Wind Chime Tuning Calculator

Tubular wind chimes ring according to free-free beam vibration physics — the tube isn't fixed at either end, it's free to flex like a suspended bar, and that boundary condition determines both its fundamental pitch and where it should be hung. This calculator inverts the fundamental frequency equation for a free-free tube, f = (cBar² · k · vBar) / (2π · L²), to solve for the length that produces your target note. vBar is the bar speed of sound in the chosen metal, sqrt(E/ρ) from its elastic modulus and density (aluminum, steel, copper, and brass are built in with real material constants), and k is the radius of gyration of the tube's annular cross-section, computed from outer diameter and wall thickness. cBar (3.0112) is the eigenvalue constant for the fundamental mode of a free-free beam. Because thicker-walled or larger-diameter tubes are stiffer for their length, the same target note requires a different cut length depending on those dimensions, not just the material.

The hang point — where you drill or tie the suspension cord — sits at 22.4% of the tube's length in from either end, which is the vibrational node of the fundamental mode; hanging anywhere else damps the tone by interfering with the tube's natural flex pattern. The second and third overtones come out at roughly 2.757x and 5.404x the fundamental — these ratios are inharmonic (unlike a taut string's whole-number harmonics), which is exactly what gives tubular chimes their bell-like, non-musical-scale shimmer rather than a simple pure tone.