DAILY DOSE of BEETHOVEN (October 20, 2020)
Recently, we traced some of the developments in the Medici salon in Florence Italy, that led directly into, among other things, the breakthroughs of J.S. Bach. One area of study that went on at the Medici Salon was the science of music, including Johannes Kepler's "Harmonies of the World." (Please review the posting on the C Minor series and Kepler, June 30, 2020). We also established that Bach followed these Italian developments closely.
At the same time, Bach's own part of Germany was undergoing a revolution especially in organ playing, that also drew on the work of Kepler. Many German organists trained in Amsterdam within the great Dutch organist Jan Pieterzoon Sweelinck (known as the "maker of organists"), then came back to Germany to lead the music in the great churches and cathedrals. Beautiful organs were built in Germany in those churches, first by Arp Schnittger and son, and later by Gottfried Silbermann, and his brother Andreas. They are still regarded as some of the most beautiful in tone and appearance today (see photos below).
The most famous organist of the 17th century was the Dane, Dieterich Buxtehude, who played at the Marienkirche in Lubeck. The then 20-year-old J.S. Bach thought enough of him to walk 250 miles to study with him, and overstayed his visit by four months! To get an idea of how Bach learned from Buxtehude, but also by how much he surpassed him, compare Buxtehude's “Ciacona in C Minor” played here on a Schnittger organ:
with Bach's “Passacaglia”, in the same key, played here on a Silbermann organ:
The challenge of the Ciacona/Passacaglia is to generate freedom and creativity out of the most restrictive form. Both feature a short bass line that repeats over and over. The composer has to create beautiful variations above that bass. In Buxtehude's work, the bass line is only 8 notes: C Ab G B C Eb D G. The Schnittger organ reveals some marvellous tone colors and combinations.
Bach's bass line is longer, 15 notes, and it begins with just the pedals: C G Eb F G Ab F G, D Eb B C F G C. At a certain point Bach marks "fugued". He takes the first half of the bass line and makes a fugue out of it. You can hear that change at 7:56 in this recording.
THE WELL-TEMPERED SYSTEM
The need to divide the octave into twelve half tones had been known to the Greeks since the fourth century B.C. Music was held back for centuries by false assumptions that mathematics was the cause of musical intervals, and that the ratios of intervals had to correspond to rational numbers. It was Kepler who finally freed music from those chains, but music still awaited a champion who could implement it by composing in all twelve tonalities (24 if you count both major and minor keys). In 1722, Bach composed preludes and fugues in all 24-keys and called it “the Well-Tempered Clavier” (keyboard). He tuned his clavier, so that it could play all of these works in tune (previous non-tempered tunings, based on rational numbers, would go out of tune as more sharps or flats were added.)
Bach's breakthrough was not just to be able to play in all the keys on the same keyboard, but to HAVE 24-keys (which had never really existed before), be able to COMPOSE in them all, and move freely from one to another WITHIN a piece.
Although there is reason to suspect that Bach was familiar with Kepler, there is no direct evidence. There is little doubt though, that Buxtehude did know Kepler, and would likely have passed the knowledge on to his students. Buxtehude was close friends with Andreas Werckmeister, who first coined the term " Well Tempered Clavier." Werckmeister wrote a book describing Buxtehude's new methods in counterpoint, and Buxtehude repaid Werckmeister with this poem., which twice puns on the meaning of Werckmeister (work master):
POEM
Wer ein Kunst-Werck recht betrachtet,
Es nicht unerkannt verachtet,
Redet frey ohn’ arge List,
Christlich, wie es billig ist;
Kömmt es denn auch auf die Proben,
Muss das Werck den Meister loben.
Er mein Freund! hat wol erwogen,
In dem Buch, und ausgezogen,
So der Kunst erspriesslich sey,
Treulich und ohn Heucheley,
Er ist auch Werckmeister worden,
Rühmlich in der Musen-Orden.
TRANSLATION
Whoever views a work of art properly,
does not disdain it anonymously,
speaks freely without arrant cunning, in a Christian manner, as is right,
for when it comes to the test,
the work must praise the master.
He, my Friend, has considered well,
in the book, and excerpted,
what is useful to art,
honestly and unfeignedly,
he has also become workmaster,
praiseworthy in the order of muses.
Buxtehude is also known to have composed a suite based on the 7 known planets of his time, which is now lost. Werckmeister wrote frequently of the need for a well-tempered system, and cited Kepler's work as the basis of a well-tempered system..
In his “Hypomnemata Musica”, a work on tempering, Werckmeister wrote:
“I wish to say something more about the excellent imperial mathematician, Johannes Kepler’s opinion, which he stated in the five volumes of De Harmoni Mundi, where he derives the cause of musical harmony out of the 5 regular solids in great detail … and says…that the Archetype is the cause in that it not only moves the stars to a more beautiful harmony (indeed not sensuous) but even more that it prepares the minds and souls of men so that they exist in such harmony and are moved through the heavenly motions, and are made joyful through sensuous, earthly music.”
Finally, to get an idea of the freedom the well-tempered system offered, compare this “Fantasia” by Sweelinck from about 1600. Despite being a pioneer, the musical system of his time did not allow for much modulation. Notice the paucity of sharps and flats in the score. (You don't have to listen to all six minutes.)
https://youtu.be/vtabszT4nos?list=TLPQMTkxMDIwMjAZaqftfkFzZQ
Compare that with the final fugue in Bach's 1722 “Well-Tempered Clavier”, where all 12 tones are featured in the fugue subject!