Herbert A. Kellner (25 December 1938, Prague, Czecho-Slovak Republic — 21 April 2003, Darmstadt, Germany) was a distinguished German mathematician, musicologist, and scholar renowned for his work on J. S. Bach's temperament. He obtained a Doctorate in Mathematics from the University of Vienna in 1961, having studied philosophy, physics, mathematics, and astronomy. In 1975, Kellner proposed an unconventional theory suggesting he had discovered a hidden "mnemonic rule" for tuning instruments, akin to the "Guidonian hand" or the "Circle of fifths," embedded in Bach's 1722 seal, utilized during his Leipzig years. Throughout his career, Kellner wrote over 50 articles from 1975 to 1987, dedicating himself to the promotion of this theory. Although he faced significant criticism from the academic community, his extensive efforts resulted in the adoption of his tuning guidelines for more than 300 organs worldwide by the late 20th century. In contemporary music production, Kellner's 12 WT temperament has been incorporated into the default Historical European tunings package in many popular digital audio workstations (DAWs) and audio software, alongside other temperaments such as those of Prelleur, Young, Werckmeister, and Kirnberger.

The "Bach temperament" continues to be a foundational aspect of Western musicology, particularly because Bach did not provide explicit instructions on tuning harpsichords, clavichords, and organs for interpreting his seminal work, the Well-Tempered Clavier (BWV 846–893). During the late Baroque period, prior to the establishment of twelve-tone equal temperament (12-TET), keyboard tuning was typically a practical skill rather than a formally notated theory, passed down through oral tradition and apprenticeship. The title of Bach's work, Wohltemperiert ("Well-tempered"), alluded to a more flexible understanding of the sonic capabilities of keyboard instruments, designed as a showcase to highlight the nuances and distinct character of all 24 major and minor keys while avoiding "wolf intervals" (imperfect fifths). Consequently, trained musicians were expected to tune their instruments by ear to achieve these objectives. In subsequent decades, numerous scholars endeavored to uncover Bach's intended tuning system, including Andreas Werckmeister (1645–1706), F. W. Marpurg (1718–1795), and Bach's student J. P. Kirnberger (1721–1783), who proposed three temperaments in his 1771 treatise, Die Kunst des reinen Satzes in der Musik ("The Art of Pure Composition in Music"). Notably, Kirnberger's "Kirnberger III" gained prominence in the 20th century, particularly through the efforts of German musicologist and composer Herbert Kelletat (1907–2007), among others.

Kellner's distinctive theory was primarily rooted in Werckmeister's work. He asserted that Bach had access to a private and unpublished tuning system, which he deemed superior and ultimately the "perfect" choice. According to Kellner, Bach—known for his systematic and organized approach—concealed this ideal temperament in plain sight within the ornamental design of his Leipzig seal. Kellner claimed to have "deciphered" this message and developed a mathematical algorithm to reconstruct Bach's intended temperament. The resulting tuning closely resembles Werckmeister III, utilizing C-G-D-A + B-F# with quarter Pythagorean comma fifths, which Kellner adjusted slightly by incorporating fifths based on one-fifth Pythagorean comma fragments instead of fourths.

Kellner's research faced substantial criticism from musicologists, particularly regarding its weak historiographical and conceptual underpinnings. Critics highlighted the lack of evidence supporting his claims about Werckmeister's influence on Bach, with some likening his arguments to numerology. Additionally, it was noted that Kellner, unlike most reputable scholars of Bach's temperament, was primarily a mathematician without formal training in music performance, theory, or composition. Nevertheless, Herbert A. Kellner's innovative thinking prompted further exploration of the visual elements in Bach's autographs and original scores. Noteworthy studies include those conducted by German mathematician Andreas Sparschuh from Technische Universität Darmstadt in 1998 and U.S. harpsichordist and music theorist Bradley Lehman in 2005, who investigated the decorative, hand-drawn vignette featured on the frontispiece of the Well-Tempered Clavier.