Equal Temperament vs. Kellner's Bach
Compare the tuning characteristics of Equal Temperament and Kellner's Bach — cent deviations per note, practical guidance, and historical context.
At a Glance
| Feature | Equal Temperament | Kellner's Bach |
|---|---|---|
| Category | equal | well-temperament |
| Formula Type | equal-division | cent-offsets |
| Historical Era | Modern | Baroque (reconstruction) |
| Key Advantage | All 12 keys are equally in-tune — transpose freely without re-tuning. | Pure-leaning C major triad; strong tonal center for common-practice Baroque keys. |
| Key Limitation | Pure fifths (2 cents flat) and major thirds (14 cents sharp) are slightly impure in every key. | Remote keys (sharps side) become noticeably bright; not ideal for chromatic Baroque works. |
| Typical Use | Standard tuning for all modern Western instruments since the 20th century. | Baroque organ music and harpsichord repertoire centered on flat and natural keys. |
Cent Deviations: All 12 Notes vs. Equal Temperament
Positive cents = sharper than equal temperament. Negative = flatter. Difference column shows Kellner's Bach minus Equal Temperament: positive means Kellner's Bach is sharper.
| Note | Equal Temperament (¢) | Kellner's Bach (¢) | Difference (¢) |
|---|---|---|---|
| C4 | 0.00 | +8.21 | +8.21 |
| Db4 | 0.00 | -1.56 | -1.56 |
| D4 | 0.00 | +2.74 | +2.74 |
| Eb4 | 0.00 | +2.35 | +2.35 |
| E4 | 0.00 | -2.74 | -2.74 |
| F4 | 0.00 | +6.26 | +6.26 |
| Gb4 | 0.00 | -3.52 | -3.52 |
| G4 | 0.00 | +5.47 | +5.47 |
| Ab4 | 0.00 | +0.39 | +0.39 |
| A4 | 0.00 | 0.00 | 0.00 |
| Bb4 | 0.00 | +4.30 | +4.30 |
| B4 | 0.00 | -0.78 | -0.78 |
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 Kellner's Bach when:
Choose Kellner's Bach 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
- Kellner's Bach
- Developed by Herbert Anton Kellner (1977) — Baroque (reconstruction) era
Compare Temperaments in Tunable — Get Tunable.
Tunable supports Equal Temperament, Kellner's Bach, and 16 other tuning systems. Hear the difference in real-time as you play.
