How do a fundamental note and its harmonic series allow brass instruments to produce different pitches?

Brass instruments produce different pitches by utilizing the fundamental note and its harmonic series. When a player vibrates their lips against the mouthpiece, the air column within the instrument is set into motion, creating a standing wave that produces a fundamental pitch determined by the length of the tubing.12

By increasing the pressure of the lip vibration—a process known as overblowing—the air column divides into smaller segments, such as halves, thirds, and fourths. These divisions produce higher pitches called overtones or harmonics, which follow a specific mathematical progression.2

Because a single tube length is limited to the notes available within its specific harmonic series, modern brass instruments incorporate valves or slides to alter the length of the tubing. By changing the length of the air column, the player gains access to multiple fundamental notes, each with its own unique harmonic series. This allows the instrument to produce a full chromatic scale.1