Since musical notations is a western phenomenon, which allows the musicians to write down the musical details more specifically, the creators in this Western art form takes on more importance than the creators of art in other cultures. So did J.S.Bach, who would be the main role in this article. Besides music, this article is more about to illustrate my thoughts and ideas when I listened and learned the music composed by Bach. As it is known to all that the composition of Bach’s music is quite related to mathematic theory, the harmony organization of each voice, the complexity in canon construction, of course, the Strange Loops. To be honest, I am not proficient in music composition, however, relating it to the construction of proofs and theorems does do me the favor to better take a good taste of the miracle and subtlety in math and the theory of computation.
Reference Book: GODEL, ESCHER, BACH: AN ETERNAL GOLDEN BRAID, Douglas R. Hofsadter.
J.S.Bach
FREDERICK THE GREAT, King of Prussia, came to power in 1740. It was said that Frederick was an admirer of pianos, as well as of J.S. Bach, an organist and composer. In those days, being an organist not only meant being able to play, but also being able to extemporize, and Bach was known far and wide for his remarkable extemporization.
The famous ten canons under the title of “Musiklisches Opfer” which means the Musicial Offering are among the most sophisticated canons Bach ever wrote. What’s more, Bach didn’t wrote them out in full, and it was deliberate that he posed them as puzzles to King Frederick. In those days, this was like a musical game that one gives a single theme, together with some more or less tricky hints, then some one else “discovers” the canon in full based on this theme.
At first, I was not really get the idea of canons or fugues. It is said that the idea of a canon is that one single theme is played against itself. But created with human intellect, they are not just simply copies of themes played by the various participating voices, in Chinese, it could be interpreted as “they are over played”, they are way more than that.