The Cyber-Cave

Reflections on the political, technological, cultural and economic trends of the world

Johann Sebastian Bach

“Let the Well-Tempered Clavier be your daily bread. Then you will certainly become a solid musician” (Robert Schumann)

Johann Sebastian Bach (1685-1750)

-Lorenz Christoph Mizler (1711-1778) was a German polymath and one of Bach’s pupils. In 1738 he founded the Society of Musical Sciences in order to encourage discussions on music theory. Mizler, inspired by Pythagorean philosophy, believed that music at its core was a mathematical science.
Mizler was also inspired by Kepler’s Harmonices mundi and Athanasius Kircher’s Musurgia universalis. Mizler’s
Notable members of the Society include Handel and Telemann. Mozart’s father (Leopold) was also invited into the Society, but he never joined it. Bach was admitted to the society after having presented the Canon triplex (BWV 1076) and Vom Himmel hoch da komm’ ich her (BWV 769).
Bach also composed ‘The Art of Fugue’ and the Musical Offering for the Society.

-Musical Offerings: 16 pieces based on a theme (21 notes) allegedly composed by Frederick the Great. Some of these pieces are ‘puzzles’ as Bach would point out how many voices were needed, but it would then write the score for only one voice leaving the reader to think about the structure of the music. For instance in the first canon (known as the ‘crab canon’) two voices are needed but only one voice is written down by Bach as a proper score- the solution to this puzzle is that the other instrument has to play the score of the first voice backwards (this is why is known as the ‘crab canon’).
Some canons of the Musical Offerings can be represented geometrically as Möbius strips.
-The Goldberg Variations: One aria and 30 variations.
-The Well-tempered Clavier: 48 preludes and fugues exploring the 12 major and 12 minor keys. This collection was intended for beginner students.
In this case the work was intended for a ‘well-tempered’ tuning, in which each octave is made of 12 semitones (the chromatic scale) with equal intervals. The ratio used is the twelfth root of 2.
-Inventions and Sinfonias: short pieces of music (like contrapuntal exercises) for young players.
-Canonic Variations on “Vom Himmel hoch da komm’ ich her”: Five variations on a Christmas hymn. This was Bach’s first contribution to Mizler’s Society.
-The Fourteen Canons: these rather short but intellectually interesting Canons utilise the first eight notes of the Aria theme from the Goldberg variations. Very little is known about Bach’s intention behind these canons. One of the Canons, the triplex with six voices, is interesting as it could be continued indefinitely as an infinite loop.
-The Art of Fugue: 20 fugues in the key of D minor (though the work is unfortunately unfinished).

-Aria: Unser Mund und Ton der Saiten BWV 1
-BWV 4
-BWV 5
-BWV 8 Coro: Liebster Gott, wann wird ich sterben?
-No.2 – Coro: Weinen, Klagen. Sorgen, Zagen BVW 12
-BVW 20
-BVW 23
-BVW 29, 32, 50, 54, 72, 74, 87, 91, 97, 103, 106, 107, 111, 119, 120, 125, 131, 136, 140,146, 147 J.S. Bach – “Jesu, Joy of Man’s Desiring” Chorale from Cantata No. 147
-Aria: Ach, bleibe doch, mein liebstes Leben BWV 11
Kaffeekantate BWV 211 (movement 4)
-Concerto for two harpsichords and strings in C minor, BWV 1060
-Sonata III BWV 1005 adagio for lute

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