Equal Temperament vs. Kirnberger III
Compare the tuning characteristics of Equal Temperament and Kirnberger III — cent deviations per note, practical guidance, and historical context.
At a Glance
| Feature | Equal Temperament | Kirnberger III |
|---|---|---|
| Category | equal | well-temperament |
| Formula Type | equal-division | cent-offsets |
| Historical Era | Modern | Classical |
| Key Advantage | All 12 keys are equally in-tune — transpose freely without re-tuning. | Near-pure thirds in C, G, D, and A major — well-suited to Classical-era common keys. |
| Key Limitation | Pure fifths (2 cents flat) and major thirds (14 cents sharp) are slightly impure in every key. | Remote keys have wider thirds; not ideal for music that ranges through all keys. |
| Typical Use | Standard tuning for all modern Western instruments since the 20th century. | Classical keyboard music in common-practice keys, particularly CPE Bach-era repertoire. |
Cent Deviations: All 12 Notes vs. Equal Temperament
Positive cents = sharper than equal temperament. Negative = flatter. Difference column shows Kirnberger III minus Equal Temperament: positive means Kirnberger III is sharper.
| Note | Equal Temperament (¢) | Kirnberger III (¢) | Difference (¢) |
|---|---|---|---|
| C4 | 0.00 | +10.26 | +10.26 |
| Db4 | 0.00 | +0.49 | +0.49 |
| D4 | 0.00 | +3.42 | +3.42 |
| Eb4 | 0.00 | +13.69 | +13.69 |
| E4 | 0.00 | -3.42 | -3.42 |
| F4 | 0.00 | +13.69 | +13.69 |
| Gb4 | 0.00 | +0.98 | +0.98 |
| G4 | 0.00 | +6.85 | +6.85 |
| Ab4 | 0.00 | +3.91 | +3.91 |
| A4 | 0.00 | 0.00 | 0.00 |
| Bb4 | 0.00 | +10.26 | +10.26 |
| B4 | 0.00 | -3.42 | -3.42 |
When to Choose Each
Choose Equal Temperament when:
Choose Equal Temperament for modern ensembles, fixed-pitch instruments (piano, guitar, wind instruments), and any music that modulates freely across all 24 keys. It is the universal standard for contemporary Western music.
Choose Kirnberger III when:
Choose Kirnberger III for Baroque keyboard repertoire spanning multiple keys — especially works that tour the circle of fifths. Its varied key color gives each tonality a distinctive musical character.
Historical Context
Well temperaments emerged in the Baroque era as practical compromises enabling all 24 keys, while Equal Temperament achieved true key equality only in the 20th century. J.S. Bach's Well-Tempered Clavier (1722) may have been composed with a specific well temperament — not equal temperament — in mind.
- Equal Temperament
- Developed by Theoretical development (12-TET standardized c. 1900) — Modern era
- Kirnberger III
- Developed by Johann Philipp Kirnberger (1779) — Classical era
Compare Temperaments in Tunable — Get Tunable.
Tunable supports Equal Temperament, Kirnberger III, and 14 other tuning systems. Hear the difference in real-time as you play.
