Shortnote

Wind-chimes are made by selecting cylinders with a given length and allowing the wind to collide the tubes together in order to make sounds. This is different from a whistle, such as an organ pipe, where the pitch is determined primarily by the length of the air column. For a whistle, the material that the pipe is made of gives the "timbre" or the "voice" but the air column gives the pitch. This is different from a wind chime, where the tubes are being struck by a clapper.

Sketch

Calculating the Tube Length

For a tube, free at both ends ¹⁾:

$\begin{eqnarray*} f &=& 1.133 * \pi * K * \frac{v}{l^{2}} \\ &\text{and}& \\ K &=& \frac{\sqrt{r^{2} + R^{2}}}{2} \end{eqnarray*}$

where:

$f$ is the frequency in Hz.
$l$ is the length in cm.
$v$ is the velocity of sound in the material of the tube wall (eg: Aluminium ²⁾ is 5.1E5 cm/s).
$r$ and $R$ represent the inner, respectively outer radius of the tube.

Choosing Notes

Any choice of notes is allowed, although, some wind-chime producers tune the wind-chimes to popular melodies. In any case, a chromatic music scale can be used to:

pick notes,
calculate their corresponding frequencies,
use the tube-formula (above) to determine the length of the tube.

An example of note selection could be the following sequence:

$A_{1}-D_{2}-F_{2}-G_{2}-A_{2}-D_{3}-F_{3}-A_{3}$

where $A$ to $G$ represent the notes on the chromatic scale and the indices indicate the octave ( $1$ the first octave, $2$ second, etc…).

Alternatively to a chromatic music scale, a pentatonic scale can be used since no combination of notes on a pentatonic is considered dissonant.

Chimes Suspension

Chimes are hung at $\approx \frac{2}{9} * l$ where $l$ represents the length of the chime and hung at $\frac{1}{2} * l$ in order to be close to the fundamental frequency ³⁾ (clear, without the ulterior reverberations).

In order to further reduce the reverberations ( $f_{1}$ , $f_{2}$ , etc…) after the collision, sometimes a dampener is used. Usually, it is cylindrical in shape and groups the tubes in the centre (see the sketch).