Well-Tempered Bach

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On Today’s Menu:
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** Share some stollen cake
for the birthday of a legendary composer.
** Linger to consider how essential & companionable music is in our lives,
** Savor a last ½ cup sampling from the many interpretations of one man’s work.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


First Sip:

There’s nothing remarkable about it.
All one has to do is hit the right keys at the right time
and the instrument plays itself.

– Johann Sebastian Bach


Slice of Cake:

Five Bach Facts
that I learned this week

Johann Sebastian Bach had quite the Musical Pedigree.

His father, his grandfather, and his great-grandfather
were all professional musicians.

Bach had 7 children with Maria Barbara, his first wife.
Two of those children had musical careers.

He had 13 children with Anna Magdalena, his second wife.
Two of those children also had musical careers.

Was it family tradition or some dominant musical gene? Who knows?

All in all, there are over 50 known musicians and several notable composers in Bach’s family.1

Johann Sebastian Bach went to prison.

By 1717, after Bach had been working for almost 10 years for Duke of Sachsen-Weimar as the ‘Organist to the Court,’ a feud started up between the Duke and his nephew, Ernst August.

Bach wanted out.

He found a better job as Kapellmeister in charge of the orchestra at the court of Anhalt-Cöthen and so he asked the duke to allow him to resign. Because Anhalt-Cöthen was a friend of Ernst August, Duke Sachsen-Weimar threw a fit—and threw Bach into jail.

While there, Bach got to work. He wrote the Little Organ Book (Orgelbüchlein), a series of organ-and-choir pieces meant to span the seasons of a church year.

After leaving Bach in prison for a full month, Duke Sachsen-Weimar recanted. He released Bach and allowed him go start his new job.1

Johann Sebastian Bach’s showboating skills were legendary.

On a memorable evening in 1747, Prussian King Frederick II gave Bach a musical phrase (called a subject), and from that short phrase, Bach improvised a fugue in several parts—he created this song on the spot, and in front of an audience.

One version of this story is that it’d been Bach’s idea to perform and he asked the king for a subject as a base for his spontaneous fugue.2

Another version said that not only had it been the king’s idea, but that the king had prepared the subject ahead of time—and had specifically created it to be as difficult as possible to use in a fugue.3

There is no question, however, that Bach amazed everyone there.

He asked the King to give him a subject for a Fugue,
in order to execute it immediately without any preparation.
The King admired
the learned manner…it was thus executed extempore.

– from Johann Sebastian Bach: His Life, Art, and Work (1820)
J.N. Forkel

What’s more, over the years—and especially after Bach died—this story was greatly embellished.

In 1774, Baron Gottfried van Swieten said that the king had told him that Bach had improvised, and played on the spot, a fugue that went from 4 to 5 to 8 parts.

This is probably not humanly possible. Even improvising a good 3-part fugue would be impressive—and is much more likely what Bach actually performed.2

Johann Sebastian Bach championed a new theory.

Bach’s collection of pieces called The Well-Tempered Clavier can be seen as an advertisement for a controversial new theory of tuning keyboard instruments.

But first, that name: The Well-Tempered Clavier

I’d always thought clavier meant a clavichord.
It doesn’t.
It just means keyboard.

side note:
A historic 18th century harpsichord and
your portable digital keyboard
can both be called claviers.

I’d always thought the term well-tempered meant in a good mood.
It doesn’t.

side note:
Although, knowing Bach’s propensity for word-play,
he probably liked that it sounded that way!

Well-tempered is a way of tuning that replaced the older meantone temperament. Meantone temperament tunes for thirds and works well in most keys.4

Most, but not all.

For meantone tuning, notes like D♯ and E♭ have slightly different pitches—even though on a keyboard there’s only one black key to play both. This means there are extra tones within the scale, which can sound discordant in some keys.

These discordant sounds have a terrific name: wolf intervals.5

side note:
A singer hitting a resonant wolf interval
can sometimes shatter glass!

For well-tempered tuning, the notes and ratios are not equidistant, but are tuned so that all notes are pleasant to the ear. (No more wolf tones!)6 Tuning begins with the keynote and its octave, then the 3rd above the keynote, and then each of the 10 remaining half-steps of the octave are derived from the 4th or 5ths of those two. In this way, some 5ths will be wider than others, some thirds thinner. 6

And each key has its own mood.

Bach didn’t create this method of tuning, but he promoted and championed it.
Especially, of course, in his composition the Well-Tempered Clavier.

Pianos today are tuned to yet a third method: equal temperament.
In equal temperament, the ratio of distance between the notes is the same.

side note:
Each note in equal temperament
is found using a logarithmic function:
the ratio of frequencies for each half-tone
is equal to the twelfth root of two.
(Just in case you were wondering…)

The advantage of equal temperament is that any piece of music can be played in any major or minor key—
And musicians can more easily transpose songs from one key to another.4

What we lose are those moods that were distinctive to each major and minor key.

It also means that when we listen to today’s musicians play the Well-Tempered Clavier, we aren’t hearing quite the same music that audiences heard in Bach’s day.

Johann Sebastian Bach was a math nerd.

Actually I don’t know this is true. But I’ve certainly noticed that no article or lecture about Bach can resist comparing his music to intricate mathematical puzzles.

Waterfall (1961)
by M C Escher

For instance, in the book Gödel, Escher, Bach: An Eternal Golden Braid, author Douglas Hofstadter compares Bach’s musical puzzles (especially his fugues and cannons) with the visual puzzles of artist M C Escher—and then compares both to the work of Austro-Hungarian mathematician Kurt Gödel.2

** Happy 335th Birthday **
Johann Sebastian Bach

– born March 31, 1685
in Eisenach
in what is now Germany


Linger Awhile:

It is the special province of music
to move the heart.
– Johann Sebastian Bach

I’ve been thinking this week about how flexible music is—
and how dependable.

There is pop music or Broadway tunes to energize me to get dishes done or laundry folded.
There’s jazz at the end of the day to help me relax.

Music makes a grey rainy day look beautiful, and my room feel more cozy.
It keeps me company on long drives, and feels like consolation when I need a good cry.

When I want some quiet, time-to-work, stick-to-it, be-productive music,
my favorite choice is Bach. I have a list that I play on repeat. It includes parts of the Brandenburg Concerto, the Christmas Oratorio, Violin Concerto in A minor, Piano Concerto No. 5 in F minor, Suite No. 3 in D major, Suite No. 2 in B minor, Double Concerto in D minor, and the gorgeous Jesu Joy of Man’s Desiring.

Orchestral Suite #2 in B Minor, (the Badinerie movement)
The English Chamber Orchestra
Raymond Leppard, conductor
William Bennett, flute solo


“Half Cup More”

Over the years, Bach’s music has been widely interpreted.
Here a few very different takes on Bach…

This is Bach’s Fugue in A minor
by the Modern Jazz Quartet featuring vibes by Milt Jackson.
(Don’t worry, the intro guy only yaks for about 30 seconds.)

Here is Bach’s Air on a G string
by guitarist Paulinho Nogueira

And here is Bach’s Fugue in G minor
by George Barnes and the Jazz Renaissance Quintet
(It’s funny that you can hear someone say: “Don’t make any mistakes, whatever you do!”)

And then, there’s Yo-Yo Ma.
I can’t even describe how much this Bach piece ‘moves my heart’ and ‘refreshes my soul.’
It’s Suite No.1 in G Major.


Take-Away Box

The aim and final end of all music
should be none other than
the refreshment of the soul.
– Johann Sebastian Bach


Thank you for reading!
Kelly J Hardesty

Thoughts? Questions?
Scroll down to the endand you can leave me note!
Always so lovely to hear from you.

You Can Read More…

notes & footnotes:

“Johann Sebastian Bach: a detailed informative biography”
© 1964-2014 M&L Sartorius

Gödel, Escher, Bach: An Eternal Golden Braid (1979)
by Douglas Hofstadter

Michael Parloff
Lecture : “The Art of Late Bach” at Music@Menlo
Dec 8, 2018

Arthur Loesser
master class lecture: Bach’s ‘Well-Tempered Clavier’
University of Michigan,
July 12, 1965

Meantone Temperament
Encyclopedia Britannica online

I owe a huge debt of gratitude
to Tim Cooney,
who diligently explained temperaments to me—twice!
while patiently keeping his own.


Please note:
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If you’d rather they stay between us, just let me know.
© Kelly J Hardesty 2024

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