Wind chimes produce inharmonic (as opposed to harmonic) spectra, although if they are hung at about 1/5th of their length (22.4%), the higher partials are dampened and the fundamental is brought out. This is common practice in high-quality wind chimes, which are also usually hung so the center ball strikes the center of the wind chime's length. Frequency is determined by the length, width, thickness, and material. There are formulas that help predict the proper length to achieve a particular note, though a bit of fine tuning is often needed. Wind chimes are thought to be good luck in parts of Asia and are used in Feng Shui. In Japan they produce pleasant ringing sounds and are hung by the windows during hot humid summers in order to bring cooling relief.
Chimes are also made of materials other than metal or wood and in shapes other than tubes or rods. Many people accept bamboo, stones, horseshoes, mechanics tools, PVC pipe, glass, seashells, old silverware, etc., as chimes. Every material makes a different sound. The sounds these make are not tunable to specific notes and range from pleasant tinkling to dull thuds. The idea seems to be that if it is moved by the wind and makes a noise, it is a wind chime.
The tone will depend on the material (steel, aluminum, brass, the exact alloy, heat treatment and so on), whether you are using a solid cylinder or a tube, and if a tube, the wall thickness. It may also depend on the hanging method. The tone quality will depend on how you strike a tube (with a hard object or a soft one, for example).
Note that with a whistle, such as an organ pipe, the pitch is determined primarily by the length of the air column. It is the air that vibrates. The pipe material helps determine the "timbre" or "voice" of the pipe, but the air column determines the pitch. In a wind chime, the pipe itself is being struck and the air column has little to do with things.
Chimes may be used to observe changes in wind directions. For instance, if a chime is positioned on the north side of the house only a north wind will move it. It may alert the inhabitants to a weather change. Conversely, for a south wind a chime is mounted on the south side.