Theobald Boehm’s 1847 system applied acoustics rigorously:

A perfectly cylindrical bore (like a clarinet) produces a strong fundamental but struggles with tuning across registers. Conical bores (saxophone, oboe) produce more even tuning but require complex hole placement.

The design of wind instruments involves a deep understanding of acoustics, physics, and materials science. Air columns and toneholes are the critical components of wind instrument design, working together to produce the characteristic sound of a particular instrument. By applying the principles discussed above, instrument makers and designers can create instruments that are highly playable, versatile, and musically expressive.