# Why is a kalimba note anharmonic?

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?

• In general, there’s no reason to expect that the frequencies will be evenly spaced. That happens for some waves, like ideal waves on a string or sound in a tube, but not for others. Jan 13, 2021 at 23:33
• The waves on a kalimba have rigidity as the restoring force, not tension. Plus they have all kinds of weird boundary conditions... Jan 13, 2021 at 23:34
• Nice, simple harmonic series are a mathematical fiction. ;) They work ok for linear oscillators, but not so well for more complex oscillators. A reasonable introduction to this topic is via the study of bells & chimes. Eg, en.wikipedia.org/wiki/Strike_tone There are some great articles on the acoustics of bells, chimes, and idiophones by Thomas D. Rossing, but I'm not having a lot of luck finding free material... Jan 14, 2021 at 0:26
• Almost every real-world structure has anharmonic overtones. A vibrating string is a very special case. Real musical wind instruments with can also be very anharmonic, but the tone is produced by forced vibration not free vibration which hides that fact. Jan 14, 2021 at 0:41