Leaps of pure fifths fail to close because intervals and octaves are incommensurable.

Evidence

The circle of fifths makes it clear how we can continue this process to generate more notes. We continue around the circle making leaps of 210.587 degrees, until we come back to C. Unfortunately, because of the Pythagorean comma, we won’t quite make it back, but instead will miss by about 24 cents, as seen in figure 26.16. — Eric J. Heller, Why You Hear What You Hear- An…, 2387

Categorization

• XREF: Connects to the book’s earlier harmonic-series material on why octaves and fifths are the ear’s foundational intervals.