Temperatio
The word comes from the Latin temperatio: the act of mixing in due proportion. In music, a temperament is a system for tuning the twelve notes of the chromatic scale. No single tuning can make every interval perfectly pure, so every temperament is a compromise, a deliberate act of proportion.
Why temperaments matter
Modern instruments almost universally use 12-tone equal temperament (12-TET), where every semitone is exactly 100 cents. This is a practical miracle: you can play in any key and everything sounds acceptably in tune. But “acceptably” is not “beautifully.” Equal temperament sacrifices the purity of individual intervals for universal compatibility.
Before the 19th century, keyboard instruments were tuned to temperaments that gave each key a distinct character. Bach's “Well-Tempered Clavier” was not written for equal temperament. It was written to explore the unique color of every key in a well temperament like Werckmeister III, where C major sounds bright and open while F-sharp major sounds dark and restless.
Today, harpsichordists, organists, and early-music ensembles still tune historically. Microtonal composers explore 19-EDO, 31-EDO, just intonation, and beyond. Even a guitarist adjusting intonation on a fretted instrument is engaging with temperament, whether they know it or not.
What temperat.io does
temperat.io ships 21 historical tuning systems grouped by era, covering the music from medieval chant to early-modern piano repertoire:
- Modern reference: 12-TET (Equal Temperament), Just Intonation
- Medieval: Pythagorean
- Renaissance: Meantone ¼-comma, Meantone ⅙-comma
- Baroque well-temperaments:Werckmeister III, Kirnberger III, Vallotti, Young II, Bach/Lehman, Neidhardt I/II/III, Kellner, Rameau, D'Alembert, Tartini-Vallotti, Sorge
- Late-Classical original: Thomas Young I (1800)
- 20th-century reconstructions: Barnes (1979), Billeter (1979)
Reference pitch is adjustable (A = 415, 432, 440, 442, or 444 Hz), and an optional Railsback-curve toggle handles piano inharmonicity.
For more on each system, see the field guide to temperaments.
Privacy
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Support
temperat.io is free, open-source, and always will be. If you find it useful, consider supporting the project.