Musical Temperaments

Temperament is the system by which all 12 pitches of the octave are tuned — the precise allocation of intervals across the chromatic scale. Different temperament systems make different trade-offs between pure (just) intervals and key flexibility: equal temperament divides the octave into 12 identical semitones for maximum key freedom, while historical systems like meantone and Pythagorean tuning prioritize purity in certain intervals at the cost of others. This page covers all 16 temperaments in the Tunable frequency reference, organized by system type.

Equal Temperament

Equal Temperament All 12 keys are equally in-tune — transpose freely without re-tuning.

Pythagorean Tuning

Pythagorean Tuning Pure perfect fifths (3:2) — ideal for medieval polyphony and chant.

Just Intonation

Just Intonation (Major) Perfectly pure major thirds (5:4) and fifths (3:2) in the home key. Just Intonation (Minor) Pure minor thirds (6:5) and fifths in the home minor key.

Meantone Temperaments

Quarter-Comma Meantone Pure major thirds (5:4) in the most common Renaissance/Baroque keys. Sixth-Comma Meantone Compromise between equal and quarter-comma: better key flexibility with acceptable thirds. Third-Comma Meantone Pure minor thirds (6:5) — better suited to minor-mode Renaissance music.

Well Temperaments

Bach-Lehman Temperament All keys in the WTC are singularly in tune; key characters precisely match Baroque affect theory. Kellner Temperament Pure-leaning C major triad; strong tonal center for common-practice Baroque keys. Kirnberger III Near-pure thirds in C, G, D, and A major — well-suited to Classical-era common keys. Neidhardt Temperament Closest well-temperament to equal temperament — very flexible key use. Vallotti Balanced well-temperament: natural keys pure, remote keys gently colored. Werckmeister III All 24 major and minor keys are playable — each key has a distinct character. Werckmeister IV Smoother key transitions compared to Werckmeister III; less dramatic key color. Werckmeister V Even-handed key color distribution — more uniform than Werckmeister III. Young Temperament Gentle key color with pure-leaning thirds in flat-side keys; very playable in all keys.

Compare Temperaments

See how any two temperaments differ in cents deviation for all 12 pitch classes.

Equal vs. Pythagorean Equal vs. Quarter-Comma Meantone Equal vs. Werckmeister III

By Historical Era

Temperament history spans ancient Greece to the 20th century — from Pythagorean stacking through the meantone experiments of the Renaissance, the well temperaments of the Baroque, and the eventual adoption of equal temperament as the modern standard.

Ancient & Medieval Renaissance Baroque Classical Modern

By Use Case

Choral & Vocal Keyboard — Baroque Keyboard — Classical String Ensemble Early Music Modern Standard

Related References

Note Frequencies Theory Hub Transposition Circle of Fifths