Pitch of brass instruments
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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.
|B♭4 or A4||2.25, 2.12 ft (69, 65 cm)||piccolo trumpet|
|E♭4||3.125 ft (95.3 cm)||soprano cornet, soprano trumpet|
|B♭3||4.5 ft (1.4 m)||trumpet, cornet, flugelhorn, soprano trombone|
|E♭3||6.75 ft (2.06 m)||alto horn, alto trombone, alto trumpet|
|B♭2||9 ft (2.7 m)||tenor and bass trombone, baritone horn, euphonium, B♭ horn, bass trumpet|
|F2||12 ft (3.7 m)||French horn|
|E♭2 or F2||13.5, 12 ft (4.1, 3.7 m)||bass tuba|
|B♭1 or C2||18, 16 ft (5.5, 4.9 m)||contrabass tuba|
The normal playing range of most three-valved brass instruments extends from three whole tones below the 2nd harmonic of the 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.
Whole tube vs half tube
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.
The modern standard orchestral horn is a double B♭/F horn. The player can switch between the two modes using a thumb-operated fourth valve. The fundamental pitch of the F horn is near that of the tuba. Horn notation is a complex subject beyond the scope of this article, but what is written as middle C for the horn is the fourth harmonic of the unlengthened instrument, not the second. Horn music makes greater use of the higher range of the harmonic series than do most other modern brass instruments.
Modern bass trombone
The modern bass trombone is the same length as a tenor trombone, but typically has two valves, one pitched in F and one in G♭. When combined, these valves put the instrument into D. Modern contrabass trombones are constructed in F and B♭. The F contrabass trombone is often fitted with a valve that puts it into D, and a valve that puts it into E♭, and when combined, these put the instrument into the key of B♭. The B♭ contrabass is often fitted with a valve in F and has been fitted with both a valve in F and G♭, so that it matches its bass trombone counterpart, but is pitched an octave lower.
The bass tuba is commonly available in F and E♭, while contrabass tubas are available in C and B♭.