Bonus Content

Audio Note: Companion to “The geometry of musical keys”

The relationships between musical keys can be described either by means of the triangles in the “Tonnetz”, or by carefully designed geometric…

May 23 •

1:11

Bonus content: The graphic nature of groups

In the main post, I mentioned that the set {0, 1, 2, 3, 4, 5} under the operation of addition modulo 6 is a group.

Jul 12, 2023 •

Bonus content: The best denominations for coins

To an outsider, an annoying feature of the US dime coin is that it is impossible to tell just by looking at it that it is worth 10 cents.

Jul 7, 2023 •

Bonus content: The symmetry of musical key changes

Jul 1, 2023 •

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