from Siglind Bruhn
J.S. Bach's Well-Tempered Clavier
In-depth Analysis and Interpretation

"Das Wohltemperirte Clavier" is the title that Bach chose in 1722 for his first collection of twenty-four preludes and fugues, and which he applied again, twenty-two years later, to his second collection. This title may have been an expression of joy and triumph during Bach's time. Today it strikes many musicians and the concert public alike as too technical, unimaginative, even austere. This description can certainly be said to be true for the long subtitle which, in its English translation, reads: 

The Well Tempered Clavier,
preludes and fugues in all tones and semitones,
in the major as well as the minor modes,
for the benefit and use
of musical youth desirous of knowledge
as well as those who are already advanced in this study.
For their especial diversion, composed and prepared by
Johann Sebastian Bach,
currently ducal chapelmaster in Anhalt Cöthen
and director of chamber music,
in the year 1722.

The conspicuous term is obviously "well-tempered". The word "to temper", when used in a musical context, refers to a slight artificial lessening or enlarging of natural intervals. Why would this have been necessary? To understand this we must begin by recalling exactly what a natural interval is.


a) The "well-tempered" scale 

In nature, intervals are created through simple multiplication of an original frequency. This can happen in one of two ways:


On a string instrument, the number of vibrations per second can be doubled by placing a finger (or an object) in the middle of the tight string and letting each half vibrate separately; similarly, the frequency will be tripled or quadrupled if we cause one third or one fourth of the string to move independently.


With wind instruments, the process is basically similar: while the length of the tube remains unchanged, increasing wind pressure modifies the vibration of the air-column not by degrees but by multiplication.

The subsequent higher frequencies or pitches created in both processes show simple numeric relationships not only to the original frequency of the bare string but also with each other. Among these related pitches, the degree of consonance is greatest where the relation is simplest. Thus 1:2 represents the interval in which the higher note vibrates at twice the speed of its root: the octave.

By tripling the frequency of the root we arrive at the next largest "natural" interval, the compound fifth. Therefore, the numeric relation of a perfect fifth (which is the interval between the 1:2 octave and the 1:3 octave + fifth of a root) is 2:3. Similarly, 3:4 results in a perfect fourth, 4:5 in a major third, and 5:6 in a minor third. (Of the intervals caused by higher frequency combinations not all are used in occidental music.)

Imagine C had a frequency of 64 vibrations per second. The numerically related notes (or overtones) of this C would then be as follows:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -







































- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

It is from these natural intervals that we derive our scales. Difficulties arise with the notion that each note entertains a variety of relationships with the others: B is not only the seventh degree of the C major scale, but also the fifth of the fifth on A, the triple fifth on D, etc. It is this latter relationship, that of superimposed fifths, which generally determines the tuning of instruments -- just as the natural fifth is still the setting interval for string instruments.

This method of tuning, however, is not flawless: it assumes notes as identical which are in truth, i.e. in terms of physics, slightly dissimilar. While a string player is expected to train his or her ear to achieve such subtle differences by intonation, an equivalent process is obviously not accessible on a fixed pitch instrument. At the same time, a keyboard cannot possibly have enough alternative keys for a single letter name note to allow for such subtleties. The result was that such not-quite identical notes ended up sharing a key which sounded perfectly in tune with a small number of its relatives but out of tune in several other of its "natural contexts". This compromise is the reason why most works written before the 1720s were confined to keys close to C and G major.

A way out of this predicament was found in the late 17th century when the organist and organ manufacturer Andreas Werckmeister suggested sacrificing the natural fifth in the tuning of keyboard instruments in favor of dividing the octave into twelve exactly equal semitones. This compromise meant to "temper" the perfect intervals, all of which would now sound slightly imperfect. In turn it had the huge advantage of guaranteeing equally acceptable results in all tonalities. It was this "well-tempered" tuning of keyboard instruments which first enabled the use of such keys as C# major and D# minor in pieces for keyboard instruments. And it was this new possibility of composing equally on all semitones of the chromatic scale that inspired Bach to compile this collection. (For more details on this topic, refer to volume I of this book.)


b) The clavier

Another question frequently asked is: what did Bach and his contemporaries mean by "clavier"? This name, while nearly identical to the modern German word for "piano" ("Klavier") and closely related to the word "clavichord", did not originally include any specification other than that the action of the instrument should contain "claves" or keys. Thus "clavier" could refer to an organ or a spinet, to a clavichord or a harpsichord, as well as to the instrument that was to become our modern piano. 

This vagueness regarding the choice of the instrument reveals a very important aspect of the "Well-Tempered Clavier": its music is meant as absolute music. This means that it is the absolute, artistic idea expressed in the music that counts, not the technical way in which it is performed. Whichever instrument might seem, in a particular situation and at a particular time, to be best suited to the content and character, message and spirit of a piece would be considered appropriate.

It is interesting to know that Mozart, undoubtedly guided by this insight, transcribed several of the "Well-Tempered Clavier" fugues for string ensemble. Others have followed his example. Far from diminishing the value of the original composition, each such arrangement bears new revelations. However, the question remains: nowadays that the "original" instruments are once again more easily available, but may still not be the ones we have spent time and effort to learn, which keyboard instruments should we choose?

Today's performing musicians seem to adopt different approaches. In comparing these approaches, four prevalent attitudes can be observed:



A first group of artists, often referred to as "purists", will interpret music only on the instrument for which it has originally been composed regardless of the distinction between instrument-specific and absolute music. This is an attitude to respect so long as it does not neglect two considerations:


One is that Baroque keyboard instruments, such as the harpsichord or the clavichord, need as much special training as the piano and can therefore not simply be chosen for certain pieces by performers who have acquired their skills on the modern piano only.


The other is that Bach, given the choices available in his time, preferred many of his pieces to be played on the clavichord with its wider possibilities of subtle shading. Forkel, one of Bach's earliest biographers, tells us that Bach himself was not too happy whenever he had to perform particularly his polyphonic pieces on the harpsichord. Therefore, even additional training on the harpsichord is frequently insufficient.

Thus, choosing to play on the "original" instrument means, in the case of almost all pieces from the Well-Tempered Clavier, that a performer has to have undergone considerable extra clavichord training. It also necessitates the acceptance of playing only in chamber music halls of the smallest size, to ensure that the playing can be heard beyond the first ten rows. If a performer agrees to submit to all these requirements, then the performance has a good chance of becoming an unforgettable experience for the audience.


A second group of performers seems to prefer a compromise: they will play on a modern grand piano, but touch their instrument only in such a way that its sound may resemble that of a harpsichord as closely as possible. Apart from the above mentioned fact that for most of the pieces in question the harpsichord was not even the "originally" intended instrument, such compromise is likely to deprive the listener both of enjoying the sound of the music and of understanding the structure. All his attention will probably be captured by the unusual way in which the performer is treating his piano. Such is certainly not the idea of music making.

For a performer who feels that the sound of a modern piano fails to do justice to the composer's intention, it would be preferable to adhere to the principles of the first group.


A third group of musicians distinguishes between instrument-specific and absolute music. They believe (as did Mozart when he wrote his transcriptions) that much of Bach's musical language is not confined to a very special type of instrument.

This view is based on the fact that many a piece in the Baroque epoch bears a title which destines it for various instruments of equal tonal range e.g. "for violin or flute or oboe"; "for violoncello or bassoon"). One can conclude from these titles that such music is in reality "absolute music", not dependent on the specific tone color and technique of an instrument but deriving its significance from within the musical structure alone.

The keyboard performers of this group will therefore shape their keyboard technique according to the musical ideas they perceive in a piece, concentrating their studies on how other instruments of the era would have articulated a line or proportioned a dynamic development, and transfer this style to their instrument with as much nuance as possible.


Finally, a fourth group of performers appear to focus mainly on the manifold possibilities of the modern piano, particularly those added to its range of expression in the late 19th century. They will freely use dynamic and agogic means engendered by the Romantic period because they feel the necessity to meet the emotional needs of today's public -- needs which, without doubt, were developed primarily through music of the Romantic style.

However, one should be permitted to ask: if it is true that today's audience cannot appreciate music which lacks Romantic attributes, would it not be easier (and better for both the audience and the music) to give them the "real thing", i.e. original Romantic compositions?

As can easily be assessed from this presentation of performance approaches, this book refers to performance along the lines of "absolute music" as introduced above in the third approach. It may also be valuable to performers in the first group who are prepared to undergo thorough training on the clavichord.


c) The preludes in Bach's Well Tempered Clavier

Bach's Preludes feature among those musical works which, by their very title, give no indication about what can be expected in the piece. While headings like Fugue or Invention comprise a clear definition of the polyphonic texture to which the piece will submit, and titles like Gigue, Bourrée, Allemande, Sarabande etc. indicate the meter as well as the character of the dance, the word Prelude reveals nothing whatsoever about the structure, the texture, the melodic / harmonic / metric organization or character of the music. The only implication of the word "Prelude" is that it originally served as some sort of an introduction to a subsequent, generally more important piece.

Socio-historically, it is of some importance to recall the venue in which any instrumental (non liturgical) music at Bach's time would have been heard. Such performances would not take place in a hall or building specifically destined for this purpose for instance a concert hall where the "audience" could be expected to attend with due respect for both the music and the performing artist. On the contrary, it was the musician who would set out to the home of a patron where he might be granted the honor of being listened to.

Imagine the situation. As soon as the musician arrives at such place, he has to assure himself of three very different preconditions: that he is acquainted with the tricks and traps of the instrument on which he will be performing; that his hands feel warm and flexible enough for the task ahead; and, last but not least, that his audience (who are in many cases not educated to truly appreciate newly composed music) have finished their ongoing conversations, have put down their glasses and are prepared to listen to him. It therefore seems most adequate that he play some brilliantly arpeggiated or meditatively rolling broken chords, perhaps even improvise on a little musical figure or motive, and thus prepare himself and his audience for the expected main composition.

Such was, for many decades, the expected and agreed purpose of a prelude. In the course of time, however, this attitude gradually changed, and the prelude rose in esteem. After having long been regarded as a musical organism which needed little prior meditation and was hardly worthy of being written down, it now became the integral part of an entity as in "Prelude and Fugue" or "Prelude and Toccata" combinations. There can be no doubt that the preludes in Bach's "Well-Tempered Clavier" all enjoy this distinction.

Besides this socio-historical background of the entire species of preludes, there is another interesting aspect regarding some of the preludes from volume one of the Well-Tempered Clavier. Their immediate source can easily be traced back to Bach's own earlier writing. A considerable number of the pieces have actually originated from preludes (mostly shorter pieces) written by the composer himself for the keyboard instruction of his eldest son Wilhelm Friedemann.

Several of those Well-Tempered Clavier preludes which derive from this source fit the same description: they appear determined primarily by broken chord patterns and a motion in equal note values, appropriate in this case for the training of Wilhelm Friedemann's pianistic skills. When integrating these compositions into what was to become the Well Tempered Clavier, Bach enlarged many of them considerably; yet their origin remains clearly discernable. (Examples for this type include the WTC I preludes in C major, C minor, D major, D minor, Bb major, G major, and E minor).

A second group of preludes seems to originate from the practice mentioned above: that of attracting an audience's attention through improvisation of some little figure or motive. Finally, there is a third group which contains intricate, highly sophisticated compositions which often rival their ensuing main piece both in beauty and artistic weight.


d) The fugues in Bach's Well Tempered Clavier

The word "fugue" can be traced back to two origins. On the one hand, the Latin word "fuga" denotes "flight, escape" and thus seems to describe the imitative process from an unusual angle: that of the opening voice running away from its followers. On the other hand, the German verb "fügen" signifies "to assemble, to put together meticulously", with the corresponding noun "Fuge" designating a joint in a parquet floor or tiles or bricks in a particularly well-ordered pattern; you may find that this explanation fits the musical "Fuge" quite appropriately.

A fugue is a strictly contrapuntal composition for a given number of parts or "voices". (The terms "part" and "voice" are interchangeable, whether the work is vocal or instrumental; hence "fugue in three voices" or "three-part fugue").

The fugue had two main forerunners: the ricercar a contrapuntal instrumental composition of the 16th-18th centuries in strict imitative style, and the medieval motet a vocal composition based on a given melody and wording to which one or more separate lines (with different texts!) were added in counterpoint. All these highly intricate polyphonic forms were natives of the Renaissance, reflections of Renaissance philosophy and religious attitude. At the beginning of that era which was to become known as the "Baroque", the religious movement of the Counter-reformation originally set out to abolish all obsolete forms and replace them with more immediately accessible patterns. However, as we all know, the counter reformation did not succeed in Northern Europe whose inhabitants remained Protestants. By the same token, North German composers were much more reluctant than their contemporaries in France and Italy to give up those serious and complex forms. For these pious men, the intricate and superbly organized forms in which each little detail had its place and meaning seemed to reflect their aesthetics and beliefs. This music was composed in the first place "for the greater glory of God"; of secondary importance was Man, his enlightenment, instruction and diversion. It is to this artistic attitude that we are indebted for the masterpieces of the species.