The title page of this collection of preludes and fugues
reads, in part:
“Das wohltemperirte Clavier oder Praeludia und Fugen durch alle
Tone und Semitonia sowohl tertiam majorem oder Ut Re Mi
anlangend, als auch tertiam minorem oder Re Mi Fa betreffend”.
This may seem like a mouthful for a title, but Bach wanted to make
sure what he was doing was understood, at least in its mechanics.
And yet some misconceptions have clung to the work which I wish to dispel
before diving into the material.
The usual English rendering of “wohltemperirte” is well-tempered, which
has to do with tuning. The ancient way, called “Pythagorean tuning”,
used harmonic resonance as a guide, making fifths and fourths conform to
exact mathematical ratios, 3:2, 4:3. This made these intervals very sonorous,
but had serious problems. The major third, which the ear wants to
hear as a different, higher harmonic (5:4), is made quite ugly by this
system, except for about three chords, greatly limiting the possibilities
of harmonic variety. And when the perfect fifth is compounded twelve
times, you don’t land on the same pitch you started on. In other
words, tuning up from Eb : Bb F C G D A E B F# C# G# creates an interval
between G# and Eb which is so far from perfect that it was called the “wolf
fifth” because it resembled the howl of a wild animal. This error,
called the “Pythagorean comma”, was overcome in practice by bending the
natural intervals slightly, called “tempering”. And by the eighteenth
century, there were about as many systems for doing this as there were
organ builders and keyboardists. The test was what sounded good on
a particular instrument, so tuning was more art than science. The
system we have today is called “equal temperament”, and simply divides
up the error so that all intervals of the same type are identical.
This idea was already being considered in Bach’s day but did not have
wide acceptance, and is probably not what he meant by “well-tempered”.
More likely he was using a system which preserved subtle differences in
intonation between the keys, differences much appreciated in that time.
So “wohltemperirte” was not a technical term denoting a specific scheme,
but just a descriptive word for a system which allowed every note on the
keyboard to be used as a tonal center. And this was the revolutionary
change which this piece worked in the minds of musicians who studied it.
The old system of seven “real” tones and at least fourteen “altered” tones,
all with different pitches, is here consolidated into twelve tones, all
equally “real”, opening up a new world of expressive possibilities through
chromatic harmony and the “circle of fifths”, which is presented here as
fact before it was ever described as theory.
The next term which is widely misunderstood is “Clavier”. By this
Bach meant “keyboard”, the playing mechanism common to organ, clavichord,
harpsichord, piano, and most contemporary synthesizers. The puzzling
failure of publishers to translate this word in early English editions
of this work has created the false impression that it was written for a
specific eighteenth-century instrument, and therefore it is somehow impure
to play it on a modern piano or digital keyboard. I contend that
Bach knew that the keyboard would evolve, and used a generic term purposefully,
aware that he was guiding the future development of music.
The part about the major and minor thirds is clear enough, even if you
don’t read German. Which leaves one last confusion, also created
by publishers, which is the idea that this piece is “Volume one” of a larger
work. The WTC is complete and unique, and the collection of preludes
and fugues which was published as “Volume two” is not related to it and
would not have been called that by Bach. These two things are as
different as an epic novel and a collection of short stories. The
WTC is one work with forty-eight movements, each unique in form, harmony,
meter, which aims to fulfill the “doctrine of affections” by defining twenty-four
distinct emotional states, and that’s just with the preludes. The
fugues connect those emotional conditions to twenty-four different formal
schemes, giving a picture of the possibilities of the twelve-tone system
so vast as to inspire composers for centuries, truly a Musician’s Cosmology.
