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The Well-Tempered Clavier

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Title-page of Das wohtemperierte Clavier
A flat major (As-dur) fugue from the second part of Das wohtemperierte Clavier (manuscript)

The Well-Tempered Clavier (Das wohltemperierte Clavier, "Clavier" meaning "keyboard instrument") 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, appearing in 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, appearing in 1744, but entitled it only "Twenty-four Preludes and Fugues". The two are now usually referred to as "WTC Book I" and "Book II". 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 harpsichord or piano.

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. 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, Haydn, Mozart studying the work closely. In the words of Howard Goodall, "the publication of Bach's Well-Tempered Clavier in 1722 is one of the landmarks of European music history. (...) In Bach's own lifetime its influence was rapid and dramatic. Later, both Mozart and Beethoven paid homage to the collection's brilliance and importance." (Goodall, p. 122f.)

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 into the required key.

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.

Later significance and influence

The Well-Tempered Clavier is a major work of music, of great breadth and depth and musical, aesthetic, and psychological diversity and complexity, that demonstrated, both technically and through its greatness, the musical potential of circular temperaments. Such temperaments allowed unlimited modulation to widely different keys, providing the harmonic basis for classical music from Bach onwards. Although Bach's work 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.

What tuning did Bach intend?

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, who received information from Bach's sons and pupils; and Friedrich Wilhelm Marpurg and Johann Kirnberger, two 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 described a rather vague tuning which was close to, but not, equal temperament (having only "most of" the fifths tempered).

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 that the pattern of Bach's signet ring and other considerations could be used to determine the correct temperament; the result being somewhat similar to Werckmeister. Kellner's temperament has been widely adopted worldwide for the tuning of organs.
  • John Barnes analysed the major-key preludes in an attempt to show that some major thirds are used more often than others. His results were broadly in agreemeent with Kellner and Werckmeister.
  • Mark Lindley has written surveys of historical temperaments in the German Baroque tradition, recommending several similar temperaments with subtle gradations of interval size; his recommendations, though, focused on the organ music rather than harpsichord or clavichord works.
  • Andreas Sparschuh, in the course of studying German Baroque organ tunings, assigned mathematical and acoustic meaning to the apparently ornamental loops on Bach's 1722 title page (see the illustration above). 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.
  • 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 computer-assisted analysis of the Bach loops including both end-points. He interpreted the design as the beat-rates per second of fourths and fifths in a contiguous twelve semitone range. Francis identified this range as cammerton Middle C to B and demonstrated mathematically that the tuning sequence proceeds C, F, Bb in the manner of Neidhardt’s 1724 ‘Canone Harmonico'.
  • Bradley Lehman in 2004 read the Bach diagram upside-down as representing fifths modified by portions of a comma (1/6, 1/12, or pure) with tuning starting on the note F. Objections to this proposal have been raised by Kenneth Mobbs and Alexander Mackenzie.

A fact common to these schemes is 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.

Media

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References

  • Howard Goodall, Big Bangs: the story of five discoveries that changed musical history (London: Vintage, 2000). See especially Chapter 5: "Accidentals Will Happen: the invention of equal temperament." ISBN 0099283549.
  • Ralph Kirkpatrick, Interpreting Bach`s Well-Tempered Clavier : A Performer`s Discourse of Method (New Haven: Yale University Press, 1987). ISBN 0300038933.
  • David Ledbetter, Bach's Well-Tempered Clavier: The 48 Preludes and Fugues (New Haven: Yale University Press, 2002). ISBN 0300097077.
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