Whoever coined the term "octave" was not familiar with addressing fencepost errors.
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The linked article poses a
The linked article poses a question similar to this, "If your fence has n posts, how many gaps does it have?" The article claims that the correct answer can be n-1, n, or n+1 depending on the fence's configuration.
At first reading I was convinced that the claim was incorrect. Only after ~15 minutes of thinking did I realize that the claim is in fact correct.
So, extra credit for anyone who can think of three fence configurations to provide the three possibly correct answers.
If linear, then N-1
If linear, then N-1
If triangular, then N
If forming bins, or stacked floor/ceiling as in an apartment building, N+1