The Well-Tempered Clavier
The Well-Tempered Clavier (German: Das Wohltemperierte Klavier), BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach. He gave the title 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." Bach later compiled a second book of the same kind, dated 1742, with the title "Twenty-four Preludes and Fugues." The two works are now considered to make up a single work, The Well-Tempered Clavier, or "the 48," and are referred to as The Well-Tempered Clavier Book I and The Well-Tempered Clavier Book II respectively. The Well-Tempered Clavier and Twenty-four Preludes and Fugues are generally regarded as being among the most influential works in the history of Western classical music.
Composition history 
The first set was compiled in the year 1722 during Bach's appointment in Köthen; the second followed 20 years later in 1742 while he was in Leipzig. Both 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.
Each set contains twenty-four pairs of preludes and fugues. The first pair is in C major, the second in C minor, the third in C-sharp major, the fourth in C-sharp minor, and so on. The rising chromatic pattern continues until every key has been represented, finishing with a B-minor fugue.
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. The C-sharp 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. The far-reaching influence of Bach's music is evident in that the fugue subject in Mozart's Prelude and Fugue in C major, K. 394, is similar in structure to that of the A-flat major Fugue in Book II of the Well-Tempered Clavier. This pattern is found also in the C major fugue subject of Book II. Another similar theme is the third movement fugue subject in the Concerto for Two Harpsichords, BWV 1061.
Bach's title suggests that he had written for a (12-note) well-tempered tuning system in which all keys sounded in tune (also known as "circular temperament"). The opposing system in Bach's day was meantone temperament in which keys with many accidentals sound out of tune. (See also musical tuning). It is sometimes assumed that 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.
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 (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 Giacomo Gorzanis (c.1520–c.1577)
- 24 groups of dances, "clearly related to 12 major and 12 minor keys" (1584) by Vincenzo Galilei (c.1528–1591)
- 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.
Ariadne musica neo-organoedum, by J.C.F. Fischer (1656–1746) was published in 1702 and reissued 1715. It 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 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 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). It was in fact written in 1745–50, and in imitation of Bach's example.
Bach's example inspired numerous composers of the 19th century, however, in his own time no similar collections were published, except one by Johann Christian Schickhardt (1681–1762), whose Op. 30 L'alphabet de la musique, contained 24 sonatas for recorder/flute/violin, in all keys.
Musical style and content 
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 individual numbers exhibit typical Baroque melodic forms, often coupled to an extended free coda (e.g. Book I preludes in C minor, D major, and B-flat major).
The Preludes are notable also for their odd or irregular numbers of measures, both as to phrases and as to the entire length of 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 (BWV 849 and 867) and one two-voiced (BWV 855) ones. The fugues employ a full range of contrapuntal devices (fugal exposition, thematic inversion, stretto, etc.), but are generally more compact than Bach's fugues for organ.
The best-known piece from either book is the first prelude of Book I, a simple progression of arpeggiated chords. The technical simplicity 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.
Later significance and influence 
The first complete recording of the Well-Tempered Clavier was made by Edwin Fischer between 1933 and 1936. Other notable recordings have been made by Wanda Landowska, Rosalyn Tureck, Glenn Gould, Friedrich Gulda, Gustav Leonhardt, Sviatoslav Richter, Ralph Kirkpatrick, Martin Galling, Vladimir Ashkenazy, Roger Woodward, Angela Hewitt, András Schiff (who does not use the sustain pedal for Bach), Daniel Barenboim and Zhu Xiao-Mei.
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-flat minor prelude (6 flats) with its enharmonic key of D-sharp minor (6 sharps) 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 (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: having only "most of" the fifths tempered, without saying which ones or 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 1/5 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 1/6 comma variant of both Kellner (1/5) and Werckmeister (1/4), 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 where 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 pattern of loops on Bach's 1722 title page. These loops (though truncated by a later clipping of the page) can be seen at the top of the title page image at the beginning of the article.
- 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.
- 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 1/6 and 1/12 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 1/6th commas is spread over three 5ths (G♯–D♯–A♯/B♭), resulting in a 1/18th comma division. Motivations for Jencka's approach involve an analysis of the possible logic behind the figures themselves and his belief that a wide 5th (B♭–F) 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
Nevertheless some musicologists say it is insufficiently proven 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.
- Luigi Swich, in his article "Further thoughts on Bach's 1722 temperament" (Early Music XXXIX/3, August 2011, pp. 401–407), 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 from Book 1 of The Well-Tempered Clavier. It differs in significant details, resulting in a circulating but unequal temperament using 1/5 Pythagorean-comma 5ths that is effective through all 24 keys and tunable by ear. It is based on the synchronicity between the 5th F–C and the 3rd F–A (c. 3 beats per second) and between the 5th C–G and the 3rd C–E (c. 2 beats per second). 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 described by Carlo Gervasoni in his La scuola della musica (Piacenza, 1800). Such a temperament with all its major 3rds more or less sharp is confirmed by Friedrich Wilhelm Marpurg's report about the way Johann Philipp Kirnberger was taught to tune in his lessons with Bach. It allows to play through all 24 keys without changing tuning nor unpleasant intervals, but with varying degrees of difference-the temperament being unequal, and the keys not all sounding the same.
See also 
- In the German of Bach's time the Clavier was a generic name meaning "keyboard instrument," most typically the harpsichord or clavichord – but not excluding the organ, either. Bach's Clavier compositions are now usually played on the piano or harpsichord. The modern German spelling is Das Wohltemperierte Klavier.
- Bach, Johann Sebastian; Novack, Saul (1983). The Well-Tempered Clavier: Books I and II, complete. ISBN 978-0-486-24532-4.
- Kassler, Michael (2006). "Broderip, Wilkinson and the First English Edition of the '48'". The Musical Times 147 (Summer 2006): 67–76. doi:10.2307/25434385. ISSN 00274666. Retrieved May 10, 2010.[dead link]
- Bach, J. S. (2004). In Palmer, Willard A. J. S. Bach: The Well-Tempered Clavier. Los Angeles, CA: Alfred Music Publishing. p. 4. ISBN 0-88284-831-3. Retrieved May 10, 2010.
- Arthur J. Ness. "Giacomo Gorzanis", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- Claude V. Palisca. "Vincenzo Galilei", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- Ian Spink. "John Wilson", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- The Diapason Press – General Series: John Wilson, "Thirty Preludes" in all (24) keys for lute
- John H. Baron. A 17th-Century Keyboard Tablature in Brasov, JAMS, xx (1967), pp. 279–85.
- Viorel Cosma. "Daniel Croner", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- John H. Baron. "Kittel.", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- Rudolf Walter. "Johann Caspar Ferdinand Fischer", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- Karl Geiringer. The Bach Family: Seven Generations of Creative Genius, pp. 268–9. Oxford University Press, 1954.
- Oswald Bill, Christoph Grosspietsch. Christoph Graupner: Thematisches Verzeichnis der musikalischen Werke. Carus, 2005. ISBN 3-89948-066-X
- Fredrich Suppig: Labyrinthus musicus, Calculus musicus, facsimile of the manuscripts. Tuning and Temperament Library, Volume 3, edited by Rudolf Rasch. Diapason Press, Utrecht, 1990.
- Jean M. Perreault. The Thematic Catalogue of the Musical Works of Johann Pachelbel, p. 84. Scarecrow Press, Lanham, Md. 2004. ISBN 0-8108-4970-4.
- Grove's Dictionary of Music and Musicians, 5th ed, 1954, Vol. IX, p. 223
- The Well-Tempered Clavier – notes, Estonian Record Productions
- Pippa Drummond, David Lasocki. "Johann Christian Schickhardt", Grove Music Online, ed. L. Macy (accessed 16 February 2008), grovemusic.com (subscription access).
- Anthony Tommasini, "Complex Bach Is Illuminated", New York Times, 28 October 2012; Retrieved 12 April 2013
- The Keyboard Tuning of J. S. Bach, John Charles Francis
- LaripS.com: Johann Sebastian Bach's tuning, Bradley Lehman, 2005
- The Tuning Script from Bach’s Well Tempered Clavier: A Possible 1/18th PC Interpretation, Daniel Jencka, 2006
- Bach 1722 – Il temperamento di Dio
- Kirkpatrick, Ralph. Interpreting Bach's Well-Tempered Clavier: A Performer's Discourse of Method (New Haven: Yale University Press, 1987). ISBN 0-300-03893-3.
- Ledbetter, David. Bach's Well-Tempered Clavier: The 48 Preludes and Fugues (New Haven: Yale University Press, 2002). ISBN 0-300-09707-7.
|Wikimedia Commons has media related to: The Well-Tempered Clavier|
- Well-Tempered Clavier, Book I, Book II: Free scores at the International Music Score Library Project
- Fugues of the Well-Tempered Clavier: Interactive scores calibrated to recordings by David Korevaar and analysis by Tim Smith
- Johann Sebastian Bach's Werke. Das Wohltemperirte Clavier, Erster Theil / Zweiter Theil (Leipzig 1851): Indiana University School of Music score in GIF format
- Scores of some of the Preludes and Fugues of the Well-Tempered Clavier through the Mutopia Project
- Bach's manuscript of Book II of the Well-Tempered Clavier: Facsimile of British Library Add MS 35021
- Complete, free midi recordings of books I & II by John Sankey
- Free midi recording of book II by Prof. Yo Tomita of The Queen's University, Belfast
- Complete, free midi recordings of books I and II by Alan Kennington
- Piano Society – Free audio records of WTC, MP3 files, video
- J.S. Bach's Well-Tempered Clavier / In-depth Analysis and Interpretation by Siglind Bruhn. Full text of the 1993 book.
- Animated visualizations of the music by Dr. Tim Smith of Northern Arizona University
- Graphical motif extraction for The Well-Tempered Clavier 1 and The Well-Tempered Clavier 2
- Essay by Yo Tomita about Book I of the Well-Tempered Clavier
- Program notes from the Los Angeles Chamber Orchestra
- Interpretation and analysis of JS Bach's Well-tempered Clavier by Philip Goeth (includes audio samples)
Proposed 'Bach' tunings derived from the title page
- Keyboard Tuning of Johann Sebastian Bach – interpreted by John Charles Francis
- Larips.com – "Bach" tuning resources – interpreted by Bradley Lehman
- Bach- and Well-Temperaments for Western Classical Music