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
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.