As regards sound generation, trumpets and horns differ from other aerophones in their use of the so-called “lip reed,” which is formed when the player’s partially closed lips vibrate as they press against the rim of a mouthpiece or mouth hole (although the behaviour of the lips, strictly speaking, is not exactly comparable to the operation of a reed). When the lips vibrate, the resulting tremor in the flow of the breath is transmitted to the air in the tube, which resonates at the frequency that most closely matches that of the lips. The experienced player adjusts his embouchure (position of the lips in relation to the mouthpiece) to produce the desired frequency.

The mouthpiece, an important accessory to sound production in trumpet-type aerophones, is an adapter used to widen the starting diameter of a bore otherwise too small to allow the lips to vibrate effectively. It has three internal elements—the cup; the throat, an opening at the base of the cup; and the backbore, which leads to the main tubing—the shape and relationship of which strongly influence an instrument’s tone and technical capacity. Mouthpieces on Western orchestral trumpets have a hemispheric cup with shallow walls that meet the throat at a sharp angle; these effect a bright tone. Mouthpieces used with cornets and trombones are deeper, with rounded-off throats, and those for orchestral horns are virtually funnel-shaped; these all produce a more mellow tone.

An instrument’s bore also influences its tone, as reflected in the subtypes trumpet and horn in the Sachs-Hornbostel classification. Trumpets normally have narrow cylindrical bores that expand in the final third of the tube’s length and terminate in a small bell, which helps to radiate the sound and to bring the harmonics into tune. This bore configuration, in conjunction with a mouthpiece with a shallow cup, favours the production of high partials. Horns, on the other hand, have expanding bores through all or part of the tube’s length and normally end in a large bell. Aided by a deep-cupped or funnel-shaped mouthpiece, they favour low partials and function most efficiently in a low range.

Ways of filling in the missing tones of the harmonic series on trumpet-type aerophones were known in the West as early as the 10th century, when finger holes, which shorten the sounding length of the tube, were cut into instruments made from animal horns. The cornett, which was made from two halves of a hollowed-out block of wood that had been glued together and bound with leather, was similarly fitted with finger holes and was widely used in Europe from the end of the 15th through the 17th century. In the late 18th and 19th centuries, makers covered the holes of trumpets and horns with keys to enable them to play a complete chromatic scale; the keyed horn was invented in Bohemia about 1770, and keys were thereafter added to the trumpet and the bugle.

Another solution to providing the missing tones was to increase the sounding length of the tube, thereby making the partials of different harmonic series available separately and producing a chromatic scale. As early as the 14th century, the term sacabuche (Spanish: “drawpipe,” or “pull push”) was used to refer to a lip-vibrated instrument, presumably with a single telescoping slide. Fifteenth-century Flemish paintings depict what appear to be slide trumpets, in which the player slid the entire instrument up and down along the long shank of the mouthpiece with one hand, steadying the mouth pipe with the other.

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Given this awkward beginning, it is easy to imagine bending the slide back upon itself, a less-cumbersome alternative that appears to have been adopted in the mid-15th century. On so-called double-slide instruments, such as the Renaissance sackbut and its successor, the modern trombone, two parallel inner tubes of the slide mechanism are attached at their upper ends to the body of the instrument by a cross stay. The mouthpiece is fit into the top of one tube, and the bell section fits on the other. The U-shaped slide moves along the two stationary tubes, lowering the fundamental by a half step with each lower slide position and making available the notes of seven harmonic series.

Crooks, detachable lengths of tubing, also were used to increase the sounding length and lower the pitch of trumpets, trombones, and horns. They are of two types: “terminal” crooks, which attach to the mouthpiece receiver, and “medial” crooks, which are inserted in a wider portion of an instrument’s tubing. First mentioned in the mid-16th century, both types of crooks are clearly depicted in Michael Praetorius’s Syntagma musicum (1619). Praetorius’s illustration of trombones, for example, features crooks inserted between the slide and bell sections. Terminal crooks were common on trumpets from the 17th through the 19th century. They were also used, singly and in combination, on the horn until the mid-18th century, when sliding medial crooks were added to the tubing inside the hoop of the German horn known as the Inventionshorn.

In the early 18th century, horn players in Bohemia discovered that the gaps in the instrument’s harmonic series could be filled by using the hand to partially stop the bell. When the hand was cupped to form an extension of the air column, the pitch of the note being played was lowered one-half step. Hand stopping, which became known throughout Europe in the 1750s thanks to the Bohemian hornist Anton Hampel, was later applied to the trumpet.

About 1815, either Heinrich Stölzel or Friedrich Blühmel, both of Berlin, invented the valved orchestral horn. When the valve was opened by depressing a key, it deflected the airstream into extra tubing, changing the effective length of the tube and lowering its pitch. The two valves of the original valved horns were used in combination: the first lowered the pitch one step and the second a half step; together they lowered the pitch one and a half steps. Later, a third valve, which lowered the pitch yet another step and a half, became a standard feature of such instruments. Used singly and in combination, these valves made the instrument completely chromatic above the second partial. The illustration below shows the harmonic series made available by the depression of different valves and combinations of valves; notes shown in black are slightly out of tune with the equally tempered scale.

Perhaps because the natural horn had more notes available than 19th-century natural trumpets did and also because the valve system, particularly on the early horns, affected the purity of tone, valved horns were accepted slowly. At first, valves were considered a convenient substitute for crooks—in effect, a means to modulate (change key) quickly—but band musicians were quick to develop virtuoso techniques of rapid chromatic playing.

Despite their convenience, valves are inherently defective in that they open a fixed amount of tubing. If the first valve on an instrument in C is depressed, lowering the pitch a whole step, the fundamental pitch of the instrument is changed from C to B♭. Using the second valve and its corresponding length of tubing (intended for a C instrument) to lower the instrument, now in B♭, a half step requires slightly more tubing than needed to lower a C instrument a half step. In many cases, the player can correct such discrepancies by adjusting his embouchure, decreasing slightly the speed of lip vibration to flatten the pitch without destroying its tone quality. The greater the amount of tubing, however, the worse the discrepancies in tuning. Most trumpets now have compensating slides that operate either manually or automatically to add length to the tubing on the first and third valves. For some large instruments, such as tubas, this device is impractical, and extra valves are added.