Well-Tempered Clavier

Well-Tempered Clavier

"The Well-Tempered Clavier" ("Das Wohltemperirte Clavier" in the original old German spelling) [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".] , BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach. He first 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, but titled it only "Twenty-four Preludes and Fugues." The two works are now usually considered to comprise the "Well-Tempered Clavier" and are referred to respectively as Books I and II. "The Well-Tempered Clavier" is generally regarded as one of the most influential works in the history of Western Classical Music.

Composition history

The first book was compiled during Bach's appointment in Köthen; the second book followed it 22 years later 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 [http://findarticles.com/p/articles/mi_qa3870/is_200607/ai_n16522881] Broderip, Wilkinson and the first English edition of the '48'] . 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 book 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 Fantasy and Fugue in C Major K. 394 is isomorphic to that of the A-flat major Fugue in Book I 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 eight modes: Johann Pachelbel's magnificat fugues (composed 1695–1706), Georg Muffat's "Apparatus Musico-organisticus" of 1690 and Johannes Speth's "Ars magna" of 1693 are but a few examples. 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) [GroveOnline|Giacomo Gorzanis|Arthur J. Ness|16 February|2008]
* 24 groups of dances, "clearly related to 12 major and 12 minor keys" (1584) by Vincenzo Galilei (c.1528–1591) [GroveOnline|Vincenzo Galilei|Claude V. Palisca|16 February|2008]
* 30 preludes for 12-course lute or theorbo by John Wilson (1595–1674) [GroveOnline|John Wilson|Ian Spink|16 February|2008] [ [http://diapason.xentonic.org/dp/dp049.html The Diapason Press - General Series: John Wilson, "Thirty Preludes" in all (24) keys for lute] ] 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. [John H. Baron. "A 17th-Century Keyboard Tablature in Brasov", JAMS, xx (1967), pp. 279–85.] [GroveOnline|Daniel Croner|Viorel Cosma|16 February|2008] His contemporary Johann Heinrich Kittel (1652–1682) also composed a cycle of 12 organ preludes in successive keys. [GroveOnline|Kittel.|John H. Baron|16 February|2008]

"Ariadne musica neo-organoedum", by J.C.F. Fischer (died 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". [GroveOnline|Johann Caspar Ferdinand Fischer|Rudolf Walter|16 February|2008] Other contemporary works include the treatise "Exemplarische Organisten-Probe" (1719) by Johann Mattheson (1681–1764), which included 48 figured bass exercises in all keys,Karl Geiringer. "The Bach Family: Seven Generations of Creative Genius", pp. 268–9. Oxford University Press, 1954.] "Partien auf das Clavier" (1718) by Christoph Graupner (1683–1760) with eight suites in successive keys, [Oswald Bill, Christoph Grosspietsch. "Christoph Graupner: Thematisches Verzeichnis der musikalischen Werke". Carus, 2005. ISBN 389948066X] 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. ["Fredrich Suppig: Labyrinthus musicus, Calculus musicus, facsimile of the manuscripts". "Tuning and Temperament Library", Volume 3, edited by Rudolf Rasch. Diapason Press, Utrecht, 1990.] 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. [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.]

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. [GroveOnline|Johann Christian Schickhardt|Pippa Drummond, David Lasocki|16 February|2008]

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).

Each fugue is marked with the number of voices, from two to five. Most are three- and four-voiced fugues. 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

Although the "Well-Tempered Clavier" was not the first pantonal (using all keys) composition, it was by far the most influential. The very nature of the piece (as implied by its title page) established a tuning requirement for harmonies which were to become the basis for all Western music developed through the early 20th century. The WTC (Well-Tempered Clavier) does not include very remote modulations, but instead demonstrates the ability of a single instrument in tempered tuning to play in all 24 keys without having to be tuned to new fundamentals. Beethoven, who made remote modulations central to his music, was heavily influenced by the "Well-Tempered Clavier", since performing it in concerts in his youth was part of his star attraction and reputation. Further reaching modulations to remote harmonic regions were mostly associated with later Romantic and post-Romantic music, ultimately leading to the functional extension in jazz harmony. The atonal system of the 20th century, although still taking the 12-tone chromatic scale (that Bach used) as a foundation, effectively did away with musical keys altogether.

In addition to its use of all keys, the "Well-Tempered Clavier" was unusual in the very wide range of techniques and modes of expression used by Bach in the fugues. No other composer had produced such vividly characterised and compelling pieces in the fugal form, which was often regarded as a theoretical exercise. Many later composers studied Bach's work in an effort to improve their own fugal writing: Verdi even found it useful for his last work, Falstaff. fact|date=January 2008

The first complete recording of the "Well-Tempered Clavier" was made by Edwin Fischer between 1933 and 1936.

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. 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 two most cited sources are Forkel, Bach's first biographer, and 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 purewhich 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 what key receives what 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 anlld 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, in his long career as an expert 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 apparently ornamental loops (above) on Bach's 1722 title page.
* 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 has 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 [http://www.eunomios.org/contrib/francis1/francis1.html derived from BWV 924] . More details are also available at the author's web site.
* Bradley Lehman in 2004 proposed [http://www.larips.com/ 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.

Despite this recent research however, many 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.


:"See List of compositions by Johann Sebastian Bach."

ee also

*Complete list of works included in the Well-Tempered Clavier listed by BWV.



* 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.

External links

heet music

* [http://jan.ucc.nau.edu/~tas3/wtc.html Fugues of the Well-Tempered Clavier] : Interactive scores calibrated to recordings by David Korevaar and analysis by Tim Smith.
* [http://www.mutopiaproject.org/cgibin/make-table.cgi?collection=bachwtk&preview=1 Scores of the Well-Tempered Clavier through the Mutopia Project.]


* [http://pianosociety.com/cms/index.php?section=101 Piano Society - Free Audio Records of WTC, MP3 files + Video]
* [http://www-personal.umich.edu/~siglind/text.htm J.S. Bach's Well-Tempered Clavier / In-depth Analysis and Interpretation] by Siglind Bruhn. Full text of the 1951 book.
* [http://jan.ucc.nau.edu/~tas3/wtc.html Animated visualizations of the music] by Dr. Tim Smith of Northern Arizona University
* [http://ritalink.org/2007/08/25/mira-como-suena/ Blog post about Juan Downey's Bachdisc, with video.(in Spanish)]
* [http://www.geocities.jp/imyfujita/index.html Music of Sacred Temperament]

Proposed 'Bach' tunings derived from the title page

* [http://launch.groups.yahoo.com/group/bach_tunings How tuned Bach?] - Discussion group
* [http://bach.tuning.googlepages.com/ Keyboard Tuning of Johann Sebastian Bach] - interpreted by John Charles Francis
* [http://www.larips.com Larips.com - "Bach" tuning resources] - interpreted by Bradley Lehman
* [http://www.strukturbildung.de/Andreas.Sparschuh/ Temperament derived from the 1722 title page (1999)] - interpreted by Andreas Sparschuh (in German)
* [http://www.bach1722.com/ Temperament derived from the 1722 title page (2007)] - interpreted by Graziano Interbartolo(in Italian)

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