Add just intonation and Pythagorean temperaments - #28
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Extend the existing temperament support with two ratio-based tuning systems alongside equal temperament: - `JustIntonation` — five-limit pure ratios above a tonic (e.g. a 3/2 fifth, 5/4 major third), giving beat-free intervals. - `Pythagorean` — pitches built from stacked pure perfect fifths. Both share a new abstract `RatioTemperament <: Temperament` that handles octave folding generically; concrete tunings only supply their 12-entry ratio table. The tonic is anchored to its equal-tempered frequency, so a just/Pythagorean scale starts on the same pitch as the equal-tempered one. Also: - Make `EqualTemperament` a subtype of `Temperament` (it previously was not), so all tunings dispatch generically through `frequency`. - Export `Temperament`, `EqualTemperament`, `JustIntonation`, `Pythagorean` and `frequency`. - Fix the equal-temperament test (`@testest` -> `@testset`) and wire it into `runtests.jl`, which never included it; add tests for the new temperaments. - Document temperaments in the README. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Summary
Builds on the existing
equal_temperament.jlto add two ratio-based tuning systems, so pitches can be sounded in tunings other than equal temperament.JustIntonation(tonic)— five-limit pure ratios above the tonic (perfect fifth = exactly 3/2, major third = exactly 5/4), giving acoustically beat-free intervals.Pythagorean(tonic)— pitches built from stacked pure perfect fifths (wide thirds, pure fifths).Both share a new abstract
RatioTemperament <: Temperamentthat handles octave folding generically (viafldmod), so a concrete tuning only supplies its 12-entry ratio table. The tonic is anchored to its equal-tempered frequency, so a just/Pythagorean scale starts on the same pitch as the equal-tempered one and only the intervals in between differ.Also in this PR
EqualTemperamentan actual subtype ofTemperament(it previously wasn't), so every tuning dispatches generically throughfrequency.Temperament,EqualTemperament,JustIntonation,Pythagorean, andfrequency(none were exported before).@testest→@testset, and add it toruntests.jl, which never included it — so it wasn't running at all. New tests cover the just and Pythagorean tunings.Test plan
Pkg.test()passes, including the now-running equal-temperament test plus the new just-intonation (10) and Pythagorean (6) assertions.Notes
The README's "Play the notes" TODO (audio synthesis/playback) is a natural follow-up that this frequency mapping enables, but it's intentionally left out of this PR to keep the package dependency-free and the change focused.
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