Hmm, not really. If we look at the "Railsback curve" someone linked below ( https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipe

Hmm, not really. If we look at the "Railsback curve" someone linked below ( https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_... ), it looks clear that around 440 Hz an octave is realized by a nearly perfect 1:2 ratio. Of course, it means the fifth (C-G, etc.) is never perfect 2:3, but that's an orthogonal issue. If piano strings were perfect, then we could easily extend the pattern to lower/higher pitches by halving/doubling frequency. The fact that it doesn't work at the extreme is due to the physical reality, as the stackoverflow answer correctly pointed out.