Well-Tempered Clavier
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''The Well-Tempered Clavier'',
BWV The (BWV; ; ) is a catalogue of compositions by Johann Sebastian Bach. It was first published in 1950, edited by Wolfgang Schmieder. The catalogue's second edition appeared in 1990. An abbreviated version of that second edition, known as BWV2 ...
846–893, consists of two sets of preludes and fugues in all 24 major and minor keys for keyboard by
Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the '' Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard wo ...
. In the composer's time, ''clavier'', meaning keyboard, referred to a variety of instruments, most typically the
harpsichord A harpsichord ( it, clavicembalo; french: clavecin; german: Cembalo; es, clavecín; pt, cravo; nl, klavecimbel; pl, klawesyn) is a musical instrument played by means of a keyboard. This activates a row of levers that turn a trigger mechanism ...
or
clavichord The clavichord is a stringed rectangular keyboard instrument that was used largely in the Late Middle Ages, through the Renaissance, Baroque and Classical eras. Historically, it was mostly used as a practice instrument and as an aid to compositi ...
, but not excluding the organ. The modern German spelling for the collection is ' (WTK; ). Bach gave the title ' to a book of preludes and fugues in all 24 keys, major and minor, 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 (24 pairs of preludes and fugues), which became known as ''The Well-Tempered Clavier'', Part Two (in German: ''Zweyter Theil'', modern spelling: ''Zweiter Teil''). Modern editions usually refer to both parts as ''The Well-Tempered Clavier, Book I'' (WTC I) and ''The Well-Tempered Clavier, Book II'' (WTC II), respectively. The collection is generally regarded as one of 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 C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
, the second in
C minor C minor is a minor scale based on C, consisting of the pitches C, D, E, F, G, A, and B. Its key signature consists of three flats. Its relative major is E major and its parallel major is C major. The C natural minor scale is: : Cha ...
, the third in
C major C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
, the fourth in
C minor C minor is a minor scale based on C, consisting of the pitches C, D, E, F, G, A, and B. Its key signature consists of three flats. Its relative major is E major and its parallel major is C major. The C natural minor scale is: : Cha ...
, and so on. The rising
chromatic Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a p ...
pattern continues until every key has been represented, finishing with a
B minor B minor is a minor scale based on B, consisting of the pitches B, C, D, E, F, G, and A. Its key signature has two sharps. Its relative major is D major and its parallel major is B major. The B natural minor scale is: : Changes n ...
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 Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...
. Bach recycled some of the preludes and fugues from earlier sources: the 1720 ''
Klavierbüchlein für Wilhelm Friedemann Bach ''Klavierbüchlein für Wilhelm Friedemann Bach'' (Bach's original spelling: ''Clavier-Büchlein vor Wilhelm Friedemann Bach'') is a collection of keyboard music compiled by the German Baroque composer Johann Sebastian Bach for his eldest son Wil ...
'', 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 In Western musical notation, a key signature is a set of sharp (), flat (), or rarely, natural () symbols placed on the staff at the beginning of a section of music. The initial key signature in a piece is placed immediately after the clef a ...
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 Johann Christian Schickhardt (or Schikardt, c. 1682c. 25 March 1762) was a German composer and woodwind player. Biography Schickhardt was born in Braunschweig (Brunswick) and received his musical education at the Braunschweig-Wolfenbüttel court ...
(1681–1762), whose Op. 30 ''L'alphabet de la musique'', contained 24 sonatas in all keys for flute or violin and
basso continuo Basso continuo parts, almost universal in the Baroque era (1600–1750), provided the harmonic structure of the music by supplying a bassline and a chord progression. The phrase is often shortened to continuo, and the instrumentalists playing the ...
, 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 Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
:
Johann Pachelbel Johann Pachelbel (baptised – buried 9 March 1706; also Bachelbel) was a German composer, organist, and teacher who brought the south German organ schools to their peak. He composed a large body of sacred and secularity, secular music, and h ...
's magnificat fugues (composed 1695–1706),
Georg Muffat Georg Muffat (1 June 1653 – 23 February 1704) was a Baroque composer and organist. He is best known for the remarkably articulate and informative performance directions printed along with his collections of string pieces ''Florilegium Primum'' a ...
's ''Apparatus Musico-organisticus'' of 1690 and
Johann Speth Johann (''Johannes'') Speth (9 November 1664 – after 1719) was a German organist and composer. He was born in Speinshart, some 150 km from Nuremberg, but spent most of his life in Augsburg, where he worked as cathedral organist for two ...
's ''Ars magna'' of 1693 for example. Furthermore, some two hundred years before Bach's time,
equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
was realized on plucked string instruments, such as the
lute A lute ( or ) is any plucked string instrument with a neck and a deep round back enclosing a hollow cavity, usually with a sound hole or opening in the body. It may be either fretted or unfretted. More specifically, the term "lute" can ref ...
and the
theorbo The theorbo is a plucked string instrument of the lute family, with an extended neck and a second pegbox. Like a lute, a theorbo has a curved-back sound box (a hollow box) with a wooden top, typically with a sound hole, and a neck extending ...
, 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 The passamezzo (plural: ''passamezzi'' or ''passamezzos'') is an Italian folk dance of the 16th and early 17th centuries. Many pieces named "passamezzo" follow one of two chord progressions that came to be named after the dance, passamezzo antico ...
saltarello The ''saltarello'' is a musical dance originally from Italy. The first mention of it is in Add MS 29987, a late-fourteenth- or early fifteenth-century manuscript of Tuscan origin, now in the British Library. It was usually played in a fast tr ...
pairs (1567) by (c.1520–c.1577) * 24 groups of dances, "clearly related to 12 major and 12 minor keys" (1584) by
Vincenzo Galilei Vincenzo Galilei (born 3 April 1520, Santa Maria a Monte, Italy died 2 July 1591, Florence, Italy) was an Italian lutenist, composer, and music theorist. His children included the astronomer and physicist Galileo Galilei and the lute virtuoso and ...
(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 (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. J.C.F. Fischer's '' Ariadne musica neo-organoedum'' (published in 1702 and reissued 1715) is a set of 20 prelude-fugue pairs in ten major and nine minor keys and the
Phrygian mode The Phrygian mode (pronounced ) can refer to three different musical modes: the ancient Greek ''tonos'' or ''harmonia,'' sometimes called Phrygian, formed on a particular set of octave species or scales; the Medieval Phrygian mode, and the modern ...
, plus five
chorale Chorale is the name of several related musical forms originating in the music genre of the Lutheran chorale: * Hymn tune of a Lutheran hymn (e.g. the melody of "Wachet auf, ruft uns die Stimme"), or a tune in a similar format (e.g. one of the th ...
-based
ricercar A ricercar ( , ) or ricercare ( , ) is a type of late Renaissance and mostly early Baroque instrumental composition. The term ''ricercar'' derives from the Italian verb which means 'to search out; to seek'; many ricercars serve a preludial funct ...
s. 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'' (1719) by
Johann Mattheson Johann Mattheson (28 September 1681 – 17 April 1764) was a German composer, singer, writer, lexicographer, diplomat and music theorist. Early life and career The son of a prosperous tax collector, Mattheson received a broad liberal education ...
(1681–1764), which included 48
figured bass Figured bass is musical notation in which numerals and symbols appear above or below (or next to) a bass note. The numerals and symbols (often accidentals) indicate intervals, chords, and non-chord tones that a musician playing piano, harpsi ...
exercises in all keys,
Karl Geiringer Karl Geiringer (April 26, 1899 – January 10, 1989)Will Crutchfield, January 12, 1989 Retrieved 2013-08-10. was an Austrian-American musicologist, educator, and biographer of composers. He was educated in Vienna but at the beginning of the Nazi yea ...
. ''The Bach Family: Seven Generations of Creative Genius'', pp. 268–269. Oxford University Press, 1954.
''Partien auf das Clavier'' (1718) by
Christoph Graupner Christoph Graupner (13 January 1683 – 10 May 1760) was a German composer and harpsichordist of late Baroque music who was a contemporary of Johann Sebastian Bach, Georg Philipp Telemann and George Frideric Handel. Life Born in Hartmannsd ...
(1683–1760) with eight suites in successive keys, and
Friedrich Suppig Friedrich Suppig was an 18th-century music theorist and composer. Practically nothing is known about him or his life, or even if he was in fact a professional composer. He is known for two manuscripts; in one of which he discussed theoretical tunin ...
's ''Fantasia'' from ''Labyrinthus Musicus'' (1722), a long and formulaic sectional composition ranging through all 24 keys which was intended for an
enharmonic keyboard An enharmonic keyboard is a musical keyboard, where enharmonically equivalent notes do not have identical pitches. A conventional keyboard has, for instance, only one key and pitch for C and D , but an enharmonic keyboard would have two differe ...
with 31 notes per octave and pure major thirds. Finally, a lost collection by
Johann Pachelbel Johann Pachelbel (baptised – buried 9 March 1706; also Bachelbel) was a German composer, organist, and teacher who brought the south German organ schools to their peak. He composed a large body of sacred and secularity, secular music, and h ...
(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 17125 February 1758). 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 (12-note) well-tempered tuning system in which all keys sounded in tune (also known as "circular temperament"). One of the opposing systems in Bach's day was
meantone temperament Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. M ...
in which keys with many accidentals sound out of tune. (See also
musical tuning In music, there are two common meanings for tuning: * Tuning practice, the act of tuning an instrument or voice. * Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Tuning practice Tun ...
.) 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 An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
, 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 An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
, 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 E minor is a minor scale based on E, consisting of the pitches E, F, G, A, B, C, and D. Its key signature has one sharp. Its relative major is G major and its parallel major is E major. The E natural minor scale is: : Changes needed ...
prelude (6 flats) with its
enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a writte ...
key of
D minor D minor is a minor scale based on D, consisting of the pitches D, E, F, G, A, B, and C. Its key signature has one flat. Its relative major is F major and its parallel major is D major. The D natural minor scale is: Changes needed ...
(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 In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths. (This is strictly true in the standard 12-tone equal temperament system — using a different system requires one interval of ...
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 Friedrich Wilhelm Marpurg (21 November 1718 – 22 May 1795) was a German music critic, music theorist and composer. He was friendly and active with many figures of the Enlightenment of the 18th century. Life Little is known of Marpurg's ear ...
, who received information from Bach's sons and pupils; and
Johann Kirnberger Johann Philipp Kirnberger (also ''Kernberg''; 24 April 1721, Saalfeld – 27 July 1783, Berlin) was a musician, composer (primarily of fugues), and music theorist. He was a student of Johann Sebastian Bach. According to Ingeborg Allihn, Kirnber ...
, one of those pupils. Forkel reports that Bach tuned his own
harpsichord A harpsichord ( it, clavicembalo; french: clavecin; german: Cembalo; es, clavecín; pt, cravo; nl, klavecimbel; pl, klawesyn) is a musical instrument played by means of a keyboard. This activates a row of levers that turn a trigger mechanism ...
s and
clavichord The clavichord is a stringed rectangular keyboard instrument that was used largely in the Late Middle Ages, through the Renaissance, Baroque and Classical eras. Historically, it was mostly used as a practice instrument and as an aid to compositi ...
s 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 Carl Philipp Emanuel Bach (8 March 1714 – 14 December 1788), also formerly spelled Karl Philipp Emmanuel Bach, and commonly abbreviated C. P. E. Bach, was a German Classical period musician and composer, the fifth child and sec ...
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 A seal is a device for making an impression in wax, clay, paper, or some other medium, including an embossment on paper, and is also the impression thus made. The original purpose was to authenticate a document, or to prevent interference with a ...
,
numerology Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...
, 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 The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...
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 Flat or flats may refer to: Architecture * Flat (housing), an apartment in the United Kingdom, Ireland, Australia and other Commonwealth countries Arts and entertainment * Flat (music), a symbol () which denotes a lower pitch * Flat (soldier), ...
. * 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 Mark Lindley (born 1937) is a noted musicologist and, more recently, a historian of modern India, and a teacher of economics. Born in Washington, D.C., he studied at Harvard University (A.B.), the Juilliard School of Music (M.S.) and Columbia Univ ...
, a researcher of historical temperaments, has written several surveys of temperament styles in the German
Baroque The Baroque (, ; ) is a style of architecture, music, dance, painting, sculpture, poetry, and other arts that flourished in Europe from the early 17th century until the 1750s. In the territories of the Spanish and Portuguese empires including ...
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

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 The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integ ...
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 Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimiza ...
under 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 (G–D–A/B), 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 (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 WTC 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
musicologist Musicology (from Greek μουσική ''mousikē'' 'music' and -λογια ''-logia'', 'domain of study') is the scholarly analysis and research-based study of music. Musicology departments traditionally belong to the humanities, although some m ...
s 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. *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 (if the swirls were so important, why did Bach's students not copy them accurately, if at all?") 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 (c. 3 beats per second) and between the fifth C–G and the third 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
Arp Schnitger Arp Schnitger (2 July 164828 July 1719 (buried)) was an influential Northern German organ builder. Considered the most paramount manufacturer of his time, Schnitger built or rebuilt over 150 organs. He was primarily active in Northern Europe, es ...
's 1688 Organ of St. Ludgeri in Norden and the temperament later described by Carlo Gervasoni in his ''La scuola della musica'' (Piacenza, 1800). 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 (instead of Werckmeister's 4) different kinds of major thirds. The manuscript Bach P415 in the
Berlin State Library The Berlin State Library (german: Staatsbibliothek zu Berlin; officially abbreviated as ''SBB'', colloquially ''Stabi'') is a universal library in Berlin, Germany and a property of the Prussian Cultural Heritage Foundation. It is one of the ...
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

Each Prelude is followed by a Fugue in the same key. In each book the first Prelude and Fugue is in
C major C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
, followed by a Prelude and Fugue in its
parallel minor In music theory, a major scale and a minor scale that have the same tonic note are called parallel keys and are said to be in a parallel relationship. Forte, Allen (1979). ''Tonal Harmony'', p.9. 3rd edition. Holt, Rinehart, and Wilson. . "When ...
key (
C minor C minor is a minor scale based on C, consisting of the pitches C, D, E, F, G, A, and B. Its key signature consists of three flats. Its relative major is E major and its parallel major is C major. The C natural minor scale is: : Cha ...
). Then all keys, each major key followed by its parallel minor key, are followed through, each time moving up a half tone: C → C → D → E → E → F → F → ... ending with ... → B → B.


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'' (1720) 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 ''Klavierbüchlein für Wilhelm Friedemann Bach'' (Bach's original spelling: ''Clavier-Büchlein vor Wilhelm Friedemann Bach'') is a collection of keyboard music compiled by the German Baroque composer Johann Sebastian Bach for his eldest son Wil ...
'' (No. 14: "Praeludium 1"). The prelude is a seemingly simple progression of
arpeggiated A broken chord is a chord broken into a sequence of notes. A broken chord may repeat some of the notes from the chord and span one or more octaves. An arpeggio () is a type of broken chord, in which the notes that compose a chord are played ...
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 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 and Fugue in C-sharp major, BWV 848 Prelude and Fugue in C sharp Major, BWV 848, is a keyboard composition written by Johann Sebastian Bach. It is the third prelude and fugue in the first book of ''The Well-Tempered Clavier'', a series of 48 preludes and fugues by the composer ...
. Prelude also in WFB ''Klavierbüchlein'', No. 21: Praeludium


No. 4: Prelude and Fugue in C minor, BWV 849

Prelude and Fugue in C-sharp 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 0 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

Prelude and Fugue in E minor, BWV 855. Early version
BWV 855a Prelude and Fugue in E minor, BWV 855, is the 10th prelude and fugue for keyboard (harpsichord) in the first book of '' The Well Tempered Clavier'', composed in 1722 by Johann Sebastian Bach. The Prelude in E minor, BWV 855a, f ...
of the Prelude in ''Klavierbüchlein für Wilhelm Friedemann Bach'' (No. 18: "Praeludium 5").


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 1


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

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

Prelude and Fugue in B-flat 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" (LO) 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 The German Bach-Gesellschaft (Bach Society) was a society formed in 1850 for the express purpose of publishing the complete works of Johann Sebastian Bach without editorial additions. The collected works are known as the Bach-Gesellschaft-Ausga ...
, a 1744 copy primarily written by
Johann Christoph Altnickol Johann Christoph Altnickol, or Altnikol, (baptised 1 January 1720, buried 25 July 1759) was a German organist, bass singer, and composer. He was a student, copyist and son-in-law of Johann Sebastian Bach. Biography Altnikol was born in Berna bei ...
(Bach's son-in-law), with some corrections by Bach, and later also by Altnickol and others.


No. 1: Prelude and Fugue in C major, BWV 870

Prelude and Fugue in C major, BWV 870.


No. 2: Prelude and Fugue in C minor, BWV 871

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

Prelude and Fugue in C-sharp minor, BWV 873.


No. 5: Prelude and Fugue in D major, BWV 874

.


No. 6: Prelude and Fugue in D minor, BWV 875

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 and Fugue in F minor, BWV 881 The Prelude and Fugue in F minor, BWV 881, is a keyboard composition written by Johann Sebastian Bach. It is the twelfth prelude and fugue in the second book of ''The Well-Tempered Clavier,'' a series of 48 preludes and fugues by the composer ...
. 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

Prelude and Fugue in G-sharp 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

Prelude and Fugue in B-flat minor, BWV 891.


No. 23: Prelude and Fugue in B major, BWV 892

.


No. 24: Prelude and Fugue in B minor, BWV 893

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 Coda or CODA may refer to: Arts, entertainment, and media Films * Movie coda, a post-credits scene * ''Coda'' (1987 film), an Australian horror film about a serial killer, made for television *''Coda'', a 2017 American experimental film from Na ...
(e.g. Book I preludes in
C minor C minor is a minor scale based on C, consisting of the pitches C, D, E, F, G, A, and B. Its key signature consists of three flats. Its relative major is E major and its parallel major is C major. The C natural minor scale is: : Cha ...
,
D major D major (or the key of D) is a major scale based on D, consisting of the pitches D, E, F, G, A, B, and C. Its key signature has two sharps. Its relative minor is B minor and its parallel minor is D minor. The D major scale is: : Ch ...
, and
B major B major (or the key of B) is a major scale based on B. The pitches B, C, D, E, F, G, and A are all part of the B major scale. Its key signature has five sharps. Its relative minor is G-sharp minor, its parallel minor is B minor, and ...
). 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, but two are five-voiced (the fugues in C minor and B minor from Book I) and one is two-voiced (the fugue in E minor from Book I). 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 Organ may refer to: Biology * Organ (biology), a part of an organism Musical instruments * Organ (music), a family of keyboard musical instruments characterized by sustained tone ** Electronic organ, an electronic keyboard instrument ** Hammond ...
. 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 In music, counterpoint is the relationship between two or more musical lines (or voices) which are harmonically interdependent yet independent in rhythm and melodic contour. It has been most commonly identified in the European classical tradi ...
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 Franz Joseph Haydn ( , ; 31 March 173231 May 1809) was an Austrian composer of the Classical period. He was instrumental in the development of chamber music such as the string quartet and piano trio. His contributions to musical form have led ...
and
Mozart Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period. Despite his short life, his rapid pace of composition r ...
studying the work closely.
Mozart Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period. Despite his short life, his rapid pace of composition r ...
transcribed some of the fugues of the ''Well-Tempered Clavier'' for string ensemble: * BWV 853 → K. 404a/1 * BWV 871 →
K. 405 K is the eleventh letter of the Latin alphabet. K may also refer to: General uses * K (programming language), an array processing language developed by Arthur Whitney and commercialized by Kx Systems * K (cider), a British draft cider manufac ...
/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 Fantasy No. 1 with Fugue, K. 394 is one of Mozart's own compositions showing the influence the ''Well-Tempered Clavier'' had on him.Brown, A. Peter, ''The Symphonic Repertoire'' (Volume 2). Indiana University Press (), pp. 423–432 (2002).
Beethoven Ludwig van Beethoven (baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classic ...
played the entire ''Well-Tempered Clavier'' by the time he was eleven, and produced an arrangement of BWV 867, for string quintet.McKay, Cory
"The Bach Reception in the 18th and 19th century"
at
Eric Schenk (author), translated from the German by Richard and Clara Winston & Winston (eds) (1959), ''Mozart and his Times'', p. 452
Hans von Bülow Freiherr Hans Guido von Bülow (8 January 1830 – 12 February 1894) was a German conductor, virtuoso pianist, and composer of the Romantic era. As one of the most distinguished conductors of the 19th century, his activity was critical for es ...
called ''The Well-Tempered Clavier'' the "Old Testament" of music (the Beethoven Sonatas were the "New Testament"). In the liner notes to the ''Clair de Lune'' compilation of piano
encore An encore is an additional performance given by performers after the planned show has ended, usually in response to extended applause from the audience.Lalange Cochrane, in ''Oxford Companion to Music'', Alison Latham, ed., Oxford University Pre ...
s 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 Dmitri Dmitriyevich Shostakovich, , group=n (9 August 1975) was a Soviet-era Russian composer and pianist who became internationally known after the premiere of his First Symphony in 1926 and was regarded throughout his life as a major compo ...
wrote his 24 Preludes and Fugues, an even closer reference to Bach's model.
Mario Castelnuovo-Tedesco Mario Castelnuovo-Tedesco (3 April 1895 – 16 March 1968) was an Italian composer, pianist and writer. He was known as one of the foremost guitar composers in the twentieth century with almost one hundred compositions for that instrument. In ...
wrote '' Les Guitares bien tempérées'' (''The Well-Tempered Guitars''), 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 Anna Magdalena Bach (née Wilcke or Wilcken) (22 September 1701 – 22 February 1760) was a professional singer and the second wife of Johann Sebastian Bach. Biography Anna Magdalena Wilcke was born at Zeitz, in the Electorate of Saxony. Whi ...
copied a short version of this prelude in her 1725 ''
Notebook A notebook (also known as a notepad, writing pad, drawing pad, or legal pad) is a book or stack of paper pages that are often ruled and used for purposes such as note-taking, journaling or other writing, drawing, or scrapbooking. History ...
'' (No. 29). The accessibility of this prelude, the "easy" key of C major, and its use of arpeggiated chords, have made it one of the most commonly studied pieces for piano students. This prelude also served as the basis for the ''
Ave Maria The Hail Mary ( la, Ave Maria) is a traditional Christian prayer addressing Mary, the mother of Jesus. The prayer is based on two biblical passages featured in the Gospel of Luke: the Angel Gabriel's visit to Mary (the Annunciation) and Mary's ...
'' of
Charles Gounod Charles-François Gounod (; ; 17 June 181818 October 1893), usually known as Charles Gounod, was a French composer. He wrote twelve operas, of which the most popular has always been ''Faust (opera), Faust'' (1859); his ''Roméo et Juliette'' (18 ...
.


Tenth prelude of Book I

Alexander Siloti Alexander Ilyich Siloti (also Ziloti, russian: Алекса́ндр Ильи́ч Зило́ти, ''Aleksandr Iljič Ziloti'', uk, Олександр Ілліч Зілоті; 9 October 1863 – 8 December 1945) was a Russian virtuoso pianist, ...
transcribed a piano arrangement of the early version of Prelude and Fugue in E minor (
BWV 855a Prelude and Fugue in E minor, BWV 855, is the 10th prelude and fugue for keyboard (harpsichord) in the first book of '' The Well Tempered Clavier'', composed in 1722 by Johann Sebastian Bach. The Prelude in E minor, BWV 855a, f ...
),
transposed In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other notations). The tr ...
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 Wanda Aleksandra Landowska (5 July 1879 – 16 August 1959) was a Polish harpsichordist and pianist whose performances, teaching, writings and especially her many recordings played a large role in reviving the popularity of the harpsichord in ...
on harpsichord for RCA Victor in 1949 (Book 1) and 1952 (Book 2).
Helmut Walcha Arthur Emil Helmut Walcha (27 October 1907 – 11 August 1991) was a German organist, harpsichordist, music teacher and composer who specialized in the works of the Dutch and German baroque masters. Blind since his teenage years, he is known f ...
, better known as an organist, recorded both books between 1959 and 1961 on a harpsichord. Daniel Chorzempa made the first recording using multiple instruments (harpsichord, clavichord, organ, and fortepiano) for Philips in 1982. As of 2013, over 150 recordings have been documented.


Audio of Book I

Harpsichord performances of various parts of Book I by
Martha Goldstein Martha Goldstein (born Martha Svendsen; June 10, 1919 – February 14, 2014) was an American harpsichordist and pianist, who gave concerts in the United States, North Africa, the Middle East, and Europe. She performed works by George Frideric Ha ...
are in the public domain. Such harpsichord performances may, for instance, be tuned in
equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
, or in
Werckmeister temperament Werckmeister temperaments are the tuning systems described by Andreas Werckmeister in his writings.A. Werckmeister: Musicalische Temperatur (Quedlinburg 1691), reprint edited by Rudolf Rasch The tuning systems are numbered in two different ways: t ...
. In addition to Martha Goldstein,
Raymond Smullyan Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher. Born in Far Rockaway, New York, his first career was stage magic. He earned a BSc from ...
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 Kimiko Douglass-Ishizaka (born 4 December 1976) is a German Japanese composer, pianist, and former Olympic weightlifter and powerlifter. Music Born in Bonn, Germany, Douglass-Ishizaka (known as Ishizaka) started playing the piano at age four ...
released a new and complete recording of Book 1 into the public domain.The Open Well-Tempered Clavier Website
"The Open Well-Tempered Clavier, Book 1"
/ref> Her performances are available below, beginning with the Prelude No. 1 in C Major (BWV 846):


References


Further reading

* Kirkpatrick, Ralph. ''Interpreting Bach's Well-Tempered Clavier: A Performer's Discourse of Method'' (New Haven: Yale University Press, 1987). . * Ledbetter, David. ''Bach's Well-Tempered Clavier: The 48 Preludes and Fugues'' (New Haven: Yale University Press, 2002). .


External links

Interactive media * (Adobe Flash
Exploring Bach's ''Well-Tempered Clavier''
– Korevaar (piano), Goeth (organ), Parmentier (harpsichord). Direct access to th

Sheet music
Open-source edition of the Well-Tempered Clavier, Book I
available in MuseScore, MusicXML, MIDI, PDF formats, released under CC0 * *
Book 1 Book one or book 1 can refer to: *'' Book One: Water'', the first season of the animated television series ''Avatar: The Last Airbender'' *'' Book One: Air'', the first season of the animated television series ''The Legend of Korra'' * "Book One," ...
(Open Source), Wikimedia Commons
''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 Recordings
Free piano recording of Book 1 by Kimiko Ishizaka (Open Well-Tempered Clavier project)


* ttp://www.music.qub.ac.uk/~tomita/midi.html 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

Free Pipe Organ recording of Books 1 & 2 by Jan Leontsky
On tuning systems
All existing 18th century quotes on J.S.Bachs temperament

Larips.com – "Bach" tuning resources
– interpreted by Bradley Lehman
Bach- and Well-Temperaments for Western Classical Music

Rosetta Revisited
– Interpreted by Dominic Eckersley Descriptions and analyses

by Siglind Bruhn. Full text of the 1993 book.

by Tim Smith and David Korevaar * Graphical motif extraction fo

an



* ttps://web.archive.org/web/20100403032831/http://www.laco.org/performances/127/?program=1 Program notesfrom the
Los Angeles Chamber Orchestra The Los Angeles Chamber Orchestra (LACO) is an American chamber orchestra based in Los Angeles, California. LACO presents its Orchestral Series concerts at two venues, the Alex Theatre in Glendale and UCLA's Royce Hall. History James Arkatov, a ...

Interpretation and analysis of JS Bach's ''Well-Tempered Clavier''
by Philip Goeth (includes audio samples) *

{{DEFAULTSORT:Well-Tempered Clavier, The Compositions covering all major and/or minor keys