The Crab Canon Isn’t a Möbius Strip. (BWV 1087 Canons Part THREE)

Though this episode starts with quite the extended introduction, this is in fact

EPISODE THREE

In a four-part study into the 14 additional canons on the back of the Goldbergs, BWV1087.

Here in this video, we dismiss a popular Bach video, and examine which videos are in fact Möbius strips. 

Here is the disproven crab canon video.

Here are two studies which don't quite go far enough:

One. I love this channel, don't get me wrong- they just didn't quite examine the consequences of chromatic inversion.

Two. The American Mathematical Society publishes similarly.

Both studies miss the technical inversions that I have pointed out in this episode.

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And now the blurb from the other two episodes studying BWV 1087:

On the back of his own personal copy of the 'Goldberg Variations', Bach notated an additional fourteen canons. These were discovered only as late as 1974(!) and are among the most interesting compositional exercises we know from the composer. 

From eight bass notes (the first 8 notes of the 'Goldberg' Aria- the structure in a sense,) Bach creates, yes, fourteen other canons. In this episode, we discuss engraving and canons 5-9.

Here is what they look like as seen on the back of Bach's own copy:

and HERE is the link to engraving- you can see how Balthasar Schmid (I accidentally added an 'S' to his name in the episode) engraved Bach's BWV988.

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