulative[i] + fifth_cents[i];
|
||||||
|
}
|
||||||
|
|
||||||
|
let mut ratios = [0.0f64; 12];
|
||||||
|
for (chain_pos, °ree) in CHAIN_CHROMATIC_DEGREE.iter().enumerate() {
|
||||||
|
let pitch_class_cents = cumulative[chain_pos].rem_euclid(1200.0);
|
||||||
|
ratios[degree] = 2f64.powf(pitch_class_cents / 1200.0);
|
||||||
|
}
|
||||||
|
|
||||||
|
TemperamentWalk {
|
||||||
|
ratios,
|
||||||
|
#[cfg(test)]
|
||||||
|
fifth_cents,
|
||||||
|
#[cfg(test)]
|
||||||
|
raw_closure_cents: cumulative[12],
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `pythagorean` (`core_spec.tex:3709-3759`): eleven pure fifths; the
|
||||||
|
/// conventional `E♭–G♯` cut leaves the wolf at `G♯–E♭` (chain arc 8).
|
||||||
|
fn pythagorean_construction() -> Construction {
|
||||||
|
use FifthTempering::{Pure, Residual};
|
||||||
|
[
|
||||||
|
Pure, Pure, Pure, Pure, Pure, Pure, Pure, Pure, Residual, Pure, Pure, Pure,
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `meantone-1/n-comma` (`core_spec.tex:3761-3812`): all eleven non-wolf
|
||||||
|
/// fifths narrowed uniformly by `1/n` of the *syntonic* comma; same
|
||||||
|
/// `E♭–G♯` cut as `pythagorean`, so the wolf is again chain arc 8.
|
||||||
|
fn meantone_construction(comma_fraction: f64) -> Construction {
|
||||||
|
use FifthTempering::{NarrowSyntonic, Residual};
|
||||||
|
let n = NarrowSyntonic(comma_fraction);
|
||||||
|
[n, n, n, n, n, n, n, n, Residual, n, n, n]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `werckmeister-iii` (`core_spec.tex:3814-3838`): `C–G, G–D, D–A, B–F♯`
|
||||||
|
/// narrowed 1/4 Pythagorean comma; the other eight pure. Circulating — no
|
||||||
|
/// residual arc.
|
||||||
|
fn werckmeister_iii_construction() -> Construction {
|
||||||
|
use FifthTempering::{NarrowPythagorean, Pure};
|
||||||
|
let quarter = NarrowPythagorean(0.25);
|
||||||
|
[
|
||||||
|
quarter, // 0: C-G
|
||||||
|
quarter, // 1: G-D
|
||||||
|
quarter, // 2: D-A
|
||||||
|
Pure, // 3: A-E
|
||||||
|
Pure, // 4: E-B
|
||||||
|
quarter, // 5: B-F#
|
||||||
|
Pure, // 6: F#-C#
|
||||||
|
Pure, // 7: C#-G#
|
||||||
|
Pure, // 8: G#-Eb
|
||||||
|
Pure, // 9: Eb-Bb
|
||||||
|
Pure, // 10: Bb-F
|
||||||
|
Pure, // 11: F-C
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `werckmeister-iv` (`core_spec.tex:3840-3866`): `C–G, D–A, E–B, F♯–C♯,
|
||||||
|
/// B♭–F` narrowed 1/3 Pythagorean comma; `G♯–E♭, E♭–B♭` widened 1/3
|
||||||
|
/// Pythagorean comma; the other five pure. Circulating.
|
||||||
|
fn werckmeister_iv_construction() -> Construction {
|
||||||
|
use FifthTempering::{NarrowPythagorean, Pure, WidePythagorean};
|
||||||
|
let narrow = NarrowPythagorean(1.0 / 3.0);
|
||||||
|
let wide = WidePythagorean(1.0 / 3.0);
|
||||||
|
[
|
||||||
|
narrow, // 0: C-G
|
||||||
|
Pure, // 1: G-D
|
||||||
|
narrow, // 2: D-A
|
||||||
|
Pure, // 3: A-E
|
||||||
|
narrow, // 4: E-B
|
||||||
|
Pure, // 5: B-F#
|
||||||
|
narrow, // 6: F#-C#
|
||||||
|
Pure, // 7: C#-G#
|
||||||
|
wide, // 8: G#-Eb
|
||||||
|
wide, // 9: Eb-Bb
|
||||||
|
narrow, // 10: Bb-F
|
||||||
|
Pure, // 11: F-C
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `vallotti` (`core_spec.tex:3868-3888`): `F–C, C–G, G–D, D–A, A–E, E–B`
|
||||||
|
/// (six consecutive) narrowed 1/6 Pythagorean comma; the other six pure.
|
||||||
|
/// Circulating.
|
||||||
|
fn vallotti_construction() -> Construction {
|
||||||
|
use FifthTempering::{NarrowPythagorean, Pure};
|
||||||
|
let sixth = NarrowPythagorean(1.0 / 6.0);
|
||||||
|
[
|
||||||
|
sixth, // 0: C-G
|
||||||
|
sixth, // 1: G-D
|
||||||
|
sixth, // 2: D-A
|
||||||
|
sixth, // 3: A-E
|
||||||
|
sixth, // 4: E-B
|
||||||
|
Pure, // 5: B-F#
|
||||||
|
Pure, // 6: F#-C#
|
||||||
|
Pure, // 7: C#-G#
|
||||||
|
Pure, // 8: G#-Eb
|
||||||
|
Pure, // 9: Eb-Bb
|
||||||
|
Pure, // 10: Bb-F
|
||||||
|
sixth, // 11: F-C
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `young-ii` (`core_spec.tex:3985-4010`): `C–G, G–D, D–A, A–E, E–B, B–F♯`
|
||||||
|
/// (six consecutive) narrowed 1/6 Pythagorean comma; the other six pure —
|
||||||
|
/// the same construction as `vallotti`, rotated to start at `C` instead of
|
||||||
|
/// `F` (compare this construction's tempered run, arcs 0-5, against
|
||||||
|
/// `vallotti`'s, arcs 11,0-4). Circulating.
|
||||||
|
fn young_ii_construction() -> Construction {
|
||||||
|
use FifthTempering::{NarrowPythagorean, Pure};
|
||||||
|
let sixth = NarrowPythagorean(1.0 / 6.0);
|
||||||
|
[
|
||||||
|
sixth, // 0: C-G
|
||||||
|
sixth, // 1: G-D
|
||||||
|
sixth, // 2: D-A
|
||||||
|
sixth, // 3: A-E
|
||||||
|
sixth, // 4: E-B
|
||||||
|
sixth, // 5: B-F#
|
||||||
|
Pure, // 6: F#-C#
|
||||||
|
Pure, // 7: C#-G#
|
||||||
|
Pure, // 8: G#-Eb
|
||||||
|
Pure, // 9: Eb-Bb
|
||||||
|
Pure, // 10: Bb-F
|
||||||
|
Pure, // 11: F-C
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `kirnberger-ii` (`core_spec.tex:3890-3937`): `D–A, A–E` narrowed 1/2
|
||||||
|
/// syntonic comma; the closing fifth (named `F♯–D♭` in the specification,
|
||||||
|
/// since Kirnberger's own chain is built outward from `D♭` — the *same
|
||||||
|
/// physical arc* as chain position 6, `F♯–C♯`, `D♭` and `C♯` being one
|
||||||
|
/// enharmonic pitch class) narrowed one schisma — the trap
|
||||||
|
/// `spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` calls out by name; the other nine
|
||||||
|
/// pure. Circulating.
|
||||||
|
fn kirnberger_ii_construction() -> Construction {
|
||||||
|
use FifthTempering::{NarrowSchisma, NarrowSyntonic, Pure};
|
||||||
|
let half = NarrowSyntonic(0.5);
|
||||||
|
[
|
||||||
|
Pure, // 0: C-G
|
||||||
|
Pure, // 1: G-D
|
||||||
|
half, // 2: D-A
|
||||||
|
half, // 3: A-E
|
||||||
|
Pure, // 4: E-B
|
||||||
|
Pure, // 5: B-F#
|
||||||
|
NarrowSchisma, // 6: F#-C# (the closing F#-Db fifth)
|
||||||
|
Pure, // 7: C#-G#
|
||||||
|
Pure, // 8: G#-Eb
|
||||||
|
Pure, // 9: Eb-Bb
|
||||||
|
Pure, // 10: Bb-F
|
||||||
|
Pure, // 11: F-C
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// `kirnberger-iii` (`core_spec.tex:3939-3983`): `C–G, G–D, D–A, A–E` (four
|
||||||
|
/// consecutive) narrowed 1/4 syntonic comma; the same closing `F♯–D♭`
|
||||||
|
/// (chain position 6) narrowed one schisma as `kirnberger-ii`; the other
|
||||||
|
/// seven pure. Circulating.
|
||||||
|
fn kirnberger_iii_construction() -> Construction {
|
||||||
|
use FifthTempering::{NarrowSchisma, NarrowSyntonic, Pure};
|
||||||
|
let quarter = NarrowSyntonic(0.25);
|
||||||
|
[
|
||||||
|
quarter, // 0: C-G
|
||||||
|
quarter, // 1: G-D
|
||||||
|
quarter, // 2: D-A
|
||||||
|
quarter, // 3: A-E
|
||||||
|
Pure, // 4: E-B
|
||||||
|
Pure, // 5: B-F#
|
||||||
|
NarrowSchisma, // 6: F#-C# (the closing F#-Db fifth)
|
||||||
|
Pure, // 7: C#-G#
|
||||||
|
Pure, // 8: G#-Eb
|
||||||
|
Pure, // 9: Eb-Bb
|
||||||
|
Pure, // 10: Bb-F
|
||||||
|
Pure, // 11: F-C
|
||||||
|
]
|
||||||
|
}
|
||||||
|
|
||||||
|
/// The twelve ratios (indexed by `cmn-12` chromatic degree) of the
|
||||||
|
/// reserved-built-in temperament named by `function`, or `None` for any
|
||||||
|
/// other id — the extension point's fail-closed path
|
||||||
|
/// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 1: "An unknown
|
||||||
|
/// `TuningFunctionId` returns `None` ... `Function` is an extension point and
|
||||||
|
/// no registry exists"). Never memoized: each of the ten constructions is
|
||||||
|
/// cheap arithmetic on twelve `f64`s, so there is no cache to keep coherent.
|
||||||
|
fn temperament_ratios(function: &TuningFunctionId) -> Option<[f64; 12]> {
|
||||||
|
let construction = match function.as_str() {
|
||||||
|
"pythagorean" => pythagorean_construction(),
|
||||||
|
"meantone-1/4-comma" => meantone_construction(0.25),
|
||||||
|
"meantone-1/5-comma" => meantone_construction(0.2),
|
||||||
|
"meantone-1/6-comma" => meantone_construction(1.0 / 6.0),
|
||||||
|
"werckmeister-iii" => werckmeister_iii_construction(),
|
||||||
|
"werckmeister-iv" => werckmeister_iv_construction(),
|
||||||
|
"vallotti" => vallotti_construction(),
|
||||||
|
"kirnberger-ii" => kirnberger_ii_construction(),
|
||||||
|
"kirnberger-iii" => kirnberger_iii_construction(),
|
||||||
|
"young-ii" => young_ii_construction(),
|
||||||
|
_ => return None,
|
||||||
|
};
|
||||||
|
Some(walk_temperament(&construction).ratios)
|
||||||
|
}
|
||||||
|
|
||||||
// ===========================================================================
|
// ===========================================================================
|
||||||
// The frequency resolver (item 3): (position, TuningSystem, ReferencePitch)
|
// The frequency resolver (item 3): (position, TuningSystem, ReferencePitch)
|
||||||
// -> Hz.
|
// -> Hz.
|
||||||
|
|
@ -438,6 +873,26 @@ fn absolute_coordinate(
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
/// The chromatic cardinality of `structure` — the "positions per octave"
|
||||||
|
/// figure [`TuningResolution::Function`] borrows from the pitch space
|
||||||
|
/// rather than carrying itself (the variant has no division-count field,
|
||||||
|
/// `core_spec.tex:3318-3324`). Both `Chromatic` and `DiatonicOverChromatic`
|
||||||
|
/// name one; `JiLattice` and `Registered` do not (a lattice or a grammar
|
||||||
|
/// plugin has no single "positions per octave" scalar), so `None` there is
|
||||||
|
/// a structural refusal, not an oversight.
|
||||||
|
fn chromatic_cardinality(structure: &PositionStructure) -> Option<u32> {
|
||||||
|
match structure {
|
||||||
|
PositionStructure::Chromatic {
|
||||||
|
positions_per_octave,
|
||||||
|
} => Some(u32::from(*positions_per_octave)),
|
||||||
|
PositionStructure::DiatonicOverChromatic {
|
||||||
|
chromatic_positions_per_octave,
|
||||||
|
..
|
||||||
|
} => Some(u32::from(*chromatic_positions_per_octave)),
|
||||||
|
PositionStructure::JiLattice { .. } | PositionStructure::Registered(_) => None,
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
/// The full-register frequency ratio of absolute coordinate `s`, relative to
|
/// The full-register frequency ratio of absolute coordinate `s`, relative to
|
||||||
/// coordinate `0` under `resolution`.
|
/// coordinate `0` under `resolution`.
|
||||||
fn coordinate_ratio(resolution: &TuningResolution, s: i64) -> Option<f64> {
|
fn coordinate_ratio(resolution: &TuningResolution, s: i64) -> Option<f64> {
|
||||||
|
|
@ -458,6 +913,18 @@ fn coordinate_ratio(resolution: &TuningResolution, s: i64) -> Option<f64> {
|
||||||
let base = f64::from(entry.ratio.numerator) / f64::from(entry.ratio.denominator.get());
|
let base = f64::from(entry.ratio.numerator) / f64::from(entry.ratio.denominator.get());
|
||||||
Some(base * 2f64.powi(octave))
|
Some(base * 2f64.powi(octave))
|
||||||
}
|
}
|
||||||
|
TuningResolution::Function { function, .. } => {
|
||||||
|
// `degree = s.rem_euclid(12)`, `octave = s.div_euclid(12)`,
|
||||||
|
// `ratio = temperament_ratios[degree] · 2^octave`
|
||||||
|
// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 1). An unknown
|
||||||
|
// `TuningFunctionId` has no registry to consult, so
|
||||||
|
// `temperament_ratios` returns `None` and this fails closed —
|
||||||
|
// never a fallback frequency.
|
||||||
|
let ratios = temperament_ratios(function)?;
|
||||||
|
let degree = i32::try_from(s.rem_euclid(12)).ok()?;
|
||||||
|
let octave = i32::try_from(s.div_euclid(12)).ok()?;
|
||||||
|
Some(ratios[degree as usize] * 2f64.powi(octave))
|
||||||
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
@ -483,14 +950,20 @@ pub fn frequency_for_position(
|
||||||
) -> Result<f64, TuningResolutionError> {
|
) -> Result<f64, TuningResolutionError> {
|
||||||
let structure = built_in_position_structure(&system.pitch_space)
|
let structure = built_in_position_structure(&system.pitch_space)
|
||||||
.ok_or_else(|| TuningResolutionError::UnresolvedPitchSpace(system.pitch_space.clone()))?;
|
.ok_or_else(|| TuningResolutionError::UnresolvedPitchSpace(system.pitch_space.clone()))?;
|
||||||
let divisions = match &system.resolution {
|
let divisions =
|
||||||
TuningResolution::EqualTemperament {
|
match &system.resolution {
|
||||||
divisions_per_octave,
|
TuningResolution::EqualTemperament {
|
||||||
} => u32::from(*divisions_per_octave),
|
divisions_per_octave,
|
||||||
TuningResolution::PerPositionRatios(table) => {
|
} => u32::from(*divisions_per_octave),
|
||||||
u32::try_from(table.len()).map_err(|_| TuningResolutionError::PositionUnavailable)?
|
TuningResolution::PerPositionRatios(table) => u32::try_from(table.len())
|
||||||
}
|
.map_err(|_| TuningResolutionError::PositionUnavailable)?,
|
||||||
};
|
// `Function` carries no division count of its own (unlike the other
|
||||||
|
// two variants); divisions comes from the *pitch space*'s chromatic
|
||||||
|
// cardinality instead — 12 for `cmn-12`
|
||||||
|
// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 1).
|
||||||
|
TuningResolution::Function { .. } => chromatic_cardinality(&structure)
|
||||||
|
.ok_or(TuningResolutionError::PositionUnavailable)?,
|
||||||
|
};
|
||||||
let s = absolute_coordinate(position, &structure, divisions)
|
let s = absolute_coordinate(position, &structure, divisions)
|
||||||
.ok_or(TuningResolutionError::PositionUnavailable)?;
|
.ok_or(TuningResolutionError::PositionUnavailable)?;
|
||||||
let s_ref = absolute_coordinate(&reference.position, &structure, divisions)
|
let s_ref = absolute_coordinate(&reference.position, &structure, divisions)
|
||||||
|
|
@ -903,22 +1376,25 @@ mod tests {
|
||||||
);
|
);
|
||||||
}
|
}
|
||||||
|
|
||||||
// -- Proof of life 5: deferred systems fail closed. -----------------------
|
// -- Proof of life 5: a deferred system fails closed. ---------------------
|
||||||
|
|
||||||
#[test]
|
#[test]
|
||||||
fn deferred_systems_fail_closed_pythagorean_and_ji_adaptive() {
|
fn deferred_ji_adaptive_fails_closed() {
|
||||||
|
// As of Push 4b tranche 2b, `pythagorean` (and the other nine
|
||||||
|
// historical temperaments) resolve — see the temperament tests
|
||||||
|
// below. `ji-adaptive-5limit` is the one remaining catalog entry
|
||||||
|
// whose resolution is still deferred (it needs `HarmonicContext`,
|
||||||
|
// which does not exist in Rust).
|
||||||
let f = fixture();
|
let f = fixture();
|
||||||
let c5 = cmn_pitch("cmn-12", CmnNominal::C, 0, 5);
|
let c5 = cmn_pitch("cmn-12", CmnNominal::C, 0, 5);
|
||||||
for deferred in ["pythagorean", "ji-adaptive-5limit"] {
|
let mut score = f.score.clone();
|
||||||
let mut score = f.score.clone();
|
score.tuning_context.default_tuning_system = TuningSystemId::new("ji-adaptive-5limit");
|
||||||
score.tuning_context.default_tuning_system = TuningSystemId::new(deferred);
|
let err = resolve_pitch_frequency(&score, &c5, f.voice_a)
|
||||||
let err = resolve_pitch_frequency(&score, &c5, f.voice_a)
|
.expect_err("ji-adaptive-5limit must not resolve to a frequency");
|
||||||
.expect_err(&format!("{deferred} must not resolve to a frequency"));
|
assert!(
|
||||||
assert!(
|
matches!(err, TuningResolutionError::NotYetSupported { .. }),
|
||||||
matches!(err, TuningResolutionError::NotYetSupported { .. }),
|
"ji-adaptive-5limit must report NotYetSupported (a known-but-deferred identifier), got {err:?}"
|
||||||
"{deferred} must report NotYetSupported (a known-but-deferred identifier), got {err:?}"
|
);
|
||||||
);
|
|
||||||
}
|
|
||||||
// A genuinely unknown identifier reports differently, so the two
|
// A genuinely unknown identifier reports differently, so the two
|
||||||
// failure modes never blur together.
|
// failure modes never blur together.
|
||||||
let mut score = f.score.clone();
|
let mut score = f.score.clone();
|
||||||
|
|
@ -979,4 +1455,229 @@ mod tests {
|
||||||
"expected ~{expected} Hz, got {freq}"
|
"expected ~{expected} Hz, got {freq}"
|
||||||
);
|
);
|
||||||
}
|
}
|
||||||
|
|
||||||
|
// =========================================================================
|
||||||
|
// Push 4b tranche 2b: the ten historical temperaments. This is the
|
||||||
|
// tranche's reason to exist, per `spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`'s
|
||||||
|
// "Proof of life" section — every assertion below recomputes its expected
|
||||||
|
// value from the walk (or from an exact comma ratio), never from a
|
||||||
|
// hardcoded cents constant copied out of the spec's tables.
|
||||||
|
// =========================================================================
|
||||||
|
|
||||||
|
/// `1200 · log2(ratio)` for chromatic `degree` in `walk` — the cents this
|
||||||
|
/// module's own walk assigns that degree, relative to C.
|
||||||
|
fn cents_of(walk: &TemperamentWalk, degree: usize) -> f64 {
|
||||||
|
1200.0 * walk.ratios[degree].log2()
|
||||||
|
}
|
||||||
|
|
||||||
|
// -- Closure 1: the six circulating temperaments sum to one Pythagorean --
|
||||||
|
// -- comma, and none of their twelve fifths is a wolf. -------------------
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn circulating_temperaments_close_to_one_pythagorean_comma_with_no_wolf() {
|
||||||
|
let comma = pythagorean_comma_cents();
|
||||||
|
let cases: [(&str, Construction); 6] = [
|
||||||
|
("werckmeister-iii", werckmeister_iii_construction()),
|
||||||
|
("werckmeister-iv", werckmeister_iv_construction()),
|
||||||
|
("vallotti", vallotti_construction()),
|
||||||
|
("kirnberger-ii", kirnberger_ii_construction()),
|
||||||
|
("kirnberger-iii", kirnberger_iii_construction()),
|
||||||
|
("young-ii", young_ii_construction()),
|
||||||
|
];
|
||||||
|
for (name, construction) in cases {
|
||||||
|
let walk = walk_temperament(&construction);
|
||||||
|
// The sum of the twelve fifths' deviations from pure equals one
|
||||||
|
// Pythagorean comma (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md`'s
|
||||||
|
// closure invariant for the circulating six), recomputed from
|
||||||
|
// the walk's raw (unreduced) closing cents rather than asserted
|
||||||
|
// directly against a constant.
|
||||||
|
let total_deviation = 12.0 * pure_fifth_cents() - walk.raw_closure_cents;
|
||||||
|
assert!(
|
||||||
|
(total_deviation - comma).abs() < 1e-9,
|
||||||
|
"{name}: twelve fifths should deviate from pure by exactly one \
|
||||||
|
Pythagorean comma ({comma} c), computed {total_deviation} c"
|
||||||
|
);
|
||||||
|
// No fifth is a wolf: every one of the twelve stays within 15 c
|
||||||
|
// of a pure fifth. 15 c comfortably exceeds this construction's
|
||||||
|
// largest single tempering (kirnberger-ii's half-syntonic-comma
|
||||||
|
// fifths, ~10.75 c) while comfortably staying below any real
|
||||||
|
// historical wolf (pythagorean's is ~23.5 c narrow; meantone's
|
||||||
|
// are 16-36 c wide).
|
||||||
|
for (i, &fifth) in walk.fifth_cents.iter().enumerate() {
|
||||||
|
let deviation = (fifth - pure_fifth_cents()).abs();
|
||||||
|
assert!(
|
||||||
|
deviation < 15.0,
|
||||||
|
"{name}: chain arc {i} deviates from pure by {deviation} c -- too large, looks like a wolf"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// -- Closure 2: the four non-circulating temperaments' residual wolf ------
|
||||||
|
// -- matches the spec's ratified value. --
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn noncirculating_temperaments_wolf_matches_the_ratified_spec_value() {
|
||||||
|
// Chain arc 8 (`G♯–E♭`) is the one `Residual` arc in each of these
|
||||||
|
// four constructions -- see each `*_construction` function's own
|
||||||
|
// comment.
|
||||||
|
const WOLF_ARC: usize = 8;
|
||||||
|
let cases: [(&str, Construction, f64); 4] = [
|
||||||
|
("pythagorean", pythagorean_construction(), 678.495),
|
||||||
|
("meantone-1/4-comma", meantone_construction(0.25), 737.637),
|
||||||
|
("meantone-1/5-comma", meantone_construction(0.2), 725.809),
|
||||||
|
(
|
||||||
|
"meantone-1/6-comma",
|
||||||
|
meantone_construction(1.0 / 6.0),
|
||||||
|
717.923,
|
||||||
|
),
|
||||||
|
];
|
||||||
|
for (name, construction, expected_wolf) in cases {
|
||||||
|
let walk = walk_temperament(&construction);
|
||||||
|
let wolf = walk.fifth_cents[WOLF_ARC];
|
||||||
|
assert!(
|
||||||
|
(wolf - expected_wolf).abs() < 0.001,
|
||||||
|
"{name}: expected the wolf at {expected_wolf} c (`core_spec.tex`'s ratified value), computed {wolf} c"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// -- Discriminators: spot values the walk must reproduce against the -----
|
||||||
|
// -- spec's own independently-derived cents tables. ----
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn pythagorean_e_and_fsharp_match_the_published_cents() {
|
||||||
|
let walk = walk_temperament(&pythagorean_construction());
|
||||||
|
let e = cents_of(&walk, CmnNominal::E.chromatic() as usize);
|
||||||
|
let fsharp = cents_of(&walk, 6); // F# = chromatic degree 6, no plain CmnNominal for it
|
||||||
|
assert!(
|
||||||
|
(e - 407.820).abs() < 0.001,
|
||||||
|
"pythagorean E: expected 407.820 c, got {e}"
|
||||||
|
);
|
||||||
|
assert!(
|
||||||
|
(fsharp - 611.730).abs() < 0.001,
|
||||||
|
"pythagorean F#: expected 611.730 c, got {fsharp}"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn meantone_quarter_comma_major_third_c_to_e_is_the_just_5_4() {
|
||||||
|
let walk = walk_temperament(&meantone_construction(0.25));
|
||||||
|
let c = cents_of(&walk, CmnNominal::C.chromatic() as usize);
|
||||||
|
let e = cents_of(&walk, CmnNominal::E.chromatic() as usize);
|
||||||
|
let third = e - c;
|
||||||
|
assert!(
|
||||||
|
(third - 386.31).abs() < 0.01,
|
||||||
|
"expected the just 5/4 major third (386.31 c), got {third} c"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn kirnberger_ii_and_iii_d_differ_though_the_chain_skeleton_is_the_same() {
|
||||||
|
// Same chain skeleton (D-A/A-E tempered, F#-Db schisma-tempered),
|
||||||
|
// different comma fraction -- a test that passes both proves the two
|
||||||
|
// are not secretly the same construction.
|
||||||
|
let ii = walk_temperament(&kirnberger_ii_construction());
|
||||||
|
let iii = walk_temperament(&kirnberger_iii_construction());
|
||||||
|
let d = CmnNominal::D.chromatic() as usize;
|
||||||
|
let d_ii = cents_of(&ii, d);
|
||||||
|
let d_iii = cents_of(&iii, d);
|
||||||
|
assert!(
|
||||||
|
(d_ii - 203.910).abs() < 0.001,
|
||||||
|
"kirnberger-ii D: expected 203.910 c, got {d_ii}"
|
||||||
|
);
|
||||||
|
assert!(
|
||||||
|
(d_iii - 193.157).abs() < 0.001,
|
||||||
|
"kirnberger-iii D: expected 193.157 c, got {d_iii}"
|
||||||
|
);
|
||||||
|
assert!(
|
||||||
|
(d_ii - d_iii).abs() > 1.0,
|
||||||
|
"kirnberger-ii and -iii should disagree audibly on D, got {d_ii} vs {d_iii}"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
// -- Resolver-level: all ten resolve to a real frequency. -----------------
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn all_ten_temperaments_resolve_and_produce_a_real_frequency() {
|
||||||
|
const TEN: [&str; 10] = [
|
||||||
|
"pythagorean",
|
||||||
|
"meantone-1/4-comma",
|
||||||
|
"meantone-1/5-comma",
|
||||||
|
"meantone-1/6-comma",
|
||||||
|
"werckmeister-iii",
|
||||||
|
"werckmeister-iv",
|
||||||
|
"vallotti",
|
||||||
|
"kirnberger-ii",
|
||||||
|
"kirnberger-iii",
|
||||||
|
"young-ii",
|
||||||
|
];
|
||||||
|
let f = fixture();
|
||||||
|
let c5 = cmn_pitch("cmn-12", CmnNominal::C, 0, 5);
|
||||||
|
for id in TEN {
|
||||||
|
let mut score = f.score.clone();
|
||||||
|
score.tuning_context.default_tuning_system = TuningSystemId::new(id);
|
||||||
|
let freq = resolve_pitch_frequency(&score, &c5, f.voice_a)
|
||||||
|
.unwrap_or_else(|e| panic!("{id} must resolve to a frequency, got error: {e}"));
|
||||||
|
assert!(
|
||||||
|
freq.is_finite() && freq > 0.0,
|
||||||
|
"{id}: expected a real, positive frequency, got {freq}"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn werckmeister_iii_c_sharp_resolves_distinctly_from_tet_12_c_sharp() {
|
||||||
|
let f = fixture();
|
||||||
|
let c_sharp = cmn_pitch("cmn-12", CmnNominal::C, 1, 5);
|
||||||
|
let mut wm_score = f.score.clone();
|
||||||
|
wm_score.tuning_context.default_tuning_system = TuningSystemId::new("werckmeister-iii");
|
||||||
|
// `f.score` already defaults to tet-12.
|
||||||
|
let wm_freq = resolve_pitch_frequency(&wm_score, &c_sharp, f.voice_a)
|
||||||
|
.expect("werckmeister-iii resolves");
|
||||||
|
let tet_freq =
|
||||||
|
resolve_pitch_frequency(&f.score, &c_sharp, f.voice_a).expect("tet-12 resolves");
|
||||||
|
let diff = cents_between(wm_freq, tet_freq);
|
||||||
|
assert!(
|
||||||
|
diff > 0.5,
|
||||||
|
"expected werckmeister-iii's C# to differ audibly from tet-12's, diff was only {diff} c"
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
// -- Fail-closed: an unreserved TuningFunctionId never yields a frequency. -
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn unknown_tuning_function_id_fails_closed() {
|
||||||
|
// Unit level: `coordinate_ratio` returns `None` directly -- the
|
||||||
|
// extension point has no registry
|
||||||
|
// (`spec/CONTRACT_PUSH4B_TEMPERAMENTS.md` item 1).
|
||||||
|
let bogus_resolution = TuningResolution::Function {
|
||||||
|
function: TuningFunctionId::new("not-a-real-temperament"),
|
||||||
|
parameters: TuningParameters,
|
||||||
|
};
|
||||||
|
assert_eq!(coordinate_ratio(&bogus_resolution, 0), None);
|
||||||
|
|
||||||
|
// Full-pipeline level: a `TuningSystem` carrying that resolution
|
||||||
|
// never produces a frequency, only an error -- `PositionUnavailable`,
|
||||||
|
// since `coordinate_ratio`'s `None` is exactly what
|
||||||
|
// `frequency_for_position` reports that way for.
|
||||||
|
let bogus_system = TuningSystem {
|
||||||
|
id: TuningSystemId::new("bogus"),
|
||||||
|
name: "bogus".to_owned(),
|
||||||
|
pitch_space: PitchSpaceId::new("cmn-12"),
|
||||||
|
resolution: bogus_resolution,
|
||||||
|
description: None,
|
||||||
|
};
|
||||||
|
let c5_position = PitchSpacePosition::Cmn {
|
||||||
|
nominal: CmnNominal::C,
|
||||||
|
alteration: 0,
|
||||||
|
octave: 5,
|
||||||
|
};
|
||||||
|
let err = frequency_for_position(&c5_position, &bogus_system, &ReferencePitch::a440())
|
||||||
|
.expect_err("an unknown TuningFunctionId must never resolve to a frequency");
|
||||||
|
assert!(
|
||||||
|
matches!(err, TuningResolutionError::PositionUnavailable),
|
||||||
|
"expected PositionUnavailable, got {err:?}"
|
||||||
|
);
|
||||||
|
}
|
||||||
}
|
}
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue