The Well Tempered Clavier BWV 846-869

Is there a better reminder of Bach as a teacher than the Well-tempered Clavier? This may be Bach's best-known keyboard work. There are actually two complete sets, book I and book II, each of which contains 24 preludes and fugues, one for each key. The first set was written in 1722, while Bach was in Weimar. (This is the work which will be performed during the May 2001 festival.) The second book comes from Leipzig in 1740.

To us, the Well-tempered Clavier is standard fare. All pianists know at least some selections from this work. But because none of us was born before 1722, we can't really appreciate the importance of the work as a historical document. The reason is because of the "well-tempered" part of the title.

In Bach's day, there were two main conventions of tuning a keyboard: mean-tone temperament or equal temperament. Both are based on the alteration of acoustically pure intervals.

Mean-tone temperament was developed first (around 1500). In this system, pure perfect fifths are made slightly smaller (by 22 cents—that has to do with cycles of vibrations per second, not cost of living!). In simple keys with one or two sharps or flats, music performed is pleasant to the ears, but the further away one moves from C, the more dissonant and out-of-tune it sounds. Think about it: if I reduce each fifth by 22 cents, starting with C, then C to G is 22 cents smaller than "pure"…C-D is 44 cents smaller than "pure"…C-A is 66 cents smaller than "pure"…C-E is 88 cents smaller than "pure,"…and so on. As we reach common "enharmonic" pitches and keys (pitches occupying the same spot on a keyboard, though notated differently, such as G-sharp and A-flat), the difference becomes so significant that the pitches are almost a full quarter-tone apart. Thus, G-sharp in this tuning system cannot substitute for an A-flat. Therefore, only music in keys with few sharps or flats really sound pleasant.

In equal temperament, which Bach calls well-tempered, the octave is divided into twelve equal semitones. Since all semitones are equal, no combination sounds worse or better than any other. Thus, F-sharp major is as pleasing and "in-tune" a key as is C major. This is what Bach was trying to show with his Well-Tempered Clavier sets—that you can play in any key and the music will still sound agreeable. It's sort of the socialist approach to tuning. (NOTE: The system of tuning known as "equal temperament" really wasn't adopted until the 19th century. We're not entirely sure if Bach's works are an early example of the use of this tuning, or of someone experimenting with something like equal temperament.)

What do you need to know about the preludes? Well, it's difficult to make generalizations which will apply to twenty-four pieces, but here are a few things.

  • We tend to think of "prelude and fugue" as being paired together, where the prelude is not complete without the subsequent fugue. This is not the case here. In fact, each prelude has a distinct ending, and in most cases, the ending is very strong and final.

  • The definition of a prelude in the 19th century (as in such works as Chopin’s 24 Preludes, Op. 28) is a small, unattached number, minimal in scope, and often based on a single melodic or rhythmic idea. This definition can be applied to many of the works in Bach's WTC Book I, as well, including
    • No. 1 in C major (constant 16th-note arpeggios, keeping one chord per measure)
    • No. 2 in c minor (constant 16th notes in a different pattern than prelude No. 1, keeping one chord per measure)
    • No. 5 in D major (again, constant 16th notes; a single note followed by a leap, then three stepwise notes in the opposite direction from the leap)
    • No. 6 in d minor (16th-note triplets, mostly leaping in arpeggios)
    • No. 10 in e minor (16th-note runs in the left hand, with a leap after the first note and 7 "rocking" 16ths following)
    • No. 14 in f-sharp minor (a group of four 16ths, three descending by step, ending with a leap up), with the motive sometimes in the left hand, sometimes in the right.
    • No. 15 in G major (16th-note triplets, again arpeggiated, usually in the right hand and occasionally in the left)
    • No. 18 in g-sharp minor (16th notes in 6/8 meter, three ascending, then a leap down, then three disjunct)
    • No. 22 in b-flat minor (starting off the beat, two 16ths, followed by three 8ths) Others seem to use one motive for a while, but then a different idea takes over.

  • Some preludes are in trio sonata style, with two clear melodic upper parts accompanied by the left hand:
    • No. 4 in c-sharp minor
    • No. 18 in d-sharp minor
    • No. 19 in A major
    • No. 23 in B major

  • Some preludes are similar to Bach’s two- and three-part inventions:
    • No. 3 in C-sharp major
    • No. 9 in E major
    • No. 11 in F major

  • Some preludes suggest dances:
    • No. 8 in e-flat minor (sarabande)
    • No. 9 in E major (siciliano)
    • No. 14 in f-sharp minor (allemande)
    • No. 23 in B major (allemande)

  • The harmonic rhythm is generally slow in these pieces, changing once per measure, and occasionally twice in one measure, though not more than that.

  • With one exception, all of the preludes are through-composed, meaning there are no internal repeats. The only exception comes in the last prelude, which is in binary form. (There are several examples of binary form in WTC Book II.)

  • Several of the preludes fall into clearly defined sections, based on distinct changes of character and/or melodic material. These include No. 7 in E-flat major (3 sections); No. 21 in B-flat major (two sections). Others include a brief change of character/texture approaching the final cadence.

What about the fugues? Anyone who knows anything about music looks to Bach as the master of the fugue, and why shouldn't we? He wrote 48 different fugues, 2 in each key, in the two books of Well-Tempered Clavier alone, and that doesn’t even account for the hundreds of other fugues for keyboard, organ, or chamber ensemble written throughout his life. His final works, in fact, are found in the Die Kunst der Fuge (The Art of the Fugue). Like Bach's preludes it is difficult to generalize about all of Bach’s fugue, even limiting ourselves to WTC I, but three are a few things to note:

  • Some fugue subjects are related to dances, especially those in compound meter (F major)
  • Some subjects make heavy use of typical ornamental figures (c minor, D major, E-flat major, F-sharp major, b minor)
  • Some use a subject in long, slow notes, in the tradition of the ricercar and earlier forms of imitative writing, including Renaissance motets (c-sharp minor, e-flat minor, f minor, f-sharp minor, b-flat minor). Since all of these are in the minor mode, they have a common "pathetic" sound.

Recipes for Fugues
Taken as a whole, the 24 fugues contained in WTC I serve as a textbook of 18th-century counterpoint. Everything you would wish to see in practice occurs within the 24. That's what's so wonderful about fugal writing -- it is at the same time both very free and flexible, yet very restrictive.

How does one create a fugue? There are a few simple steps to follow. The opening is quite restrictive, and must be followed precisely:

  • Create a subject. This is the main theme of the fugue. It must be interesting enough to stand on its own, because the first time we hear it, it appears unaccompanied.
  • Choose the number of voices. These are the independent parts, not singers. In WTC I, Bach writes for as few as 2 voices (in e minor) and as many as 5 (in c-sharp minor, b-flat minor. This is an important decision, because it governs how many individual statements of the subject will appear to open the fugue.
  • Begin by deciding which voice (soprano, alto, tenor, bass ranges) will perform the subject first. When the subject is complete (it usually runs just a measure or two, but could be longer in a piece with short measures and a quick tempo), begin the subject in a second voice. Now make sure that the first part continues to perform, playing something which sounds good with the subject. Continue this procedure until all parts are playing. You have two basic choices in this "filler" material: 1) to write a new melody of independent character, which will be a recurring feature of the fugue, usually appear with subsequent statements of the original subject [this is called a countersubject]; or 2) "simply" fill in the music with pitches that complete the harmony and help to propel the motion forward. The later is much more difficult.

Once you've completed the steps above, you are done with the exposition of the fugue. The rest of the recipe is yours to create, without restrictions or guidelines except that you have to occasionally bring back the original subject. Here are your optional ingredients:

stretto overlapping statements of the subject
augmentation doubling all the note values of the subject (quarters become halves, eighths become quarters, etc.)
diminution cutting in half all the note values of the subject (quarters become eighths, eighths become sixteenths)
inversion turning the intervals upside (ascending becomes descending)
retrograde playing the subject backwards
invertible counterpoint designed so that the lower part and upper part can be reversed (usually the parts are transposed up and down an octave, respectively) [see below]
double counterpoint invertible counterpoint in two parts (upper and lower parts are interchangeable)
triple counterpoint invertible counterpoint in three parts
pedal point sustaining or re-articulating a single pitch, especially in the bass register (happens often near the final cadence)
episode section of the fugue which does not contain a complete statement of the subject
real answer a statement of the subject which employs exactly the same intervals as the original, both in terms of quality and size (major third, perfect fifth, etc.), even if the subject begins on a different pitch from the original; an answer is also considered real if the transposition is diatonic (that is, the quality of some intervals changes in order to fit the new key, but the size of the intervals is retained)
tonal answer a statement of the subject which is altered is some way


Lee's look at one fugue in detail to see how Bach constructed it. This is Fugue 16 in g minor. (To be honest, I chose this one because it's one of the shortest.) All statements of the subject, tonal and real, are marked in orange. [Where you see two or more simultaneously orange lines, you are looking at stretto.] A circled "T" indicates a tonal answer; a circled "R" indicates a real answer. The end of the exposition is marked with a vertical red line. The countersubject is shown in yellowish-green. The key invoked at the time is indicated in purple. Look at the measures with no orange. These are episodes, sections with no complete statement of the subject. Notice how full these passages are with incomplete statements of the subject or countersubject. This is very dense contrapuntal writing.

Here's the opening of this fugue. Bach did not know the piano, though that is the instrument of choice for most people performing WTC today. (Pianos are simply more accessible than harpsichords.) The performance at May Festival will take place on the harpsichord, but because it's a little easier to hear individual lines on the piano, I've selected a brief excerpt on piano for you to listen to.



Here are some more detailed analyses of individual preludes and fugues you can find on the Internet:

Prelude and fugue in C major

Prelude and fugue in c minor

Prelude and fugue in c-sharp minor

©2003 Carol Traupman-Carr

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