A timpani drum is a two-dimensional system. The resonant frequencies are not related by integral multiples, meaning that the resonances or overtones are inharmonic. This is one reason why a tune played on timpani is more difficult to follow than a tune played on a violin or trumpet. To eliminate this problem, many tuned bar instruments, like the xylophone, include tubular resonators which incorporate some of the resonant frequencies of wind or string instruments. These resonators render a clearer pitch because they reinforce the overtones which are actually harmonics of the tube.
In conclusion, all music is constituted of vibration. Sound is specifically made up of the periodic motion of waves. When the human ear perceives music, it is receiving sound waves. All acoustic music instruments work in the same fundamental way. They produce a complex vibration, which is then amplified, and transmitted through air to the listener. Physical differences, namely timbre and tone, in these waveforms allow human ears to discern different instruments playing the same frequency of note. All acoustic musical instruments use the same principles to move from one note to the next and to tune. They alter the length of the resonant medium which changes the wavelength and frequency of the waves produced.
Future directions and applications for the study of the physics of music lie with electronic reproduction of sound. Traditional acoustic instruments relied on heuristics to build the ideal instrument. With the modern understanding of the physics of waves, traditional instruments have been redesigned. Musicians have not been entirely satisfied with the new mathematically perfect designs and have rebelled returning to classic instrument design. As a result, much of the research is going into electronic devices such as electronic keyboards, digitizers, and synthesizers to produce new types of musical sounds.