Pitch of brass instruments

The pitch of a brass instrument is determined by its vibratory length, which determines the fundamental frequency of the open instrument and the frequencies of its overtones. Additional pitches are achieved by varying the length using the instrument's valve, slide, key or crook system. The fundamental frequency is not playable on some brass instruments. The table provides the pitch of the second overtone (an octave above the fundamental frequency) and length for some common brass instruments in descending order of pitch. This pitch is notated transpositionally as middle C for many of these brass instruments.

The normal playing range of most three-valved brass instruments extends from three whole tones below the 2nd harmonic of the condensed instrument to the 10th harmonic. Skilled players can produce tones outside this range. For many transposing brass instruments, this range is written as extending from F♯ below middle C to E two octaves and a third above middle C.

The orchestral horn is an exception as it was classically assigned a range beginning at its fourth harmonic.

The ease with which a player produces the fundamental note of each harmonic series for each tubing length of a modern brass instrument varies with the instrument's design. As bore width increases relative to length, it becomes easier for the player to resist the instrument's tendency to jump to the second harmonic instead of producing the fundamental frequency. Brass instruments with sufficient bore to allow the "whole tube" to vibrate easily, as opposed to "half the tube" (i.e., the second harmonic), are called "whole-tube" instruments.

Certain low brass instruments such as trombone, tuba, euphonium, and alto horn are whole-tube and can play the fundamental tone of each harmonic series with relative ease. Furthermore, the low brass often use extra valves to extend their range uniformly, since the fundamental is chromatically discontinuous with the lowest 2nd harmonic reachable on a three-valve instrument or via the seven-position slide on a trombone. Trombone and tuba in particular are often called upon to play pedal notes (fundamental notes) and so-called "false harmonics" and "false tones" below their normal range.

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Wikipedia