Kirnberger III
Near-pure thirds in C, G, D, and A major — well-suited to Classical-era common keys.
Quick Facts
- Creator
- Johann Philipp Kirnberger (1779)
- Historical Era
- Classical
- Formula Type
- cent-offsets
- Key Advantage
- Near-pure thirds in C, G, D, and A major — well-suited to Classical-era common keys.
- Key Limitation
- Remote keys have wider thirds; not ideal for music that ranges through all keys.
- Typical Use
- Classical keyboard music in common-practice keys, particularly CPE Bach-era repertoire.
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.
Kirnberger III Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Kirnberger III (Hz) | Cents from Equal | Tunable Offset |
|---|---|---|---|---|
| C4 | 261.626 | 263.182 | +10.27 | 0 |
| Db4 | 277.183 | 277.261 | +0.49 | -9.775 |
| D4 | 293.665 | 294.246 | +3.42 | -6.843 |
| Eb4 | 311.127 | 311.919 | +4.40 | -5.865 |
| E4 | 329.628 | 328.977 | -3.42 | -13.686 |
| F4 | 349.228 | 350.908 | +8.31 | -1.955 |
| Gb4 | 369.994 | 370.099 | +0.49 | -9.776 |
| G4 | 391.995 | 393.547 | +6.84 | -3.422 |
| Ab4 | 415.305 | 415.892 | +2.44 | -7.82 |
| A4 | 440.000 | 440.000 | 0.00 | -10.265 |
| Bb4 | 466.164 | 467.878 | +6.36 | -3.91 |
| B4 | 493.883 | 493.465 | -1.47 | -11.731 |
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
Kirnberger III originates from the Classical era, developed by Johann Philipp Kirnberger (1779). It was primarily used for Classical keyboard music in common-practice keys, particularly CPE Bach-era repertoire..
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 Kirnberger 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 Kirnberger III — Get Tunable.
Tunable supports Kirnberger 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.
