A4 in Bach/Lehman

A4 is 440.000 Hz in all tuning systems that use A=440 as their reference. In Bach/Lehman, the surrounding chromatic notes are tuned according to a reconstruction by Bradley Lehman (2005) of Bach's intended tuning, decoded from the decorative loops on the title page of the Well-Tempered Clavier autograph.

This system was used for Bach's Well-Tempered Clavier and Late Baroque German keyboard music.

Chromatic Scale at A4=440 Hz in Bach/Lehman

The table below shows all 12 chromatic notes at octave 4. A4 is the tuning reference — its frequency is 440.000 Hz in all temperaments at this concert pitch. The other notes show how Bach/Lehman tunes each interval relative to A4.

Positive cents = sharper than equal temperament. Negative = flatter. 100 cents = 1 semitone.

Bach/Lehman: Mathematical Formula

Bradley Lehman's 2005 reconstruction interprets the ornamental squiggle on Bach's title page of the Well-Tempered Clavier as a tuning diagram specifying the size of each fifth. Reading the loops as instructions (large loop = wider fifth, small loop = narrower fifth, no loop = pure fifth), Lehman proposes a specific distribution: several fifths narrowed by 1/12 comma, several pure, and a few slightly widened. The resulting system places C, G, D, A, E, B, and F# major in near-equal temperament, while remote keys like Eb, Ab, and Db have notably wider thirds. The tuning gives good keys a slightly warmer sound and remote keys a brighter, more brilliant character.

Formula type: Cent offsets from equal temperament

How Bach/Lehman Sounds

The Bach-Lehman temperament produces a sound that many performers describe as ideally suited to the Well-Tempered Clavier. The near-key signatures have a smoothness and warmth slightly richer than equal temperament, while the more distant keys — particularly F# major — take on a luminous, crystalline quality that sounds distinctive rather than out of tune. Key characters are present but gentle, creating a sense of tonal variety without the strong contrasts of Werckmeister or Kirnberger temperaments. Performers and recording artists who have adopted the Bach-Lehman system report that the Well-Tempered Clavier sounds "right" in a way that other temperaments, including equal temperament, do not fully capture.

Historical Context

Bradley Lehman published his Bach-Lehman reconstruction in the February and May 2005 issues of Early Music, arguing that Bach encoded his preferred tuning as a calligraphic diagram on the title page of the 1722 Well-Tempered Clavier autograph. The proposal generated significant scholarly debate: supporters found it elegant and acoustically convincing, while skeptics argued the ornamental loops were decorative rather than instructional. Lehman subsequently recorded the 48 preludes and fugues in his proposed tuning, providing an audible demonstration. The Bach-Lehman temperament has attracted substantial interest among harpsichordists and pianists working on Baroque repertoire, even among those who remain uncertain about its historical authenticity.

Other Tuning Systems for A4

See A4 in all temperaments →

For a full deep dive into Bach/Lehman, see the Tunable guide to Bach/Lehman.