There are string instruments (Chordophones), wind instruments (Aerophones), percussion instruments (Membranophones & Idiophones) and then there’s the Kalimba.
The Kalimba sings not by strings or air, but by vibrating cantilever tines — each a slender beam fixed at one end, free at the other.
Every tine bends, releases, and hums its note, its pitch shaped by the silent mathematics of length, stiffness, and steel.
Usually, a Kalimba spans just a single octave.
But if each tine is an Euler–Bernoulli beam, the equation tells a secret:
f_1=\dfrac{\lambda_1^2}{2\pi L^2}\sqrt{\dfrac{EI}{\rho A}}where, λ = first cantilever root, L = length (m), E = Young’s modulus (Pa), ρ = density (kg/m³), A = cross-sectional area (m²), I = second moment of area (m⁴).
and since
I=\dfrac{bh^3}{12}, \quad A=b\cdot h,where, b = width (m) and h = thickness (m)
it follows that,
f_1 \propto h
So, double the thickness → double the frequency → one octave higher.
Along with Strings → half the length → one octave higher
Wind instruments → half the length → one octave higher
That’s elegant symmetry.
In the end, music is just matter learning to do poetry.
Links
• About Kalimba: https://medium.com/@amanagrawal2098/kalimba-a-soul-stirring-journey-through-music-cb3b36e8fc4b
• Euler-Bernolli Beam Theory https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory
• Play Kalimba online: https://kalimba-online.ru
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