The Well-Tempered Clavier

• 1. Introduction

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  The Well-Tempered Clavier is a collection of preludes and fugues by Johann Sebastian Bach that set out to do something no one had fully done before: fill every one of the 24 major and minor keys with a pair of fully worked keyboard pieces. Bach wrote the first book in 1722. He wrote the second 20 years later, in 1742. Together, the two books span BWV 846 through BWV 893. The collection is generally regarded as one of the most important works in the history of classical music.

  Bach himself described the purpose plainly on the title page of his 1722 manuscript: he composed the work "for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study." That double audience, student and master alike, tells us something important about the collection's range. What does it mean for music to travel through all 24 keys, and what kind of tuning system makes that even possible? And why did Beethoven, Mozart, Chopin, and Shostakovich all circle back to this one collection, generation after generation?

• 2. The Question of Keys

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  Johann Pachelbel composed his Magnificat fugues between 1695 and 1706, covering all eight modes of pre-modern music. Georg Muffat published his Apparatus Musico-organisticus in 1690. Both were reaching toward the idea of comprehensiveness, but neither worked in the full system of 24 major and minor keys that Bach would later master.

  Even earlier, lute players had beaten keyboard players to the goal. Because lutes were built with equal temperament, composers writing for them could range through all keys freely. Vincenzo Galilei, born around 1528, published 24 groups of dances in 1584 that were, in his own terms, "clearly related to 12 major and 12 minor keys." A 1567 cycle of 24 passamezzo-saltarello pairs had appeared even before that. These were plucked strings, not keyboards.

  For keyboard instruments, the puzzle was harder. J. C. F. Fischer published his Ariadne musica neo-organoedum in 1702, later reissued in 1715. It covered 20 prelude and fugue pairs, touching ten major and nine minor keys plus the Phrygian mode. Bach knew Fischer's collection and borrowed some of its themes for his own work. Daniel Croner, born in 1656, had compiled a cycle of organ preludes in successive keys as early as 1682. But none of these predecessors produced a complete circuit of all 24 keys with fully developed paired preludes and fugues. That distinction belongs to Bach's 1722 book.

• 3. The Tuning Debate

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  Bach's title refers to a keyboard "well-tempered" to play in all keys, but historians and musicians have argued for centuries about exactly what kind of tuning he intended. Meantone temperament, the rival system of Bach's day, made keys with many accidentals sound badly out of tune on a standard 12-pitch keyboard. A "well temperament" or "circulating temperament" solved that problem, though not all such systems sound equally convincing in all keys.

  Forkel, Bach's first biographer, reported that Bach tuned his own harpsichords and clavichords himself, found other people's tunings unsatisfactory, and could modulate into distant keys almost without listeners noticing. Friedrich Wilhelm Marpurg and Johann Kirnberger, one of Bach's own students, both agreed that Bach required all major thirds to be sharper than pure. That condition is satisfied by several different temperaments, which has kept the debate alive.

  Johann Georg Neidhardt described a range of unequal and near-equal temperaments in writings from 1724-1732. Carl Philipp Emanuel Bach, the composer's son, published a tuning method that was close to, but not quite, equal temperament. He wrote that it had only "most of" the fifths tempered, without specifying which ones or by how much.

  Since 1950 numerous researchers have proposed specific solutions. Herbert Anton Kellner argued from the mid-1970s onward that Bach's signet ring, numerology, and related considerations could point to the correct tuning. His temperament, containing seven pure fifths and five comma fifths, was widely adopted for tuning pipe organs around the world. John Barnes analyzed the major-key preludes statistically, observing which major thirds appear most often. Mark Lindley wrote surveys of temperament styles in the German Baroque and published a key article on the subject in 1985. Modern scholars now generally favor some form of unequal well temperament rather than the equal temperament that became standard after Bach's death.

• 4. The Loops on the Title Page

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  Bach's personal 1722 manuscript, now catalogued as P415 in the Berlin State Library, carries a handwritten doodle of loops at the top of the title page. Starting in the late 20th century, a series of researchers proposed that these loops encode Bach's actual tuning method. The manuscript is described as most probably the working copy Bach used in lessons with his students.

  Andreas Sparschuh assigned mathematical and acoustic meaning to the loops in 1999. He read each loop as representing a fifth in a tuning sequence starting from A, and derived a recursive algorithm resembling the Collatz conjecture in mathematics. In 2006 he retracted his original proposal, which had been based on A = 420 Hz, and replaced it with a new one at A = 410 Hz. Michael Zapf in 2001 reinterpreted the loops differently, reading them as indicating beat rates for different fifths in terms of seconds per beat, and starting the tuning sequence on C instead of A.

  B. Lehman published his own reading in 2005 across three music journals, proposing a specific comma layout derived from the loops. Reaction was, by the source's own description, both vigorous and mixed. D. Jencka that same year proposed a variation of Lehman's layout in which one of the commas is spread over three fifths, objecting in particular to the wide fifth B-F that appears in Lehman's scheme. Interbartolo, Venturino, and Bof followed in 2006 with yet another interpretation, published as a book the following year.

  Not everyone is persuaded. D. Schulenberg in 2006 called Lehman's argument "ingenious" but countered that it "lacks documentary support," asking why Bach's students did not copy the loops accurately if they carried such meaning. The loops appear in no other known copy of the Well-Tempered Clavier.

• 5. Architecture of 48

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  Each of the two books opens with a prelude and fugue in C major, followed immediately by one in C minor. Then the pattern rises by half-steps through every key, major followed by its parallel minor, until it finishes with a B minor fugue. The 24 pairs in Book 1 run from BWV 846 through BWV 869; those in Book 2 run from BWV 870 through BWV 893.

  Bach recycled material freely. Eleven of the Book 1 preludes appear in earlier form in the Klavierbüchlein fur Wilhelm Friedemann Bach, which dates to 1720, two years before the 1722 autograph. The C major prelude, BWV 846, for instance, had already appeared there as "Praeludium 1," labeled BWV 846a. There also exists an almost complete collection of "Prelude and Fughetta" versions predating the autograph, known only from a later copy by an unidentified scribe.

  Book 2 has a more complex manuscript history. The primary source called the "London Original" is dated between 1739 and 1742, with scribes including Bach himself, his wife Anna Magdalena, and his oldest son Wilhelm Friedemann. A second version, which the 19th-century Bach-Gesellschaft used as its basis, is a 1744 copy primarily in the hand of Johann Christoph Altnickol, Bach's son-in-law, with later corrections by Bach, Altnickol, and others.

  Within each book the preludes are formally free, though many show typical Baroque melodic forms and often attach an extended free coda. The fugues range from two voices to five, with most written in three or four voices. Two fugues from Book 1, those in C minor and B minor, each deploy five voices. Only one fugue in Book 1 uses just two voices: the one in E minor. Wilhelm Werker and Johann Nepomuk David both attempted analyses of motivic connections between preludes and their paired fugues. The closest connection they identified is in the B major set from Book 1, where the fugue subject uses the first four notes of the prelude, placed in the same metric position but played at half speed.

• 6. Reception and Legacy

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  Printed copies of the Well-Tempered Clavier did not appear until 1801-51 years after Bach's death. Three publishers released editions nearly simultaneously in Bonn, Leipzig, and Zurich. Bach's contrapuntal style had gone out of fashion around the time he died, and the early Classical period favored simpler textures in fewer keys. By the 1770s, as the Classical style matured, the collection began influencing composers again. Haydn and Mozart both studied it closely.

  Mozart transcribed a number of the fugues for string ensemble, including BWV 853, 871, 874, 876, 877, 878, 882, and 883. His own Fantasy No. 1 with Fugue, K. 394, shows the collection's direct influence on his compositional thinking. Beethoven played through the entire Well-Tempered Clavier by the time he was eleven years old and later arranged BWV 867 for string quintet.

  Hans von Bulow gave the collection what became its most memorable label: the "Old Testament" of music, placing the Beethoven Sonatas as the "New Testament." In 1835 Chopin began his 24 Preludes, Op. 28, directly inspired by Bach's model. In the 20th century, Dmitri Shostakovich wrote his own 24 Preludes and Fugues as an even closer reference. Vsevolod Zaderatsky composed a full cycle of 24 preludes and fugues in 1940 under Gulag camp conditions; the work remained unpublished and virtually unknown until its premiere in 2014. Mario Castelnuovo-Tedesco wrote Les Guitares bien temperees, a set of 24 preludes and fugues for two guitars in all 24 keys, naming both the title and the structure after Bach's example.

  The first complete recording came from Edwin Fischer, who recorded the entire collection on piano for EMI between 1933 and 1936. Wanda Landowska recorded it on harpsichord for RCA Victor in 1949 and 1952. Daniel Chorzempa made the first recording to use multiple instruments, covering harpsichord, clavichord, organ, and fortepiano for Philips in 1982. As of 2013 more than 150 recordings had been documented. The Glenn Gould recording of BWV 870 was included on the Voyager Golden Record, sending one of Bach's 48 pairs beyond the solar system.

• 7. The First Prelude

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  Anna Magdalena Bach copied a short version of the C major prelude, BWV 846, into her 1725 Notebook, entering it as No. 29. The piece moves through a progression of arpeggiated chords, a technique that French lutenists had long associated with the act of preluding. Its accessibility, its uncrowded key of C major, and its arpeggiated texture have made it one of the most commonly studied pieces for piano students across the centuries.

  Charles Gounod built his Ave Maria directly on this prelude as a harmonic foundation, giving the piece a second life in sacred music. Alexander Siloti also took an interest in the early version of another prelude, BWV 855a, transposing it from E minor into B minor for a piano arrangement. The prelude and its sibling pieces continue to draw performers and listeners, and in 2024 pianist Natalya Pasichnyk released a recording called Rethinking the Well-Tempered Clavier, a reimagination of Book 1 that won the Golden Medal at the Global Music Awards that year.