Each set contains 24 pairs of prelude and fugue. The first pair is in
C major, the second in
C minor, the third in
C major, the fourth in
C minor, and so on. The rising
chromatic pattern continues until every key has been represented, finishing with a
B minor fugue. The first set was compiled in 1722 during Bach's appointment in
Köthen, and the second followed 20 years later in 1742 while he was in
Leipzig. Bach recycled some of the preludes and fugues from earlier sources: the 1720
Klavierbüchlein für Wilhelm Friedemann Bach, for instance, contains versions of eleven of the preludes of the first book of the
Well-Tempered Clavier. In Bach's own time just one similar collection was published, by
Johann Christian Schickhardt (1681–1762), whose Op. 30 ''L'alphabet de la musique'' (circa 1735) contained 24 sonatas in all keys for flute or violin and
basso continuo, and included a transposition scheme for
alto recorder.
Precursors Although the
Well-Tempered Clavier was the first collection of fully worked keyboard pieces
in all 24 keys, similar ideas had occurred earlier. Before the advent of modern tonality in the late 17th century, numerous composers produced collections of pieces in all eight
modes:
Johann Pachelbel's
Magnificat fugues (composed 1695–1706),
Georg Muffat's
Apparatus Musico-organisticus of 1690 and
Johann Speth's
Ars magna of 1693 for example. Furthermore, some two hundred years before Bach's time,
equal temperament was realized on plucked string instruments, such as the
lute and the
theorbo, resulting in several collections of pieces in all keys (although the music was not yet tonal in the modern sense of the word): • a cycle of 24
passamezzo–
saltarello pairs (1567) by () • 24 groups of dances, "clearly related to 12 major and 12 minor keys" (1584) by
Vincenzo Galilei () • 30 preludes for 12 course lute or theorbo by
John Wilson (1595–1674) One of the earliest keyboard composers to realize a collection of organ pieces in successive keys was
Daniel Croner (1656–1740), who compiled one such cycle of preludes in 1682. His contemporary Johann Heinrich Kittel (1652–1682) also composed a cycle of 12 organ preludes in successive keys.
J. C. F. Fischer's
Ariadne musica neo-organoedum (published in 1702 and reissued 1715) is a set of 20 prelude and fugue pairs in ten major and nine minor keys, and the
Phrygian mode, plus five
chorale-based
ricercars. Bach knew the collection and borrowed some of the themes from Fischer for the
Well-Tempered Clavier. Other contemporary works include the treatise
Exemplarische Organisten-Probe (1719) by
Johann Mattheson (1681–1764), which included 48
figured bass exercises in all keys,
Partien auf das Clavier (1718) by
Christoph Graupner (1683–1760) with eight suites in successive keys, and
Friedrich Suppig's
Fantasia from
Labyrinthus Musicus (1722), a long and formulaic sectional composition ranging through all 24 keys which was intended for an
enharmonic keyboard with both 31 notes per octave and pure
major thirds. Finally, a lost collection by
Johann Pachelbel (1653–1706),
Fugen und Praeambuln über die gewöhnlichsten Tonos figuratos (announced 1704), may have included prelude-fugue pairs in all keys or modes. It was long believed that Bach had taken the title
The Well-Tempered Clavier from a similarly named set of 24
Preludes and Fugues in all the keys, for which a manuscript dated 1689 was found in the library of the
Brussels Conservatoire. It was later shown that this was the work of a composer who was not even born in 1689: Bernhard Christian Weber (1 December 1712 – 5 February 1758). In fact, it was written in 1745–1750 in imitation of Bach's earlier example.
Intended tuning Bach's title suggests that he had written for a 12 note tuning system, in which all keys sounded in tune (called a "circulating temperament" or a "
well temperament"). One of the opposing systems in Bach's day was
meantone temperament in which keys with many
accidentals sound out of tune on keyboards limited to 12 pitches per octave. Bach would have been familiar with different tuning systems, and in particular as an organist would have played instruments tuned to a meantone system. During much of the 20th century it was presumed, possibly mistakenly, that Bach intended
equal temperament, which after Bach's death became popular as the standard keyboard tuning, and had been described by theorists and musicians for at least a century before Bach's birth. Accounts of Bach's own tuning practice are few and inexact. The three most cited sources are
Forkel, Bach's first biographer;
Friedrich Wilhelm Marpurg, who received information from Bach's sons and pupils; and
Johann Kirnberger, one of those pupils. Despite the presumption of equal temperament, research has continued into various unequal systems contemporary with Bach's career; there is debate whether Bach might have meant a range of similar temperaments, perhaps altered slightly in practice from piece to piece, or possibly some single, specific, "well-tempered" solution for all purposes. Modern scholars suggest some form of unequal
well temperament instead of equal temperament. Forkel reports that Bach tuned his own
harpsichords and
clavichords and found other people's tunings unsatisfactory, and also that Bach's personal tuning system allowed him to play in all keys, and to modulate into distant keys almost without the listeners noticing. In the course of a heated debate, Marpurg and Kirnberger appear to agree that Bach required all the major thirds to be sharper than pure – which is not very informative, since it is essentially a prerequisite for
any temperament to sound tolerable in all keys. Johann Georg Neidhardt, writing in 1724–1732, described a range of unequal and near-equal temperaments (as well as equal temperament itself), which can be successfully used to perform some of Bach's music, and were later praised by some of Bach's pupils and associates. J.S. Bach's son
Carl Philipp Emanuel Bach himself published a rather vague tuning method which was close to, but still not equal temperament: He wrote that it had only "most of" the
fifths tempered, without saying which ones nor by how much. Since 1950 there have been many other proposals and many performances of the work in different and unequal tunings, some derived from historical sources, some by modern authors. Whatever their provenances, these schemes all promote the existence of subtly different musical characters in different keys, due to the sizes of their intervals. However, they disagree as to which key receives which character: • Herbert Anton Kellner argued from the mid-1970s until his death that esoteric considerations such as the pattern of Bach's
signet ring,
numerology, and more could be used to determine the correct temperament. His result is somewhat similar to
Werckmeister's most familiar "correct" temperament. Kellner's temperament was widely adopted worldwide for the tuning pipe organs, and contains seven pure fifths and five
comma fifths. It is especially effective as a moderate solution to play 17th century music, if one avoids music that requires more than two
flats. • John Barnes analyzed the
Well-Tempered Claviers major-key preludes statistically, observing that some major thirds are used more often than others. His results were broadly in agreement with Kellner's and Werckmeister's patterns. His own proposed temperament from that study is a comma variant of both Kellner () and Werckmeister (), with the same general pattern tempering the naturals, and concluding with a tempered fifth B–F. •
Mark Lindley, a researcher of historical temperaments, has written several surveys of temperament styles in the German
Baroque tradition. In his publications he has recommended and devised many patterns close to those of Neidhardt, with subtler gradations of interval size. Since a 1985 article in which he addressed some issues in the
Well-Tempered Clavier, Lindley's theories have focused more on Bach's organ music than the harpsichord or clavichord works.
Title page tuning interpretations More recently there has been a series of proposals of
temperaments derived from the handwritten doodle of loops on the title page of Bach's personal 1722 manuscript. • In the course of studying German Baroque organ tunings, Andreas Sparschuh in 1999 assigned mathematical and acoustic meaning to the loops. • B. Lehman (2004, 2005) proposed a and comma layout derived from Bach's loops, which he published in 2005 in articles of three music journals. Reaction to this work has been both vigorous and mixed, with other writers producing further speculative schemes or variants. • D. Jencka (2005) proposed a variation of Lehman's layout where one of the commas is spread over three fifths (
G–
D–
A=
B), resulting in a comma division. Motivations for Jencka's approach involve an analysis of the possible logic behind the figures themselves, and his belief that a wide fifth (
B–
F) found in Lehman's interpretation is unlikely in a well-temperament from the time. • Interbartolo, Venturino, & Bof (2006) proposed a tuning system deduced from the W.T.C. title page. Their work was published the next year in a book by the same title. Nevertheless, some
musicologists say there is insufficient proof that Bach's looped drawing signifies anything reliable about a tuning method. Bach may have tuned differently per occasion, or per composition, throughout his career. • D. Schulenberg (2006) and concludes that the swirls cannot "be unambiguously interpreted as a code for a particular temperament". more recently presented an alternative reading from that of Lehman, and others, of Bach's tuning method as derived from the title page calligraphic drawing: It differs in significant details, resulting in a circulating but unequal temperament using Pythagorean-comma fifths that is effective through all 24 keys and, most important, tunable by ear without an electronic tuning device. Swich's proposal A system like Swich's, with all its major thirds more or less sharp, is confirmed by Friedrich Wilhelm Marpurg's description of the way Bach's famous student
J.P. Kirnberger was taught to tune in his lessons with Bach: Kirnberger's tuning allows all 24 keys to be played through without changing tuning nor unpleasant intervals, but with varying degrees of difference. The temperament is unequal, and the keys do not all sound the same. Compared to Werckmeister III, the other 24 key-circulating temperaments, Kirnberger's version of Bach's tuning is much more differentiated, with its 8 different kinds of major thirds (instead of Werckmeister's 4). The manuscript Bach P415 in the
Berlin State Library is the only known copy of the W.T.C. that shows the doodle. It would be a bit too cryptic for Bach's spirit, but seems to the hopeful to represent the purpose for which the masterpiece was written, and at the same time, a clue to its decipherment. In perspective, this is not surprising, since the document with the doodle is most probably the working copy Johann Sebastian Bach used in classes with his students. ==Content==