Jorgensen on Temperament
About the Temperament Used by J. S. Bach and Others
By Owen Jorgensen
It was a significant historical event when J. S. Bach (1685 1750) titled
his volume of the 24 preludes and fugues finished in 1722 as "Das wohltemperierte
Clavier" (The Well-tempered Clavier). This was the first time a great composer
had written serious and lengthy keyboard music equally extensive throughout
all the possible major and minor tonalities. Also, this was the only time
in history that a composer mentioned on the music score a required tuning
or temperament for the music to be performed.
Link to Well-Tempered Clavier played in Young's Well Temperament
The necessary specification in Bach's title that the keyboard must be
"wohltempirte" was used to inform musicians who knew the meaning of the words
"well-tempered" that Bach's new set of preludes and fugues could not be performed
in any form of the traditional meantone temperament. Meantone temperament
had been the standard common practice on keyboards since the early Renaissance.
In this, the philosophy was to tune the most commonly used intervals as in-tune
or harmoniously as possible at the expense of the other intervals that were
never used during the earlier centuries.
In any meantone temperament form, two-thirds of the chords are far more
harmonious and intune sounding than the same chords played in the modern
equal temperament that is universally practiced today. Unfortunately, the
remaing one-third of the harmony in meantone temperament is completely ruined
by all of the out-of-tune intervals called "wolf" intervals. These are pushed
into the remote, lesser used keys or tonalities on standard keyboard instruments.
Bach knew that his music could never be performed in meantone temperament
because of the extreme out-of-tuness among the raised keys (black keys on
In equal temperament, one can perform in all the major and minor keys without
encountering any "wolf" intervals. Close approximations of equal temperament
were used on most fretted instruments such as lutes and viols since the early
Renaissance. Listening to the fretted instuments, musicians in history have
always been familiar with the qualities and sounds of the quasi-equal
temperaments. Regardless of this, "no Renaissance keyboard musician is known
to have advocated or adopted equal temperament".(1) Musicians continued to
use meantone temperament on keyboards even into the Baroque period. The basic
harmony among the natural keys (white keys on modern pianos) that they used
did not require equal temperament, and the music sounded significantly more
harmonious and intune when performed in meantone temperament.
During the seventeenth century, there were a few progressive keyboard musicians
who were beginning to modulate into the previously unused remote tonalities
using many flats and sharps. This action required that the meantone temperament
had to be altered somewhat. The practice of these musicians eventually culminated
in the work of J. S. Bach who modulated through all the tonalities on his
Bach's term "wohltempirte" was based on the writings of Andreas Werckmeister
(1645-1706) who was a prominent organist, organ examiner, music theorist,
author, and composer. In 1681, Werckmeister wrote about "ein Clavier wohl
zu temperiren und zu stimmen sey"(2) (a keyboard well to temper and to tune).
In his book of 1691, he described the "wol temperirt stimen" and "der
temperaturen wohl".(3) This terminology is now translated simply as "well
temperament" in contemporary writing. For an example, see Willard A. Palmer's
edition of Bach's Das wohltemperirte Clavier.(4) In some books, it
is defined as "irregular temperament."
Werckmeister's well temperament published in 1681 was a continuation of the
earlier process of altering meantone temperament to be more practical. His
temperament was the first to modify meantone temperament enough so that one
could perform throughout all the keys without hearing any "wolf" intervals,
the same as can be done in equal temperament. The purpose of this well
temperament was to preserve as much of the meantone temperament harmoniousness
in the commonly used natural keys as possible while at the same time providing
for unlimited modulation. This gave the progressive musicians an opportunity
to avoid using the various quasi-equal temperaments which had always been
despised because they destroy the harmoniousness in the commonly used keys
that keyboard musicians had been accustomed to hearing for centuries. A valuable
by-product of Werckmeister's temperament philosophy was the establishment
of a variety of effects throughout all the keys that always provided interesting
and refreshing color changes during modulations. This along with the
harmoniousness in the popular tonalities were the advantages that well
temperament held over equal temperament.
As a consequence of the more intune harmony in the natural keys of well
temperament, it was necessary to allow the triads among the lesser used chromatic
keys with many sharps or flats to become a little more dissonant than the
same triads in equal temperament. Nevertheless, these rarely used triads
were never considered to be intolerable. (With the great acoustical changes
in the development of the modern piano, it has been found that these previously
harsh harmonies add a significant resonance and beauty to the tone of modern
pianos. This may be one reason why Chopin preferred the black keys.(5)
Conversely, Haydn and Mozart composed mostly among the white keys because
they began their training on harpsichords that did not have this acoustical
advantage. However, they often modulated into the most remote keys in order
to feature contrasting effects.)
Major thirds determine the color qualities or effects of triads or chords
more than any other interval. Second in importance in this way are the major
sixths and minor thirds. As the philosophy of well temperament developed,
it eventually became apparent that the tonic major third C-E in the key of
C must be tempered the least of any because there are no flats or sharps
in the key signature for C major. In the keys of F and G which contain one
flat and one sharp, respectively, the major thirds F-A and G-B were tempered
alike and also a shade more than C-E. Continuing, B flat-D and D-F sharp
were tempered more again because of the two flats and two sharps in the
respective key signatures. E flat-G and A-C sharp were tempered still more
and also very similar to equal temperament major thirds. This process continued
around the circle of fifths until the ultimate was reached in the Pythagorean
major third G flat-B flat which was the largest or most tempered major third
allowed. This Pythagorean third (ditone) along with the four just intonation
fifths involved was a final last remnant of the Greek thought from ancient
From the above, it is apparent that well temperament was not a haphazardly
constructed temperament. Instead, it was governed by major thirds that gradually
and evenly changed in their color effects around the circle. In this way,
the major thirds supported the rules of tonality as it developed. Also, musicians
could be secure in knowing what to expect as they proceeded to perform throughout
all the tonalities.
According to theory, there can be only one equal temperament on the standard
keyboard. In contrast to this, well temperament is an unequal temperament;
therefore, an unlimited number of varieties of it are possible. When the
major third rules are followed, the countless varieties of well temperament
can be compared by measuring the amounts of tempering degrees done between
C-E and G flat-B flat. The changing effects in various well temperaments
can be either highly contrasting or very mildly contrasting, depending on
the tastes of the tuners.
The tuning of equal temperament is a science based on following precise
mathematical rules. In contrast to this, the tuning of well temperament can
be a highly developed art depending on musical instinct, experience, and
The slightly unequal tones of well temperament were the physical reason why
the so-called "characters of the keys" existed on keyboards in the past.
Most eighteenth-century musicians were aware of this fact. By the "characters
of the keys", it was understood that each key such as C major, D major, etc.,
had its own unique distinctive qualities, personality, or key-color effects.
Composers of the past chose the key for a piece that would enhance the spirit
of their composition the most.
The "characters of the keys" cannot exist on keyboards when they are tuned
in equal temperament. The reason for this is that intervals of a kind in
equal temperament are identical in their sizes; therefore, there can be no
varieties in this. Anyone of today who professes to hear any "characters
of the keys" on an equal-tempered piano are psychologically deceived. It
is psychological in equal temperament when one imagines that when one reads
music written in sharps it sounds quite different from when it is written
in flats. It is also psychological when playing music among the white keys
it sounds different than when it is transposed into the black keys. Some
musicians have acquired a second-hand appreciation of the "characters of
the keys" through the spirits of the pieces in certain keys that they learned
Werckmeister included the descriptions of several temperaments in his books,
but he is famous only for his temperament known as the "Werckmeister III"
published in 1681 and 1691. This is called "Werckmeister's Correct Temperament
No. 1" in some books. His book of 1691, Musicalische Temperature, was highly
successful and was distributed throughout Germany. It became a standard text
book on tuning in Germany throughout the eighteenth century.
Werkmeister near the end of his life changed his mind about the unacceptability
of equal temperament on keyboards. His new books published between 1702 and
1707 caused Werkmeister to be acknowledged as the prophet who made the practice
of equal temperament on keyboards possible in Germany. To Germans, he is
the father of equal temperament. Nevertheless, Werckmeister himself still
preferred well temperament at the end of his life. He wrote that he was still
willing "to have the diatonic thirds left somewhat purer, than the other,
less often used ones". (6)
Bach had an indirect connection to Werckmeister through his very close friend
and cousin Johann Gottfried Walther who was a disciple of Werckmeister. Walther
visited or studied under Werckmeister in 1704. Werckmeister and Walther continued
to correspond with each other. Walther's greatest contribution in music history
was the completion of his monumental Musicalisches Lexicon published in 1732.
The most commonly used term for equal temperament in Germany in 1722 was
"die gleichschwebende Temperatur". The fact that Bach did not use the title
Das gleichschwebende Clavier for his preludes and fugues is a strong indication
that he did not accept equal temperament as the best solution for his new
music in 1722.
All the musicians of the past who were against the adoption of equal temperament
on keyboard instruments referred to the loss of distinctive key-characteristics
in equal temperament as the greatest tragedy in music. In 1722, each tonality
had a special quality, and this provided a reason for Bach to compose in
all the keys,
It is unlikely that Bach would have considered equal temperament for his
project. For example, what purpose would there have been for Bach to compose
in keys like C sharp major if he was using equal temperament? In equal
temperament, the Prelude and Fugue in C sharp major sounds identical to its
transpositions into C and D major. In C sharp major, music is significantly
more difficult to read and play, and there is nothing to be gained by using
C sharp major in equal temperament.
Bach's intellectual feat of writing music in the difficult keys like C sharp
major and F sharp major is by itself not impressive. Any amateur
eighteenth-century composer could have written a piece in C major and then
proceeded afterwards to add seven sharps or seven flats to the key signatures.
Obviously, there were other reasons like the "characters of the keys" to
compose in the difficult lesser known remote tonalities. At this time in
history, both Mattheson and Bach obviously were exploring for new effects
in the previously untapped remote-key resources of well temperament. The
current popular notion that Bach composed in order to demonstrate equal
temperament is ridiculous. Lute musicians already did this centuries before
The knowledge of how to tune equal temperament by ear according to today's
standards did not begin to exist until 1887 and was not fully developed until
1917. (7) All equal temperament by ear attempts done before 1887 were only
rough versions of quasi-equal temperaments. During the eighteenth century,
it was believed that a monochord was necessary for tuning equal temperament.
In contrast to this, no monochords were required for tuning many of the well
temperaments. These were easily done by ear because they were unequal
temperaments that did not require the exact mathematical alterations such
as those needed for equal temperament.
There is no known evidence that Bach needed a monochord while tuning. Also,
it is obvious that none of the listening techniques discovered between 1887
and 1917 were known to Bach. If they were, this valuable information would
have been passed along to his students and relatives. Instead, Bach's son,
C. P. E. Bach in 1753, described in very faulty and deficient terms how equal
temperament was tuned by ear. (8) The results of this could only have been
a rough quasi-equal temperament.
Johann Mattheson (1681-1764) was a German composer, theorist, and the most
important writer concerning music and musicians from the Baroque period.
His education was exceptionally broad, and his musical abilities evidently
were unlimited. As an avant-garde composer, Mattheson was writing in all
twenty-four major and minor keys by 1719, predating Bach's effort by three
years. As a spokesman of the times in 1719, Mattheson wrote, "It is not the
purpose of music that all the twelve semitones be of equal size; rather they
should all sound pure and lovely
. But when they are tuned equally they
all sound false. So, why make this effort" (9) to tune in equal temperament?
This attitude remained strong among musicians through the end of the century.
Mattheson's Forty-Eight Thorough-Bass Test-Pieces in all the keys was finished
in the same year as the above statement. This is an indication that in Bach's
time musicians did not find it desirable to apply equal temperament even
though the music was written in all the keys.
In 2002, Mark Lindley wrote, "None of the masterworks of late Baroque and
Classical German keyboard music was, in fact, created in a pervading ambience
of equal-tempered intonational sameness among the various triads and keys,
although some forward-looking composers did tend, like C. P. E. Bach, to
think in such terms". (10) In consideration of all the above, equal temperament
is not used by Frank French in his new CD recording of J. S. Bach's The
Johann Philipp Kirnberger (1721-1783) was a very important German music theorist
who had studied composition and performance under J. S. Bach for two years
beginning in 1739. In 1771, he wrote that equal temperament was still "impossible
to tune without using a monochord
. Equal temperament abolishes the
variety between the keys and leaves us with only two characters since all
the major keys on the one hand and all the minor keys on the other are completely
alike. Therefore, we have not only gained nothing by (expanding to) twenty-four
keys, but have instead lost a great deal. For the simple diatonic scales
as the ancients used them
produced different keys with distinct
characters, from which that key was best suited in expression could always
be chosen. Equal temperament abolishes this and leaves the composer only
with the choice between major and minor." (11)
The above thoughts by Kirnberger reflected those of late eighteenth-century
musicians. He also wrote, "Each key has its own special degrees (Sayten)
and intervals through which it receives its own character, its own impression,
both in the harmony and melody, and through which it is distinguished from
all the others". (12)
Kirnberger revered J. S. Bach as being the supreme composer of all time.
He dedicated his life to transmitting the theoretical principles of J. S.
Bach. He also struggled very hard to get some of Bach's music published.
In 1779, Kirnberger created a temperament known as Kirnberger III. In some
books this is called Prinz or Aron-Neidhardt temperament. This is a wonderful
temperament, and it is simply the Werckmeister III altered and improved.
In the original Werckmeister, the major third C-E was tempered a small amount
wide. In the Kirnberger, C-E was made completely pure in just intonation.
This had the effect of increasing the amount of contrast between the least
tempered and most tempered thirds. Thus, the contrasts were more striking,
and the "characters of the keys" were supported to a stronger degree.
Since J. S. Bach trained Kirnberger in harpsichord tuning, it would be very
easy to assume that the Kirnberger III temperament was Bach's tuning.
Kirnberger's writings are a very strong indication that J. S. Bach preferred
well temperament over equal temperament, and this also explains why Bach
did not use the term Das gleichswebende Clavier for his music.
Friedrich Wilhelm Marping (1718-1795) was a German music theorist who began
to promote the idea of equal temperament on keyboards in 1756. Evidently
it was still not very commonly practiced even though it was acknowledged
and approved of in Werckmeister's latest books. As an avant-garde equal
temperament enthusiast, Marpurg became an archenemy of Kirnberger. In 1776,
Marpurg reported that he learned from Kirnberger himself that J. S. Bach's
temperament contained no just intonation thirds. Therefore, Kirnberger's
temperament is also not used in the new recording of The Well-tempered Clavier
by Frank French.
The Werckmeister III temperament of 1681 was the first primitive attempt
at creating a good well temperament, and it contained a few crudities. Because
of the minor flaws and the following considerations, the Werckmeister III
temperament also is not used in the present recording by Frank French.
Forty-one years elapsed between 1681 and Bach's great composition of 1722.
During this time, refinements were done. Bach tuned by ear. By applying his
experienced musical instincts and great aesthetic taste judgements he could
have very easily tuned according to Werckmeister's philosophy while at the
same time instinctively eliminating all the flaws and crudities. Bach's tuning
was certainly more refined than Werckmeister's published mathematical
specifications which were no more than a theory on paper. Bach in applying
his talent would not have been concerned about any mathematics or specific
numbers of beats. These are needed only for theoretically precise methods
like the modern equal temperament.
Since the Werckmeister III temperament roughly followed the key-signature
rules of tonality that had been developing, the temperament can be classed
as a musical temperament more than as a scientific temperament such as equal
temperament. As an artful temperament it was better to tune it through music
testing rather than by the monochord directions provided by Werckmeister.
Concerning the theory on paper, corrections and refinements continued to
be done. Francesco Antonio Vallotti (1697-1780) was an Italian composer and
theorist. He corrected F-A and G-B to become the same size because of the
one flat and one sharp, respectively. In the same way, he also corrected
the pairs E-G sharp and A flat-C as well as B-D sharp and D flat-F. In addition,
he reduced the beatings of the tempered fifths significantly so they would
become much more pleasant to listed to; otherwise, this was still the
Werckmeister III temperament.
Thomas Young (1773-1829) was a natural philosopher, physician, writer,
administrator of science, musician, and master of many languages including
ancient Egyptian. He is famous in history for his undulatory theory of light.
He had a thorough knowledge of acoustics and temperament history including
that of equal temperament. His Temperament No. 1, written down in 1799, was
the Werckmeister III corrected to the ultimate degree. As such, it was almost
identical to the Vallotti correction except that the major third C-E was
made slightly smaller than the paired thirds F-A and G-B. Also, the paired
major thirds B-D sharp and D flat-F were made slightly smaller than F sharp-A
sharp or G flat B flat. The major third C-E was tempered only an extremely
small amount wider than in the original Werckmeister III. Young's theoretical
temperament was the first in history to follow the rules of tonality completely.
More clearly, in progressing through the circle of fifths, each tonic major
third changed in its size or tempering according to its key signature in
an extremely even and dependable manner. Young's temperament is the most
musically perfect temperament that has ever been published.
Young wrote that this temperament represented "the actual practice of the
best instrument makers". (13) Thomas Young was certainly accomplished enough
as a qualified acoustic scientist to make this judgement honestly. Young
also wrote, "Indeed, in practice, this method, under different modifications,
has been almost universal". (14) This temperament represented the common
eighteenth-century practice more than any other; thus, it is often referred
to as The Thomas Young Representative Eighteenth-Century Well Temperament
of 1799. This is the tuning used in the new recording of The Well-tempered
Clavier by Frank French.
Admittedly, this is still only another mathematical theory on paper; however,
Bach and others who tuned from a musical standpoint rather than using monochords
no doubt instinctively and empirically arrived at results very similar to
the above. The process was simple. By ear they tuned the natural keys somewhat
like in the old one-fifth comma meantone temperament, they let the fifths
in the chromatic keys become pure, and they averaged everything in between
so that triads when played in the order of modulation would change their
color effects gradually and evenly. In any case, by using the theoretically
correct Young temperament, authenticity is approached very closely according
to present day knowledge. Bach's tuning certainly was more like the Young
temperament than the Werckmeister III or any of the other known theoretical
The Effects on the Music
The Prelude No. 1 in C major from Book One of The Well-Tempered Clavier is
an introduction to the whole set of preludes and fugues. It is written in
a style that is quite different from the others. C major is the most harmonious
key in all the well temperaments, and Bach's arpeggiated writing in such
a high register reveals this clearly.
The major third between middle C and a higher E in the lowest parts is the
only major third featured in this piece through measure ten. In measure eleven
there is a lower G-B and in measure thirteen a lower F-A. These rather high
major thirds are in a very exposed position, and they are ruined when played
in equal temperament. Middle C-E in equal temperament has a beating frequency
rate of 10.4 per second. This is entirely too fast to be pleasurable, and
it gives C-E a very harsh quality. The lower G-B beats 7.8 per second, and
F-A beats 6.9 per second which is still not good. As has been written previously,
major thirds determine the effects or coloration in triads more than any
other interval. Anyone who has become accustomed to hearing Prelude No. 1
in well temperament will realize how harsh this piece sounds in equal temperament
and how unlikely it was that Bach used equal temperament.
If Bach had used equal temperament, he would have written this prelude in
a much lower position in order to reduce the objectionable beating. In the
high register that Bach chose for this piece, the arpeggiated harmonies sound
like harps in heaven when played in well temperament.
In the Thomas Young Representative Well Temperament, the above major thirds
C-E, G-B, and F-A beat 4.1, 4.3, and 3.8 per second respectively. In the
original Werckmeister III, C-E beats 3.0 per second. In the Vallotti temperament
C-E beats 4.4 per second. Any of these are a reduction by more than half
from the objectionable beating of C-E in equal temperament. The fact that
C-E, G-B, and F-A beat virtually at the same rate in the Young temperament
facilitates the tuning process. Even though G-B and F-A beat roughly the
same as C-E and therefore in vertical harmony they sound just like C-E, they
nevertheless are tempered to be larger then C-E. Temperament scholars understand
In well temperament when Prelude No. 1 is transposed either a semitone higher
or a semitone lower, it sounds unusually bad. This explains why there was
much writing during the eighteenth century against the practice of transposition.
Conversely, when transposition is done in equal temperament, nothing happens.
The vertical harmony in Prelude No.1 in C major sounds abrasive and less
harmonious when it is transposed into C-sharp major in well temperament.
Bach no doubt knew this. In his Fugue No. 3 in C sharp major he wrote the
music from a melodic standpoint rather than a vertical harmony standpoint.
By doing this, the vertical harmony problems in C sharp major were eliminated.
Among the black keys, all melodies are greatly enhanced by the sharper leading
tones and wider major sixths and major thirds in these keys. This offsets
the losses in harmoniousness. Just as Prelude No. 1 is ruined when it is
transposed into C sharp major, the Fugue No. 3 is spoiled when it is transposed
down into C major. In this latter transposition, Fugue No. 3 sounds very
lifeless and dead because of the much flatter leading tones and narrower
major sixths and major thirds among the natural or white keys in well temperament
In the original meantone temperament published by Pietro Aaron in 1523, the
three augmented seconds F-G sharp, B flat-C sharp, and E flat-F sharp were
not the minor thirds F-A flat, B flat-D flat, and E-flat-G flat that everyone
is accustomed to hearing as an interval having a ratio of 5 to 6. The augmented
seconds in this temperament were smaller intervals that had a ratio of 6
to 7. These smaller intervals are often called small minor thirds. As an
interval, they do not exist in equal temperament. In the well temperaments,
the three above named augmented seconds were preserved as being the smallest
minor thirds available in the temperaments. A fourth narrow minor third G
sharp-B was added to the group.
The extreme narrowness of these intervals caused them to sound extra minor
or sad and depressed in the keys of E flat minor, F minor, G sharp minor,
and B flat minor. As a result, many authors in the past described the
"characters" or emotions from these tonalities as being fit for extreme sadness,
depression, grief, death, funerals, etc. (15) When listening to Bach's music
in these keys, notice how closely he adhered to this spirit, especially in
Many sets of pieces through all the keys are arranged through the circle
of fourths or fifths in the natural order of modulation. Bach's unusual and
unique manner of arranging each prelude and fugue pair in a major key tied
to a pair in the parallel minor key in chromatic step-wise motion may have
been done for the following reason: In well temperament, when one plays a
series of chords through a circle of fourths or fifths in the natural order
of modulation, the changes in key-color effects are only mildly noticeable
because they are so gradual. Conversely, when one plays the chords in chromatic
succession up or down the scale, fantastic differences in qualities and effects
are heard. To place a prelude and fugue in C major that has no sharps in
the key signature nearby a pair in C sharp major containing seven sharps
brings out the extreme differences in key-characters. The placing of the
C minor prelude and fugue pair in between C major and C sharp major moderates
the contrasting effects to be more tasteful. When listening to Bach's music
arranged in chromatic order, the changing "characters of the keys' are always
noticeable, and this adds interest to the music.
1. Mark Lindley. "Temperaments" in The New Grove Dictionary of Music and
Musicians, second edition (New York: Macmillan Publishers Limited, 2002),
2. Andreas Werckmeister. Musicalische Temperature (Quedlinburg: Theodori
Philippi Calvisii, 1691; reprint with an added preface and commentary notes
by Rudolf Rasch, Utrecht: The Diapason Press, 1983), Rasch, 14.
3. The above reprint, 1.
4. J. S. Bach. The Well-Tempered Clavier edited by Willard A. Palmer (Sherman
Oaks: Alfred Publishing Co., Inc., 1981), 3.
5. Owen Jorgensen. "The Well-tempered Clavier, Part 4." Piano Technicians
Journal (November 2003), 33. "Part 5." (December 2003), 32. "Part 6." (January
6. Mark Lindley. "Temperaments." 25:254.
7. Owen Jorgensen. Tuning (East Lansing: Michigan State University Press,
8. C. P. E. Bach. Essay on the True Art of Playing Keyboard Instruments (1753).
Translated by William J. Mitchell. (New York: W. W. Norton, 1948), 37.
9. Rita Steblin. A History of Key Characteristics in the Eighteenth and Early
Nineteenth Centuries, second edition (Rochester: The University of Rochester
Press, 2002), 51.
10. Mark Lindley. "Temperaments." 25:257.
11. Rita Steblin. A History of Key Characteristics. 74.
12. Ibid., 75.
13. Thomas Young. "Outlines of Experiments and Inquiries Respecting Sound
and Light." Philisophical Transactions 90, Part 1 (January 1800), 144.
15. Rita Steblin. A History of Key Characteristics. 225-298.