Bach Temperament

A Bach Temperament refers to the way the composer Johann Sebastian Bach tuned his harpsichords and clavichords for the interpretation, among other pieces, of his masterpiece Das wohltemperirte Clavier (1722 / 1740-1742).

There exists little certainty on how this temperament is structured. Bach did not leave written instructions on how he tuned. He was famous for tuning his keyboard in a swift and easy way, but it is not clear how. It should also be kept in mind that Bach's musical education was based on the meantone, the "dominating" keyboard tuning during the Baroque period (ca. 1600 to ca. 1750).

Interpretations
The earliest known source for the tuning is the publication in 1753 of Versuch über die wahre Art das Clavier zu spielen by Carl Philipp Emanuel Bach. This work describes how to tune the fifths slightly different from purity, accompanied by an aural control of major and minor thirds, as well as full chords, so that all twenty-four keys sound clean and crisp, even to the highly trained ear. This method is purely auditory in nature, but Bach failed to prescribe an unambiguous description of his reconstruction of the meantone temperament.

There have been multiple attempts to rediscover Bach's intended tuning system.

Johann Kirnberger published Die Kunst des reinen Satzes in der Musik in 1771. As a student of Bach, he claims to follow Bach's teachings. However, this source also does not offer full certainty on how Bach tuned his keyboard.

Friedrich Wilhelm Marpurg published in 1776 Versuch über die musikalische Temperatur. He proposes that Bach used equal temperament (12TET). This hypothesis has been widely adopted in many publications, but the vast majority of scientific publications in this field no longer support this hypothesis since Kelletat (1960).

Johann Nikolaus Forkel published in 1802 Über Johann Sebastian Bach's Leben, Kunst und Kunstwerke. Forkel, a friend of Bach's sons and, therefore, an important source of information, also does not indicate exactly how Bach tuned the keyboard. Forkel knew from correspondence with Kirnberger that the latter did not agree with his former student Marpurg.

Robert Holford Macdowall Bosanquet (1876) questioned whether Bach would have applied the equal temperament.

Herbert Kelletat (1960) suggests that Kirnberger III, or a similar temperament, was Bach's temperament.

A. Sparschuh, a mathematician, was the first to propose a concrete hypothesis for a Bach tuning in 1998, based on a row of decorative curls above the title of Das wohltemperirte Clavier. His initial hypothesis leads to an alternative diapason, is thus uncertain, and he subsequently has proposed a number of successive alternatives.

Harpsichordist Bradley Lehman published an alternative hypothesis in 2005, also based on the row of decorative curls above the title of Das wohltemperierte Klavier. In this way he constructed another possible tuning method. This idea also prompted others, such as John O'Donnell and John Francis, to adopt their own interpretation of the curls, resulting in alternative temperaments.

The harpsichord manufacturer Jobin E. published in 2005 a hypothesis with two pure major thirds, and three unconventionally very slightly augmented fifths (those on A-flat, E-flat and B-flat). This configuration of fifths leads to a very good match of the characteristics of the fifths with the characteristics of the corresponding curls on the Bach figure.

The precise definition of the Bach tuning still remains unclear. The only certainty has become that it must be well-tempered, and preferably not the equal temperament.