Well Tempered Clavier BWV 846-869
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.
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of the work as a historical document.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.
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.
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.
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
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.
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
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
1 in C major (constant 16th-note arpeggios, keeping
one chord per measure)
2 in c minor (constant 16th notes in a different
pattern than prelude No. 1, keeping one chord per measure)
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)
6 in d minor (16th-note triplets, mostly leaping
10 in e minor (16th-note runs in the left hand, with
a leap after the first note and 7 "rocking" 16ths
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.
15 in G major (16th-note triplets, again arpeggiated,
usually in the right hand and occasionally in the left)
18 in g-sharp minor (16th notes in 6/8 meter, three
ascending, then a leap down, then three disjunct)
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.
preludes are in trio
sonata style, with two clear melodic upper parts accompanied
by the left hand:
4 in c-sharp minor
18 in d-sharp minor
19 in A major
23 in B major
preludes are similar to Bach’s two- and three-part inventions:
3 in C-sharp major
9 in E major
11 in F major
preludes suggest dances:
8 in e-flat minor (sarabande)
9 in E major (siciliano)
14 in f-sharp minor (allemande)
23 in B major (allemande)
rhythm is generally slow in these pieces, changing once
per measure, and occasionally twice in one measure, though not
more than that.
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.)
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.
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:
fugue subjects are related to dances, especially those in compound
meter (F major)
subjects make heavy use of typical ornamental figures (c minor,
D major, E-flat major, F-sharp major, b minor)
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.
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.
does one create a fugue? There are a few simple steps to follow.
The opening is quite restrictive, and must be followed precisely:
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.
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.
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.
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:
statements of the subject
all the note values of the subject (quarters become halves,
eighths become quarters, etc.)
cutting in half all the note values of the subject (quarters
become eighths, eighths become sixteenths)
turning the intervals upside (ascending becomes descending)
the subject backwards
designed so that the lower part and upper part can be reversed
(usually the parts are transposed up and down an octave, respectively)
invertible counterpoint in two parts (upper and lower parts
counterpoint in three parts
sustaining or re-articulating a single pitch, especially in
the bass register (happens often near the final cadence)
section of the fugue which does not contain a complete statement
of the subject
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)
statement of the subject which is altered is some way
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.
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