Bach's musical Möbius strip
Do you want to know how much of a musical genius Johann Sebastian Bach really was? Prepare to be amazed.
Do you want to know how much of a musical genius Johann Sebastian Bach really was? Prepare to be amazed.
Last week, if you were paying attention, you might have seen mathemusician Vi Hart fold space-time using music. One of her samples was a few bars of Bach — and the conclusion of the video was a musical Möbius strip.
As it turns out, Bach was way ahead of her with a little crab canon — that is, a piece of music that can be played both backwards and forwards, from The Musical Offering of 1747-48.
However, Bach's piece does something a little different to the norm with crab canons. The piece was not only written to be played both backwards and forwards — it was also written to be played backwards and forwards simultaneously. But then, as this animated visualisation by mathematician Jos Leys reveals, the stave can actually be flipped upside down and played in an endless Möbius loop.
Holy musical genius, Batman!