Why are the brass instruments coiled and shaped differently?

Brass instruments are coiled and shaped differently to alter their pitch and tone while maintaining a manageable size for playability. The length and configuration of the tubing affect the instrument's fundamental frequency, allowing musicians to produce a wide range of notes. Additionally, the unique shapes can enhance specific tonal qualities and make the instruments easier to hold and play. Overall, these design variations contribute to the distinct sound characteristics of each brass instrument.