= First overtone
{title2=$n=1$}
The <first overtone> is the lowest oscillatory <normal mode> above the <fundamental mode>. It is an ordering by <frequency>, not a claim that its <frequency> is an exact <integer multiple> of the fundamental. If the fundamental is labeled $n=0$, the <first overtone> is $n=1$; another common convention labels them one and two.
For a string fixed at both ends, the <frequencies> are $f_n=nc/(2L)$ with $n\geq1$, so the <first overtone> is the second <harmonic> at twice the fundamental. For an ideal pipe closed at one end, the next allowed mode is at three times the fundamental. <Geometry> and <boundary conditions> determine the relation.
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