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A string fixed at both ends vibrates in standing waves sin(nπx/L), with frequencies fₙ = n·f₁ = (n/2L)√(T/μ). On the A string, f₁ = 110 Hz, the first eight are A2, A3, E4, A4, C#5, E5, G5, A5. Six sit within 2 cents of a piano key; the 5th is 14 cents flat and the 7th, 770 · XDL