Xylophone and Marimba
The Marimba's bars are tuned by cutting up on the underside of the bar. The normal free bar modes are not a harmonic sequence, but they can be altered by removing material. They are tuned so that the first overtone is the fourth harmonic. The length of bar required for a given frequency is also diminished by the cutting process. The tubes underneath are tuned to the fundamental of the bar. For a xylophone (shown above) the bars have a shallower underside cut and the first overtone is tuned to the third harmonic of the fundamental. Closed resonance tubes reinforce both these frequencies if they are tuned to the fundamental.
The playing range of a concert marimba is A2 to C7 (110 to 2093 Hz) and bass marimbas extend down to C2 (65 Hz). The undercutting of the bars on the marimba produce overtones which are described as two octaves up, and then three octaves plus a minor third. Two octaves is the fourth harmonic, and the other overtone is close to the 10th harmonic (48/5 if just intervals are used). These upper resonances are not reinforced by the closed tube resonator since it produces only odd harmonics.
For a xylophone a typical playing range is F3 to C8(349 - 4186Hz), this top note being the same as the top note on a piano. It has narrower and thicker bars than the marimba, contributing to a higher wave velocity and higher pitch for a given length than for the marimba. The xylophone has a sharp, bright sound which is attributed to the thick, stiff bars and the presence of the reinforced first overtone.