Johann Sebastian Bach. The Well-Tempered Clavier (WTC), page 2


The Well-Tempered Clavier (WTC) book I, from 1722
BWV 846–869

There is no clear dramatic progression in WTC book I. But, you can say that the collection goes from the simple and clear in the C major prelude, to the complexity of the last fugue in B minor, where all of the scales 12 notes are present in the subject. One could talk about a progression from simple joy (C major prelude), to despair (fugue in C-sharp Major), and virtuosity and festivity (prelude and fugue in D Major) all ending in Divine inspiration, in the very long concluding fugue in B minor with its complex subject. The literature about the two books of WTC is extensive. One of the more odd ones can be mentioned. In this commentary the author sees the progression and events from both the Old and the New Testament in the WTC!


The title-page of WTC book I

On the title page of book I, Bach himself has written: "The Well-Tempered Clavier, or preludes and fugues in all tones and semitones, in major as well as minor. For the use and improvement of musical youth eager to learn, and for the particular delight of those already skilled in this discipline. Composed and presented by Johann Sebastian Bach, currently Kapellmeister to the Prince of Anhalt-Cöthen and director of his chamber music, in the year 1722".


The term "Clavier" 

Clavier is the German word for "keyboard instrument". There is no evidence whatsoever to permit interpreting Bach’s use of the word as indicating anything other than the general term keyboard, in other words: "any keyboard instrument". In Bach’s time, the harpsichord was the main keyboard instrument. Even then, however, the question of which instrument to use did not have a simple or a single answer. Along with the harpsichord, the clavichord and a chamber organ were in common use. 

But, the most important thing in the rather fatiguing discussion of “what is the correct instrument to play Bach on” would in my opinion be: I would rather hear a good performance on the piano, than a bad on either the harpsichord or the clavichord!


The Well-Tempered tuning

A more in-depth discussion of what well-tempered tuning is, its history and its specific problems in practically tuning any instrument, has to involve the problem of inharmonicity of the strings. This problem is discussed in the tuning pages on this site. (The inharmonicity is in real life a big problem that will directly affect the tuning of any temperament more than is commonly known by theorists. The bending stiffness of the strings causes the harmonics of any given tone to be at a higher pitch than mathematically expected. The tuning has to be altered from the theoretical frequencies or stretched, to salvage this problem. I have seen very little mention of this problem in the theoretical pages on tuning, in books or on the Internet. As the difference affects the temperament quite a lot, it has to be taken in account with, otherwise the theory and the practical side of tuning won’t match.

The term "equal temperament" comes from the organ builder Andreas Werckmeister (1645–1706). He says himself that he first considered the tuning as early as 1675, but only mentioned it for the first time in his book "Musicalische Temperatur" (1691), which is now considered to be the "birth-date" of equal temperament. In the book, oddly enough, he principally recommends two unequal temperaments (!), of which the most influential has been known as Werckmeister III.

According to the title page of WTC, the idea of the work is to demonstrate the possibility of writing and playing in all 24 major and minor keys. The tuning itself was not the only idea behind WTC, even if it would be impossible to play in all keys without the new tuning system. So one can conclude that both the idea of being able to play in all keys, and the idea of the tuning, formed the basis of the WTC.

At the time of WTC book I, Bach probably used something different from the well-tempered tuning system we know today. Later on in the 1730s and 1740s, at the time of book II, he changed his opinions regarding tuning. We know that from a study of several documents concerning the tuning of organs that Bach was known to have played. The evidence points overwhelmingly to equal or near-equal temperament. As an example: in September 1739 Bach visited and tested the organ in the Hofkapelle, Altenburg. The tuning of this organ had been the subject of much debate. The records of the debate – in which five different temperaments were proposed – show that the tuning decided upon was equal temperament. "The newest and the best" according to the court organist Lorenz. Another piece of evidence would be J. S. Bach's obituary written by C.P.E. Bach and Johann Friedrich Agricola. Bach’s tuning of harpsichords is described as so pure and correct "that all tonalities sounded handsome and agreeable, and there were none that had to be avoided because of impure intonation."

In short one can surmise that Bach probably started with some version of Werckmeister III, and then he moved towards something more evenly tempered. By the first book of the WTC in 1722, he would have used something in which every key could be used equally as a tonic. By 1744 equal temperament was well established in musical society, though in practice was "humanised" a bit to retain a nuance of the old traditional key character. So probably Bach didn’t quite use the well-tempered tuning of today, but he must have been very close. So close that the debate of exactly which temperament he actually used is of less importance.

My conclusion is that one can use the equal temperament without any feeling of making any serious mistake. The actual tuning of the instruments at use is more of a problem, as the quality of tuners varies a lot. More on that on the tuning pages.



The 12 first Preludes and Fugues of book I


1. Prelude and Fugue a 4 in C-major


The prelude is a succession of soft broken chords and no melody. The difference in tension between the chords forms the basis of the structure, as it at the same time forms the phrasing. 

A basic understanding of the harmonic system is an absolute necessity in order to play this piece properly. The player has to underscore certain chords and notes by means of subtle rubato. 

The prelude belongs to the group of 11 preludes written for Wilhelm Friedemann Bach. There are three earlier versions of the prelude, all shorter than the piece as it exists in its final form.


The fugue subject, evolving from an organ fugue of the Weimar period (1708–1717), consists of 14 notes that are of great significance. Bach, interested in numerology, regarded the figure 14 as representing his name. (Numbering the alphabet, B is 2; A is 1; C is 3; and H is 8. The letters added together equal 14. J-S-B-A-C-H equals 41).  

The theme is presented 24 times in only 27 bars, 18 of those entries in the middle section occupy only 19 bars! Of the 24 entries of the subject, 22 run to completion. The 12th entry is nearly complete, but when the subject is presented the 14th time, it’s incomplete!


The fugue is a stretto fugue in four parts and divided into four sections with a coda. Stated in simpler terms it might read: the fugue lacks the normal counter subject and the theme is both subject and counter-subject at the same time. It’s like the ad for the Chocolate bar Snickers: "No matter how you slice it, it comes up peanuts". The peanut in the C-major fugue would be the theme, and it’s always present in the piece.

The Fugue has a very noble and distinguished character and is quite difficult to play. Students who begin their study of the WTC with the C-major Prelude – which is easy to play – can easily be discouraged from playing more Bach as they encounter the surprising difficulty of even just fingering the fugue – not to mention meeting the further challenges of clearly bringing out all four voices with a noble character and correct phrasing. The playing can easily sound clumsy and unclear.



2. Prelude and Fugue a 3 in c-minor

The prelude is an enlargement of the version in "the Clavier-Büchlein vor Wilhelm Friedemann Bach", and exhibits a harmonic similarity to the C major prelude. In this case, it's not broken chords, but a repeated motion that is heard on the surface. And likewise will the difference in tension between the chords form the basis of the structure, as well as it forms the phrasing. Bach increases the tension at the end of the prelude and inserts a little cadenza with a rare tempo indication in the text (Presto). There are only six tempo markings by Bach in all of the 24 preludes and fugues of book I. I this prelude he uses three of them (presto–adagio–allegro)!  

This is the chord structure of the second prelude in C minor with a proposed phrasing.


The fugue has achieved great popularity and has become a must for both pianists and for theorists. It's easily the most written-about fugue in the entire WTC. In spite of its minor key, it exhibits a streak of humour and is great fun to listen to and to play. At the same time, it’s very carefully composed, making use of a very exacting triple counterpoint. The fugue has not one, but two, countersubjects! The second countersubject, containing mainly slow notes, is much more difficult to hear than the first countersubject, despite being just as consistent in its appearances.  


3. Prelude and Fugue a 2 in C-sharp Major

This prelude, of which an earlier shorter version exists, is a two-part piece with the quality of a badinerie, a jocular dance that appeared in the suites of the 17th and 18th centuries. It's a very brilliant piece and should be played – in my opinion – brilliantly. Bach was known for his fantastic technique and to play him always seriously, as some pianists do, I think, is a mistake. So this prelude and very brilliant fugue has to be played with great virtuosity and showmanship in the best sense of the word.  

The fugue is in three sections, including a recapitulation. This construction is similar to da capo design. I think that the music has an instrumental character. Witness its wide leaps and fast running figures. The fugue is one of the most difficult to play in the whole of Book I, as the unusual key of C-sharp Major forces to put the fingers in between the black keys in many of the fast passages. At full speed this is not comfortable thing to do ... 


4. Prelude and Fugue a 5 in C-sharp Minor

Bach rarely used the key of C-sharp minor; his best-known work in this key is the Adagio from the Violin Concerto in E major. The prelude stems from a shorter version in the Wilhelm Friedemann note book, and is an arioso of great expressiveness and beauty.

The C-sharp minor fugue is one of only two five-voice fugues in both books of the WTC (the other being the B-flat minor fugue, also in Book I). The fugal theme – C-sharp, B-sharp, E, and D-sharp – was used by Fischer in Ariadne music, Corelli, and others. Baroque composers regarded it as the symbol of the cross; if, on paper, one connects the B-sharp and D-sharp by a line, and C-sharp with E, the figure created is a diagonal, resting cross. Bach later used the theme in the crucifixion choruses of the St. John and St. Matthew Passions. The very serious symbolism in the theme also sets the very dark atmosphere for the piece.

This fugue is a triple fugue and it's very long. In fact with its 115 measures, this fugue is the second longest in the Well-Tempered Clavier. The fugue opens with the exposition of the first subject; the second subject enters in measure 36, and the third subject enters in measure 49. There are 30 entries of the first subject, 16 entries of the second subject, and 36 entries of the third subject that often overlap, with sometimes as many as four entries of different subjects running at the same time in the five voices. But, Bach was careful to introduce all three subjects separately so that the audience would be able to hear each of them individually. Large-level planning is particularly crucial in a triple fugue, otherwise it would be completely impossible to follow. Bach has divided this fugue into three main sections, which are easy to hear.  


5. Prelude and Fugue a 4 in D Major

Baroque composers ascribed a festive quality to the tonality of D major. Other significant examples in Bach’s output would be the Magnificat, the Gloria of the B minor Mass and the Christmas Oratorio.  

The prelude is a very fast piece that reminds me of Paganini's molto perpetue in his Caprices for solo-violin. Surely Paganini must have seen and heard Bach's WTC and was influenced by it. The prelude (in my mind) has to sound brilliant, otherwise I think one has not understood the character of the piece. Especially after the sombre mood in the C sharp minor fugue, the listener needs a contrast. 

The fugue's musical language, particularly the dotted rhythms, reminds of the style of a French overture. Handel's Water music comes to my mind, especially in the festive ending. The fugue is constructed in four sections and a coda. An interesting thing about this fugue is that in the final 11 measures out of a total of 27 (sections three and four); there are actually no entries at all of the complete fugue subject! Quite uncommon.



6. Prelude and Fugue a 3 in D Minor  

Bach composed significant works in D minor, including the Partita for solo violin and the Chromatic Fantasy for organ. The same intensity that pervades these pieces is evident in this prelude and in the following fugue. The prelude toys with a rhythmic idea, where the right hand put its accent one 16th note earlier than the bass line. This gives a special light-weight swing to the piece.

The fugal subject is often played lyrically. But, Bach clearly showed to us that he wanted to avoid this type of interpretation. The subject rises from D to B-flat, and Bach marked the latter note with staccato sign. This is the only case of such a marking in the autograph of the WTC! The marking adds a bit of offensive character to the subject, which also is rich with dissonances. To emphasize his intended offensiveness, Bach maintained the staccato sign throughout the entire fugue.

In this fugue Bach uses both melodic and contrapuntal inversion. Melodic inversion is when a single line is turned upside down. Contrapuntal inversion is when the relationship between two parts is turned upside down. This fugue’s contrapuntal inversion, involving the first and second episodes, is very subtle. Compared with the melodic inversion, it isn’t easy to hear.


7. Prelude and Fugue a 3 in E-flat Major

This piece does not have many prelude-like qualities. It opens with a nine-measure introduction that leads to a fugato section, which in turn continues as a two-subject fugue. It's one of the longest preludes and difficult to bring out in a convincing way.

The fugue on the other hand, is quite short, clear and brilliant in its character. Both subject and the countersubject never at the same time have both slow notes or fast notes. This opposition between the subject and the countersubject, presents all of the musical lines clearly to the listener and also makes the structure in this fugue easy to follow. 


8. Prelude and Fugue a 3 in E-flat/D-sharp minor  

The E-flat minor prelude is paired with a fugue in D-sharp minor. The key of E-flat minor was used by Bach only once in another composition – the second minuet from the Harpsichord Suite in E-flat major (BWV 819). The uncommon tonality and the 3/2-meter lend the prelude a strange quality floating quality, almost like a nocturne by Chopin.

Although conceived independently from the prelude, the fugue is now inseparably bound with it. It is an achievement of high artistry – six expositions with stretto, inversion and augmentation of the subject. (Inversion: the subject is turned upside down. Augmentation: all the notes of the subject are twice their usual length).

Near the end there is a counter exposition in stretto, with the subject running in all three voices practically simultaneously: with augmentation of the subject in the soprano, a rhythmically altered version of the subject in the alto, and an ornamented version of the subject in the bass. The varied use of stretto is one of this fugue’s most apparent features.



9. Prelude and Fugue a 3 in E Major

This prelude appears in a copy of the sixth French Suite for harpsichord (BWV 817). Notice that virtually the entire prelude uses slow notes, except for one measure, and that is of course measure 14! Again its Bach’s name that he has cleverly concealed for us. The character is relaxed and has a pastoral character. I usually think of a sunny day at the country-side while playing this piece.

The fugue is similar to the prelude in its shortness, but not thematically. It has a happy radiant, self-confident, high-spirited character. This fugue is the shortest in the Well-Tempered and takes less than 80 seconds to perform. Its very instrumental in its concept. It would be very difficult to sing all of these scales in the subject, running fast up and down the keyboard.


10. Prelude and Fugue a 2 in E Minor  

Of all the preludes that Bach transferred from Wilhelm Friedemann note book to the WTC, this one underwent the most changes. In the earlier version, only 23 measures long, the bass moves in sixteenth notes, while the right hand contributes only short chords. Bach adds a portion in the end of the piece for the VVTC, which requires an increase in tempo (indicated by Bach as Presto). The piece is usually conceived as a barcarole with a moving bass line.

This is the only fugue for two voices in Bach’s output. It is amazing that Bach was able to write such a good fugue with only two voices. To do so, since the available techniques are limited, Bach sometimes can only hint. Two of the many special devices used in this fugue are a chromatic subject (actually notes borrowed from another key) and sequential episodes. All four episodes in this fugue are sequential canonical episodes. The only difference between the first and third, the second and fourth episodes, is that the parts are contrapuntally inverted (turned upside down). The fugue is an energetic and fast piece.  


11. Prelude and Fugue a 3 in F Major

Bach transferred this short prelude from the Wilhelm Friedemann note book almost without alternation. It is a two-part invention, designed almost as a finger exercise. The 12/8-meter is quite uncommon. In the Wilhelm Friedemann copy of this prelude, the drills are only to be performed long in bars 12–15. I think that this is a better sounding idea and gives the piece a better and clearer structure with a under-lined stronger central passage! I play the piece according to this notation.

The subject of the fugue, stated first by the middle voice, stems from Fischer’s Ariadne musica. The 3/8-meter, the four-measure theme and the binary form of the subject unite, gives the piece the quality of a light dance that is rhythmically related to a passepied.



12. Prelude and Fugue a 4 in F Minor

Bach often chose the key of F minor to express grief and sombreness, which is also the character of this prelude. Really one of the most beautiful preludes in the whole of WTC. As in the C major prelude, the even stream of notes creates a continuum, which the player can mould expressively. To avoid any squareness, Bach has constructed this prelude with variable phrase shapes and lengths.

The fugue is one of the most distinctive in the entire WTC. The fugue has a mourning quality of vast beauty. While the subject moves in quarter notes, the countersubject (can also be seen as a second subject) moves in sixteenths. Dissonances and harshness results from collisions in harmony from the complex subject, yet there are also diatonic passages. The main principle of construction is the alternation of chromatic and diatonic episodes. 

In this fugue Bach gives a demonstration of quadruple counterpoint but, it is not just a demonstration of a compositional technique for its own sake, but of how to make it playable on the keyboard. The quadruple counterpoint is presented in full five times in the course of the piece.

Note that all twelve tones of the chromatic scale is present, not in the subject alone, but in the combined subject and answer.

It is noteworthy that the final B minor fugue also presents all twelve notes, and that these two fugues mark the middle and the end of Book I. 


In the first half of Book I (Nr. 1–12), the grand fugues are Nr. 4, 8 and 12. Out of a total 24 this gives the harmonic proportions 2:1, or the proportion of the octave

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