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'''Well-Tempered Clavier''' (in the original German: ''Das Wohltemperirte Clavier''^[2]) 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 1744, but entitled 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

Contents

Composition history

Musical style and content

Later significance and influence

Intended tuning

Title page tuning interpretations

Media

Footnotes

References

See also

External links

Sheet music

Websites

Proposed 'Bach' tunings derived from the title page

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 ^[3]. 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 for 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.
Although the ''Well-Tempered Clavier'' was the first collection of fully worked pieces in all 24 keys, similar ideas had occurred earlier: notably "Ariadne musica neo-organoedum" by the organist J.C.F. Fischer. Published in 1702 and reissued 1715, it is a set of 20 preludes and fugues in ten major and nine minor keys and the Phrygian mode, plus five chorale-based ricercars. Bach later borrowed Fischer's E-major fugue subject for his own E-major fugue of book 2. Johann Mattheson's Exemplarische Organisten-Probe of 1719 also included figured bass exercises in all keys. Bach may also have known of Friedrich Suppig's ''Fantasia'' from "Labyrinthus Musicus" of 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. Notwithstanding some similarities in presentation, Bach's aesthetic aims and inspiration were a world away from Suppig's.
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.

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 most well-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. 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. The possibility of modulating to remote harmonic regions and thereby creating unusual psychological and aesthetic effects, which became fully developed in Romantic and post-Romantic music, ultimately led to the dissolution of the tonal system itself in the work of Schoenberg and other early 20th-century atonal composers.
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.
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 listener's 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 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, unequal tunings; some derived from historical sources, some devised by modern authors:

★ 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, 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

There has been a recent series of proposals of temperaments derived in a variety of ways from the handwritten pattern of apparently ornamental loops (above) on Bach's 1722 title page.
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.
Many musicologists believe 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.

★ 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 derived from BWV 924. Details are available at the author's web site.

★ Bradley Lehman in 2004 proposed a 1/6 and 1/12 comma layout derived from Bach's loops, published 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.

Media

Footnotes

1.

★ Title page translated
2. 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 contemporary German spelling is ''Das wohltemperierte Klavier''.
3. http://findarticles.com/p/articles/mi_qa3870/is_200607/ai_n16522881] Broderip, Wilkinson and the first English edition of the '48'

References

★ 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.

See also

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

External links

Sheet music

★ Piano Sheet Music of Compositions by J S Bach including the Well Tempered Clavier (Out of Copyright Editions)

★ Fugues of the Well-Tempered Clavier: Interactive scores calibrated to recordings by David Korevaar and analysis by Tim Smith.

★ Scores of the Well-Tempered Clavier through the Mutopia Project.

★

Websites

★ J.S. Bach's Well-Tempered Clavier / In-depth Analysis and Interpretation by Siglind Bruhn. Full text of the 1951 book.

★ Animated visualizations of the music by Dr. Tim Smith of Northern Arizona University

★ Blog post about Juan Downey's Bachdisc, with video.(in spanish)

Proposed 'Bach' tunings derived from the title page

★ How tuned Bach? - Discussion group

★ Keyboard Tuning of Johann Sebastian Bach - interpreted by John Charles Francis

★ Larips.com - "Bach" tuning resources - interpreted by Bradley Lehman

★ Temperament derived from the 1722 title page (1999) - interpreted by Andreas Sparschuh (in German)