Bach-Lehman Temperament
All keys in the WTC are singularly in tune; key characters precisely match Baroque affect theory.
Quick Facts
- Creator
- Bradley Lehman reconstruction (2005), attributed to J.S. Bach
- Historical Era
- Baroque
- Formula Type
- cent-offsets
- Key Advantage
- All keys in the WTC are singularly in tune; key characters precisely match Baroque affect theory.
- Key Limitation
- The reconstruction remains debated — not universally accepted as Bach's intended tuning.
- Typical Use
- Well-Tempered Clavier and Bach keyboard works performed with historical awareness.
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.
Bach-Lehman Temperament Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Bach-Lehman Temperament (Hz) | Cents from Equal |
|---|---|---|---|
| C4 | 261.626 | 262.515 | +5.87 |
| Db4 | 277.183 | 277.810 | +3.91 |
| D4 | 293.665 | 293.998 | +1.96 |
| Eb4 | 311.127 | 311.830 | +3.91 |
| E4 | 329.628 | 329.255 | -1.96 |
| F4 | 349.228 | 350.809 | +7.82 |
| Gb4 | 369.994 | 370.413 | +1.96 |
| G4 | 391.995 | 392.881 | +3.91 |
| Ab4 | 415.305 | 416.244 | +3.91 |
| A4 | 440.000 | 440.000 | 0.00 |
| Bb4 | 466.164 | 467.747 | +5.87 |
| B4 | 493.883 | 493.324 | -1.96 |
Frequencies in Hz at A4=440Hz. Positive cents = sharper than equal temperament. Negative = flatter. Formula: f = f_equal × 2(cents/1200)
Historical Context
Bach-Lehman Temperament originates from the Baroque era, developed by Bradley Lehman reconstruction (2005), attributed to J.S. Bach. It was primarily used for Well-Tempered Clavier and Bach keyboard works performed with historical awareness..
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 Bach-Lehman Temperament 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 Bach-Lehman Temperament — Get Tunable.
Tunable supports Bach-Lehman Temperament and 15 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.