Werckmeister III
All 24 major and minor keys are playable — each key has a distinct character.
Quick Facts
- Creator
- Andreas Werckmeister (1691)
- Historical Era
- Baroque
- Formula Type
- cent-offsets
- Key Advantage
- All 24 major and minor keys are playable — each key has a distinct character.
- Key Limitation
- Simpler keys are purer than remote keys; not the brightest choice for remote tonality.
- Typical Use
- Baroque keyboard music, particularly works exploiting key color contrasts.
Mathematical Basis
This well temperament distributes the Pythagorean comma unevenly across the circle of fifths, giving pure or near-pure intervals in closely-related keys while making distant keys progressively more tempered.
Sound Character
Well temperaments feature varied key color: keys near C major sound purer and more consonant, while distant keys (many sharps or flats) have more harmonic tension and a brighter, more chromatic character. This gives each key a distinctive musical affect, making well temperaments particularly suited to multi-key keyboard repertoire.
Werckmeister III Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Werckmeister III (Hz) | Cents from Equal | Tunable Offset |
|---|---|---|---|---|
| C4 | 261.626 | 263.405 | +11.73 | 0 |
| Db4 | 277.183 | 277.496 | +1.96 | -9.775 |
| D4 | 293.665 | 294.329 | +3.91 | -7.82 |
| Eb4 | 311.127 | 312.183 | +5.87 | -5.865 |
| E4 | 329.628 | 330.000 | +1.96 | -9.775 |
| F4 | 349.228 | 351.205 | +9.78 | -1.955 |
| Gb4 | 369.994 | 369.994 | 0.00 | -11.73 |
| G4 | 391.995 | 393.770 | +7.82 | -3.91 |
| Ab4 | 415.305 | 416.244 | +3.91 | -7.82 |
| A4 | 440.000 | 440.000 | 0.00 | -11.73 |
| Bb4 | 466.164 | 468.274 | +7.82 | -3.91 |
| B4 | 493.883 | 495.000 | +3.91 | -7.82 |
Frequencies in Hz at A4=440Hz. Positive cents = sharper than equal temperament. Negative = flatter. Formula: f = f_equal × 2(cents/1200)
Tunable Offset shows the cent values in Tunable's custom temperament format (C=0 reference). To enter this temperament manually: Settings → Tuner → Alternate Temperament → Add → enter these 12 values.
Historical Context
Werckmeister III originates from the Baroque era, developed by Andreas Werckmeister (1691). It was primarily used for Baroque keyboard music, particularly works exploiting key color contrasts..
Well temperaments emerged in the Baroque era as practical compromises between meantone purity and equal temperament flexibility. J.S. Bach's Well-Tempered Clavier (1722) may have been composed with a specific well temperament in mind.
Who Uses Werckmeister III Today
Well temperaments are used today by harpsichordists, fortepiano players, and historically-informed keyboard performers. Many period instrument specialists choose specific well temperaments to match the repertoire being performed.
Tune with Werckmeister III — Get Tunable.
Tunable supports Werckmeister III and 17 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.
