Even the perfect octave is routinely violated in piano tuning

Evidence

By now, you may be convinced that a musical scale is a rather arbitrary compromise of choices: How many notes per octave—5, 7, 12, 19, or 31? What temperament system? Dissonance is absolutely unavoidable, except for the most elementary monophony. We have seen perfect intervals like 3:2 go by the boards (although not in a cappella performance, string quartets, and the like). Untouched by any of this, the octave at exactly 2:1 may be the one immutable principle in music apart from consonance. It is possible, though, to violate even that in several ways. In fact, as we discussed in chapter 19 (see figure 19.2), the piano is usually tuned with stretched octaves, in order to stay in tune with its own sharp partials from lower notes. — Eric J. Heller, Why You Hear What You Hear- An…, 2408

Categorization

• CANDY: A fun, tweetable fact — pianos are deliberately tuned with stretched octaves, so even the ‘immutable’ 2:1 ratio is compromised.
• XREF: Cross-references chapter 19’s discussion of piano partials being sharp, echoing brass/partial inharmonicity earlier in the book.