Table of Contents

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:

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:

  1. pick notes,
  2. calculate their corresponding frequencies,
  3. 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).

1)
from "Music, Physics and Engineering" by Harry F. Olson
2)
which has the lowest internal damping
3)
Sethares, William A. (2005). Tuning, Timbre, Spectrum, Scale, p.115. ISBN 9781846281136