Double-kink string modes produce the octave via a center node

Evidence

It is not difficult to see that double-kink modes are possible; one is shown in figure 18.6. The string is always stationary in the center in this mode, which means that is equivalent to a normal single-kink mode on half the string, implying that the tone is an octave higher. Or we can say that the mode is built out of only the even-numbered modes of the full string (all having a node in the middle), which amounts to the same thing. — Eric J. Heller, Why You Hear What You Hear- An…, 1753

Categorization

• DEFINE: Shows the harmonic relationship between kink modes and normal string modes, proving octaves arise from the middle node.
• XREF: connects to: A string’s nth mode has n+1 nodes and n antinodes — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1081; Plucked-string spectra reveal the plucking point through nulled harmonics — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1127