Instrument Design

Mathematics also plays an important role in the contruction of musical instruments.  On a flute or recorder for example, the holes must be placed in exactly the right position in order to produce the correct notes at an accurate pitch.   Similarly, the frets on a guitar must be accurately positioned so that all the notes remain in tune wherever they are played along the neck of the guitar. 

For this reason, the shapes and designs of most musical instruments has changed very little over the last few centuries, and they are now made to highly accurate specifications.  The tone of an instrument also depends on its dimensions.   A large guitar with a deep body has a fuller sound than a smaller, shallower instrument. 

The materials with which it is made will also effect an instrument's tone because each material has its own resonant (natural) frequency which could cause the body to reinforce important harmonics or buzz annoyingly.