Why is a kalimba note anharmonic?

Question

I play a kalimba, and have also recently written a toy program that helps me tune it using a "naively applied FFT" without any sophisticated DSP. The Nyquist frequency is 24 kHz.
The kalimba is tuned, so the fundamental for C4 shows as very close to 261.6 Hz. The biggest surprise is that there is no significant harmonic energy, and significant, narrow, stable anharmonic energy between harmonics 6-7. The biggest non-fundamental peak shows up at about 1.714 kHz which is 6.55x the fundamental. This 6.55x component appears in almost all of the notes in the first octave (C4-C5).

I've ruled out interaction with the other keys by manually dampening them while C4 is plucked. What physical mechanism could plausibly be creating this 1.714 kHz peak?

niels nielsen · Answer

The kalimba tine is modelled as a cantilever which is clamped hard at its fixed end but which is elastically preloaded into hard contact upon a bridge point some distance away from the fixed end. the constraint at the bridge point prevents up-and-down movement but the tine is free to vibrate in a mode that has a displacement node at the bridge point. In this mode, the tine length between the bridge point and the clamped end can support a fundamental vibration which will show up in a spectral analysis, and that mode will have no harmonic relationship with the vibration of the free end of the tine.
In addition, an ideal cantilever, when struck, will itself not produce a harmonic series of overtones as would a plucked string because of the boundary conditions enforced by the clamped end.
Finally, because the vibrating tine is well-coupled with the sound board of the kalimba body, the width of the resonant peak for the tine fundamental will be broad which supports anharmonic modes.

Why is a kalimba note anharmonic?

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