How does the shape of a wind instrument's tube affect its tone colour?

The shape of a wind instrument's bore—the internal tube—is a primary determinant of its tone colour because it dictates which harmonics are present in the sound spectrum.1

Bore Geometry and Harmonics

• Cylindrical vs. Conical: Both shapes can produce resonances that are harmonics of the fundamental frequency. However, bores that flare faster than a cone produce nonharmonic overtones, resulting in raucous, unmusical sounds.1
• Open vs. Closed Tubes: The acoustic behavior of the tube determines the harmonic content:
  • Open Tubes: Instruments like the flute or recorder function as open tubes, containing all harmonics. Adding a mouthpiece and bell to a tube—as seen in brass instruments like the trumpet or cornet—also allows for all harmonics.1
  • Closed Tubes: A cylindrical tube with a reed, such as the clarinet, functions as a closed tube. This configuration emphasizes odd harmonics, creating a distinct, hollower tone colour compared to instruments that produce a full harmonic spectrum, such as the oboe, bassoon, or saxophone.1