Bach was a genius; Mozart the consummate professional and Beethoven somewhere in between. In the time—pun intended—of Johann Sebastian Bach (1685-1750) people did not view time as we do today. When he walked 322 kilometres from the heart of Germany to nearly the Baltic coast to meet Dietrich Buxtehude, the appointment was for, hypothetically, Tuesday; not 9am Tuesday. We know when the Age of Accurate Timekeeping began, because the person who invented the clock used it to tell the time! More correctly, it was Christiaan Huygens (1629-1695) and his invention was the mechanical clock, not the calendar year, which was, by the way, 1656.
The invention of the pendulum clock made the modern world possible. Along with a plethora of experiments requiring quantified time that were now possible, navigation at sea was also greatly facilitated. Before the clock games like basketball and cricket could not be contemplated, they being dependent on quantified time. Nor could the metronome be contemplated, at least until mechanical clocks were commonplace – the late 18th century. We should note in passing that the clock has two faces; the breaking up of time could be seen as a fracturing of human existence.
Despite the clock being invented well before Bach’s death, he worked to the sundial’s pace, not a pendulum clock. But he definitely quantified time within the bounds of his music.
One of the ‘tricks of the trade’ composers, Bach included, have long used is a theme and variations. A musical theme can be divided up into finer gradations, be inverted upside down and back to front, it’s pulse—clock—can be sped up or slowed, it can be raised or lowered in pitch without affecting the speed, and played with different harmony. Bach’s great Chaconne from the Dm Partita BWV 1004 for solo violin is a 15 minute monument to the baroque yet is founded on a four note line of notes through four bars duration. Bach is as relentless in their use throughout the masterpiece as he is inventive in application.
Then there is the Crab Cannon, a musical palindrome in his Musical Offering BWV 1079. The cannon works, and is played simultaneously, both forwards and backwards. Bach was a genius. As for mathematics generally, one of his children reflected that he had no great love of ‘dry mathematics’. Still, he had enough interest to let himself be head-hunted into the Mizler Society, a group interested in the science of music and mathematics. But there is no record of his wide participation in the Society (H. T. David, Bach, vol 1 no.2 1970).
‘Bach is pure mathematics’ is a comment I’ve heard more than once in my life. I think there is more tangible evidence for the opposite: Bach is pure emotion – the spiritual, non-material element of music. At the very least, the truth is halfway in between.
To finish Part 1, here are two of my most memorable musical experiences: First, hearing young Australian virtuoso Andrew Blanch playing the Fugue BWV 1000 in concert. (The link is to a recording of Julian Bream.) I’ve played this fugue; the technical demands are profound, on both hands and mind. I know them. Blanch played it in such a way as the technical and intellectual obstacles vanished; all that was left was the music. By which I mean, emotion. Another is from my own work, playing the aforementioned Chaconne. The work finishes with a final restatement of the four bar theme; the same four bars repeated as finale as introduction. To see the emotional impact on an audience returning after such a musical journey is deeply moving for me, the musician.
To be continued.