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I'm not sure if it's properly called ""fifth tuning"" or ""perfect fifth tuning"" or what, but it does exist. The octave is slightly sharper than twice the frequency, but according to the book it sounds better that way because the first overtone of a piano is itself sharp. I don't have a piano, so I've never tried it; besides, the second overtone is even sharper than the first (stiff strings do that). -"