The Well-Tempered Clavier
The Well-Tempered Clavier, BWV 846–893, is a collection of two sets of preludes and fugues in all 24 major and minor keys, composed for solo keyboard by Johann Sebastian Bach. In Bach's time Clavier was a generic name indicating a variety of keyboard instruments, most typically a harpsichord or clavichord – but not excluding an organ.
The modern German spelling for the collection is Das wohltemperierte Klavier. Bach gave the title Das Wohltemperirte Clavier to a book of preludes and fugues in all 24 major and minor keys, dated 1722, composed "for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study". Some 20 years later Bach compiled a second book of the same kind, which became known as The Well-Tempered Clavier, Part Two.
Modern editions usually refer to both parts as The Well-Tempered Clavier, Book I and The Well-Tempered Clavier, Book II, respectively. The collection is generally regarded as being among the most important works in the history of classical music.
Composition history
Each set contains twenty-four 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; 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. The C major prelude and fugue in book one was originally in C major – Bach added a key signature of seven sharps and adjusted some accidentals to convert it to the required key.
In Bach's own time just one similar collection was published, by Johann Christian Schickhardt, whose Op. 30 L'alphabet de la musique, 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 seven modes: Johann Pachelbel's magnificat fugues, 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 :- a cycle of 24 passamezzo–saltarello pairs by
- 24 groups of dances, "clearly related to 12 major and 12 minor keys" by Vincenzo Galilei
- 30 preludes for 12-course lute or theorbo by John Wilson
J.C.F. Fischer's Ariadne musica neo-organoedum is a set of 20 prelude-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 by Johann Mattheson, which included 48 figured bass exercises in all keys, Partien auf das Clavier by Christoph Graupner with eight suites in successive keys, and Friedrich Suppig's Fantasia from Labyrinthus Musicus, a long and formulaic sectional composition ranging through all 24 keys which was intended for an enharmonic keyboard with 31 notes per octave and pure major thirds. Finally, a lost collection by Johann Pachelbel, Fugen und Praeambuln über die gewöhnlichsten Tonos figuratos, 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. It was in fact written in 1745–50, and in imitation of Bach's example.
''Well-Tempered'' tuning
Bach's title suggests that he had written for a well-tempered tuning system in which all keys sounded in tune. The opposing system in Bach's day was meantone temperament in which keys with many accidentals sound out of tune. Bach would have been familiar with different tuning systems, and in particular as an organist would have played instruments tuned to a meantone system.It is sometimes assumed that by "well-tempered" Bach intended equal temperament, the standard modern keyboard tuning which became popular after Bach's death, but modern scholars suggest instead a form of well temperament. There is debate whether Bach meant a range of similar temperaments, perhaps even altered slightly in practice from piece to piece, or a single specific "well-tempered" solution for all purposes.
Intended tuning
During much of the 20th century it was assumed that Bach wanted equal temperament, which had been described by theorists and musicians for at least a century before Bach's birth. Internal evidence for this may be seen in the fact that in Book 1 Bach paired the E minor prelude with its enharmonic key of D minor for the fugue. This represents an equation of the most tonally remote enharmonic keys where the flat and sharp arms of the circle of fifths cross each other opposite to C major. Any performance of this pair would have required both of these enharmonic keys to sound identically tuned, thus implying equal temperament in the one pair, as the entire work implies as a whole. However, research has continued into various unequal systems contemporary with Bach's career. 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.Forkel reports that Bach tuned his own harpsichords and clavichords and found other people's tunings unsatisfactory; his own allowed him to play in all keys and to modulate into distant keys almost without the listeners noticing it. Marpurg and Kirnberger, in the course of a heated debate, appear to agree that Bach required all the major thirds to be sharper than pure—which is in any case virtually a prerequisite for any temperament to be good in all keys.
Johann Georg Neidhardt, writing in 1724 and 1732, described a range of unequal and near-equal temperaments, 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: having 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, with seven pure fifths and five comma fifths, has been widely adopted worldwide for the tuning of organs. It is especially effective as a moderate solution to play 17th-century music, shying away from tonalities that have more than two flats.
- John Barnes analyzed the Well-Tempered Clavier 's 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
- Andreas Sparschuh, in the course of studying German Baroque organ tunings, assigned mathematical and acoustic meaning to the loops. Each loop, he argued, represents a fifth in the sequence for tuning the keyboard, starting from A. From this Sparschuh devised a recursive tuning algorithm resembling the Collatz conjecture in mathematics, subtracting one beat per second each time Bach's diagram has a non-empty loop. In 2006 he retracted his 1998 proposal based on A = 420 Hz, and replaced it with another at A = 410 Hz.
- Michael Zapf in 2001 reinterpreted the loops as indicating the rate of beating of different fifths in a given range of the keyboard in terms of seconds-per-beat, with the tuning now starting on C.
- John Charles Francis in 2004 performed a mathematical analysis of the loops using Mathematica under the assumption of beats per second. In 2004, he also distributed several temperaments derived from BWV 924.
- Bradley Lehman in 2004 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.
- Daniel Jencka in 2005 proposed a variation of Lehman's layout where one of the commas is spread over three fifths, 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 found in Lehman's interpretation is unlikely in a well-temperament from the time.
- Graziano Interbartolo and others in 2006 proposed a tuning system deduced from the WTK title page. Their work was also published in a book: Bach 1722 – Il temperamento di Dio – Le scoperte e i significati del 'Wohltemperirte Clavier, p. 136 – Edizioni Bolla, Finale Ligure.
- David Schulenberg, in his book The Keyboard Music of J. S. Bach, allows that Lehman's argument is "ingenious" but counters that it "lacks documentary support and concludes that the swirls cannot "be unambiguously interpreted as a code for a particular temperament".
- Luigi Swich, in his article "Further thoughts on Bach's 1722 temperament", more recently presents an alternative reading from that of Bradley Lehman and others of Johann Sebastian 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. It is based on the synchronicity between the fifth F–C and the third F–A and between the fifth C–G and the third C–E. Such a system is reminiscent of Herbert Anton Kellner's 1977 temperament and even more, among the others, the temperament of the 1688 Arp Schnitger organ in Norden, St Ludgeri and the temperament later described by Carlo Gervasoni in his La scuola della musica. Such a system with all its major thirds more or less sharp is confirmed by Friedrich Wilhelm Marpurg's report about the way a famous student of Bach's, Johann Philipp Kirnberger, was taught to tune in his lessons with Bach. It allows all 24 keys to be played through without changing tuning nor unpleasant intervals, but with varying degrees of difference-the temperament being unequal, and the keys not all sounding the same. Compared to Werckmeister III, the other 24 keys-circulating temperament, Bach's tuning is much more differentiated with its 8 different kinds of major thirds. The manuscript Bach P415 in Berlin Staatsbibliothek is the only known copy of the WTC to show this drawing which represents, a bit cryptically in Bach's spirit, the purpose for which the masterpiece was written and its solution at the same time. Not surprisingly, since this is most probably the working copy that Johann Sebastian Bach used in his classes.
Content
Book I
The first book of the Well-Tempered Clavier was composed in the early 1720s, with Bach's autograph dated 1722. Apart from the early versions of several preludes included in W. F. Bach's Klavierbüchlein there is an almost complete collection of "Prelude and Fughetta" versions predating the 1722 autograph, known from a later copy by an unidentified scribe.Title page
The title page of the first book of the Well-Tempered Clavier reads:No. 1: Prelude and Fugue in C major, BWV 846
An early version of the prelude, BWV 846a, is found in Klavierbüchlein für Wilhelm Friedemann Bach. The prelude is a seemingly simple progression of arpeggiated chords, one of the connotations of 'préluder' as the French lutenists used it: to test the tuning. Bach used both G and A into the harmonic meandering.No. 2: Prelude and Fugue in C minor, BWV 847
. Prelude also in WFB Klavierbüchlein, No. 15: Praeludium 2.No. 3: Prelude and Fugue in C major, BWV 848
. Prelude also in WFB Klavierbüchlein, No. 21: Praeludium .No. 4: Prelude and Fugue in C minor, BWV 849
. Prelude also in WFB Klavierbüchlein, No. 22: Praeludium .No. 5: Prelude and Fugue in D major, BWV 850
. Prelude also in WFB Klavierbüchlein, No. 17: Praeludium 4.No. 6: Prelude and Fugue in D minor, BWV 851
. Prelude also in WFB Klavierbüchlein, No. 16: Praeludium 3.No. 7: Prelude and Fugue in E major, BWV 852
No. 8: Prelude in E minor and Fugue in D minor, BWV 853
. Prelude also in WFB Klavierbüchlein, No. 23: Praeludium . The fugue was transposed from D minor to D minor.No. 9: Prelude and Fugue in E major, BWV 854
. Prelude also in WFB Klavierbüchlein, No. 19: Praeludium 6.No. 10: Prelude and Fugue in E minor, BWV 855
. Early version BWV 855a of the Prelude in Klavierbüchlein für Wilhelm Friedemann Bach.No. 11: Prelude and Fugue in F major, BWV 856
. Prelude also in WFB Klavierbüchlein, No. 20: Praeludium 7.No. 12: Prelude and Fugue in F minor, BWV 857
. Prelude also in WFB Klavierbüchlein, No. 24: Praeludium .No. 13: Prelude and Fugue in F major, BWV 858
No. 14: Prelude and Fugue in F minor, BWV 859
No. 15: Prelude and Fugue in G major, BWV 860
No. 16: Prelude and Fugue in G minor, BWV 861
No. 17: Prelude and Fugue in A major, BWV 862
No. 18: Prelude and Fugue in G minor, BWV 863
No. 19: Prelude and Fugue in A major, BWV 864
No. 20: Prelude and Fugue in A minor, BWV 865
No. 21: Prelude and Fugue in B major, BWV 866
No. 22: Prelude and Fugue in B minor, BWV 867
No. 23: Prelude and Fugue in B major, BWV 868
No. 24: Prelude and Fugue in B minor, BWV 869
Book II
The two major primary sources for this collection of Preludes and Fugues are the "London Original" manuscript, dated between 1739 and 1742, with scribes including Bach, his wife Anna Magdalena and his oldest son Wilhelm Friedeman, which is the basis for Version A of WTC II, and for Version B, that is the version published by the 19th-century Bach-Gesellschaft, a 1744 copy primarily written by Johann Christoph Altnickol, with some corrections by Bach, and later also by Altnickol and others.No. 1: Prelude and Fugue in C major, BWV 870
No. 2: Prelude and Fugue in C minor, BWV 871
No. 3: Prelude and Fugue in C major, BWV 872
No. 4: Prelude and Fugue in C minor, BWV 873
No. 5: Prelude and Fugue in D major, BWV 874
No. 6: Prelude and Fugue in D minor, BWV 875
No. 7: Prelude and Fugue in E major, BWV 876
No. 8: Prelude and Fugue in D minor, BWV 877
No. 9: Prelude and Fugue in E major, BWV 878
No. 10: Prelude and Fugue in E minor, BWV 879
No. 11: Prelude and Fugue in F major, BWV 880
No. 12: Prelude and Fugue in F minor, BWV 881
. Prelude as a theme with variations. Fugue in three voices.No. 13: Prelude and Fugue in F major, BWV 882
No. 14: Prelude and Fugue in F minor, BWV 883
No. 15: Prelude and Fugue in G major, BWV 884
No. 16: Prelude and Fugue in G minor, BWV 885
No. 17: Prelude and Fugue in A major, BWV 886
No. 18: Prelude and Fugue in G minor, BWV 887
No. 19: Prelude and Fugue in A major, BWV 888
No. 20: Prelude and Fugue in A minor, BWV 889
No. 21: Prelude and Fugue in B major, BWV 890
No. 22: Prelude and Fugue in B minor, BWV 891
No. 23: Prelude and Fugue in B major, BWV 892
No. 24: Prelude and Fugue in B minor, BWV 893
Style
Musically, the structural regularities of the Well-Tempered Clavier encompass an extraordinarily wide range of styles, more so than most pieces in the literature. The preludes are formally free, although many of them exhibit typical Baroque melodic forms, often coupled to an extended free coda. The preludes are also notable for their odd or irregular numbers of measures, in terms of both the phrases and the total number of measures in a given prelude.Each fugue is marked with the number of voices, from two to five. Most are three- and four-voiced fugues, and there are only two five-voiced fugues, and one two-voiced fugue. The fugues employ a full range of contrapuntal devices, but are generally more compact than Bach's fugues for organ.
Several attempts have been made to analyse the motivic connections between each prelude and fugue, – most notably Wilhelm Werker and Johann Nepomuk David The most direct motivic reference appears in the B major set from Book 1, in which the fugue subject uses the first four notes of the prelude, in the same metric position but at half speed.
Reception
Both books of the Well-Tempered Clavier were widely circulated in manuscript, but printed copies were not made until 1801, by three publishers almost simultaneously in Bonn, Leipzig and Zurich. Bach's style went out of favour in the time around his death, and most music in the early Classical period had neither contrapuntal complexity nor a great variety of keys. But, with the maturing of the Classical style in the 1770s, the Well-Tempered Clavier began to influence the course of musical history, with Haydn and Mozart studying the work closely.Mozart transcribed some of the fugues of the Well-Tempered Clavier for string ensemble:
- BWV 853 → K. 404a/1
- BWV 871 → K. 405/1
- BWV 874 → K. 405/5
- BWV 876 → K. 405/2
- BWV 877 → K. 405/4
- BWV 878 → K. 405/3
- BWV 882 → K. 404a/3
- BWV 883 → K. 404a/2
Hans von Bülow called The Well-Tempered Clavier the "Old Testament" of music. In the liner notes to the Clair de Lune compilation of piano encores issued by CBS Masterworks, Philippe Entremont relates an anecdote in which von Bülow, having a distaste for the endless clamor for encores, was facing a thunderously applauding house and raised his hand, saying "Ladies and Gentlemen! If you do not stop this immediately I shall play you Bach's 48 preludes and fugues from beginning to end!" The audience laughed but also stopped applauding as they knew von Bülow was able to perform the work from memory.
Bach's example inspired numerous composers of the 19th century, for instance in 1835 Chopin started composing his 24 Preludes, Op. 28, inspired by the Well-Tempered Clavier. In the 20th century Dmitri Shostakovich wrote his 24 Preludes and Fugues, an even closer reference to Bach's model. Mario Castelnuovo-Tedesco wrote Les Guitares bien tempérées, a set of 24 preludes and fugues for two guitars, in all 24 major and minor keys, inspired in both title and structure by Bach's work.
First prelude of Book I
The best-known piece from either book is the first prelude of Book I. Anna Magdalena Bach copied a short version of this prelude in her 1725 Notebook. The accessibility of this C major prelude has made it one of the most commonly studied piano pieces for students completing their introductory training. This prelude also served as the basis for the Ave Maria of Charles Gounod.Tenth prelude of Book I
transcribed a piano arrangement of the early version of Prelude and Fugue in E minor, transposed into a Prelude in B minor.Recordings
The first complete recording of the Well-Tempered Clavier was made on the piano by Edwin Fischer for EMI between 1933 and 1936. The second was made by Wanda Landowska on harpsichord for RCA Victor in 1949 and 1952. The first complete recording of the work on a clavichord was made by Ralph Kirkpatrick in 1959 and 1967 for Deutsche Grammophon. Helmut Walcha, better known as an organist, recorded both books between 1959 and 1961 on a harpsichord. Another noteworthy version of both books was recorded by Australian pianist Roger Woodward in 2007 in Bavaria. Daniel Chorzempa made the first recording using multiple instruments for Philips in 1982. Artists to have recorded the collection twice include Ralph Kirkpatrick and Angela Hewitt, João Carlos Martins, András Schiff, Rosalyn Tureck, and Tatiana Nikolayeva. Anthony Newman has recorded it three times – twice on harpsichord and once on piano. As of 2013, over 150 recordings have been documented, including the above keyboard instruments as well as transcriptions for ensembles and also synthesizers. Wendy Carlos recorded the Prelude and Fugue in E major and the Prelude and Fugue in C minor in versions for Moog synthesizer on her album Switched-On Bach.A recording of 2.1 by Glenn Gould was sent into space in 1977 on the Voyager Golden Record.
Audio of Book I
Harpsichord performances of various parts of Book I by Martha Goldstein are in the public domain. Such harpsichord performances may, for instance, be tuned in equal temperament, or in Werckmeister temperament. In addition to Martha Goldstein, Raymond Smullyan is another well-known artist for whom several performances from Book I are in the public domain.In March 2015, the pianist Kimiko Douglass-Ishizaka released a new and complete recording of Book 1 into the public domain. Her performances are available below, beginning with the Prelude No. 1 in C Major :