Kellner's Bach
Pure-leaning C major triad; strong tonal center for common-practice Baroque keys.
Quick Facts
- Creator
- Herbert Anton Kellner (1977)
- Historical Era
- Baroque (reconstruction)
- Formula Type
- cent-offsets
- Key Advantage
- Pure-leaning C major triad; strong tonal center for common-practice Baroque keys.
- Key Limitation
- Remote keys (sharps side) become noticeably bright; not ideal for chromatic Baroque works.
- Typical Use
- Baroque organ music and harpsichord repertoire centered on flat and natural keys.
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.
Kellner's Bach Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Kellner's Bach (Hz) | Cents from Equal | Tunable Offset |
|---|---|---|---|---|
| C4 | 261.626 | 262.870 | +8.21 | 0 |
| Db4 | 277.183 | 276.933 | -1.56 | -9.775 |
| D4 | 293.665 | 294.130 | +2.74 | -5.474 |
| Eb4 | 311.127 | 311.549 | +2.35 | -5.865 |
| E4 | 329.628 | 329.107 | -2.74 | -10.948 |
| F4 | 349.228 | 350.492 | +6.26 | -1.955 |
| Gb4 | 369.994 | 369.243 | -3.52 | -11.73 |
| G4 | 391.995 | 393.236 | +5.47 | -2.737 |
| Ab4 | 415.305 | 415.399 | +0.39 | -7.82 |
| A4 | 440.000 | 440.000 | 0.00 | -8.211 |
| Bb4 | 466.164 | 467.324 | +4.30 | -3.91 |
| B4 | 493.883 | 493.660 | -0.78 | -8.993 |
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
Kellner's Bach originates from the Baroque (reconstruction) era, developed by Herbert Anton Kellner (1977). It was primarily used for Baroque organ music and harpsichord repertoire centered on flat and natural keys..
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 Kellner's Bach 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 Kellner's Bach — Get Tunable.
Tunable supports Kellner's Bach and 17 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.
