Type of brass instrument
The French horn (since the 1930s known simply as the horn in professional music circles) is a brass instrument made of tubing wrapped into a coil with a flared bell. The double horn in F/B♭ (technically a variety of German horn) is the horn most often used by players in professional orchestras and bands, although the descant and triple horn have become increasingly popular. A musician who plays a horn is known as a horn player or hornist.
Pitch is controlled through the combination of the following factors: speed of air through the instrument (controlled by the player's lungs and thoracic diaphragm); diameter and tension of lip aperture (by the player's lip muscles—the embouchure) in the mouthpiece; plus, in a modern horn, the operation of valves by the left hand, which route the air into extra sections of tubing. Most horns have lever-operated rotary valves, but some, especially older horns, use piston valves (similar to a trumpet's) and the Vienna horn uses double-piston valves, or pumpenvalves. The backward-facing orientation of the bell relates to the perceived desirability to create a subdued sound in concert situations, in contrast to the more piercing quality of the trumpet. A horn without valves is known as a natural horn, changing pitch along the natural harmonics of the instrument (similar to a bugle). Pitch may also be controlled by the position of the hand in the bell, in effect reducing the bell's diameter. The pitch of any note can easily be raised or lowered by adjusting the hand position in the bell. The key of a natural horn can be changed by adding different crooks of different lengths.
Three valves control the flow of air in the "single horn", which is tuned to F or less commonly B♭. The more common "double horn" has a fourth, trigger valve, usually operated by the thumb, which routes the air to one set of tubing tuned to F or another tuned to B♭ which expands the horn range to over four octaves and blends with flutes or clarinets in a woodwind ensemble. Triple horns with five valves are also made, usually tuned in F, B♭, and a descant E♭ or F. There are also double horns with five valves tuned in B♭, descant E♭ or F, and a stopping valve, which greatly simplifies the complicated and difficult hand-stopping technique, though these are rarer. Also common are "descant" doubles, which typically provide B♭ and alto F branches.
A crucial element in playing the horn deals with the mouthpiece. The mouthpiece is usually placed about 2/3 on the lips with more on the upper. Because of differences in the formation of the lips and teeth of different players, some tend to play with the mouthpiece slightly off center. Although the exact side-to-side placement of the mouthpiece varies for most horn players, the up-and-down placement of the mouthpiece is generally two-thirds on the upper lip and one-third on the lower lip. When playing higher notes, the majority of players exert a small degree of additional pressure on the lips using the mouthpiece. However, this is undesirable from the perspective of both endurance and tone: excessive mouthpiece pressure makes the horn sound forced and harsh and decreases the player's stamina due to the resulting constricted flow of blood to the lips and lip muscles. Added pressure from the lips to the mouthpiece can also result in tension in the face resulting in what brass players often call "pushing". As mentioned before, this results in an undesirable sound, and loss of stamina. 
Name.
The name "French horn" first came into use in the late 17th century. At that time, French makers were preeminent in the manufacture of hunting horns and were credited with creating the now-familiar, circular "hoop" shape of the instrument. As a result, these instruments were often called, even in English, by their French names: "trompe de chasse" or "cor de chasse" (the clear modern distinction between "trompes" [trumpets] and "cors" [horns] did not exist at that time).
German makers first devised "crooks" to make such horns playable in different keys—so musicians came to use "French" and "German" to distinguish the simple hunting horn from the newer horn with crooks, which in England was also called the Italian name "corno cromatico" (chromatic horn).
More recently, "French horn" is often used colloquially, though the adjective has normally been avoided when referring to the European orchestral horn, ever since the German horn began replacing the French-style instrument in British orchestras around 1930. The International Horn Society has recommended since 1971 that the instrument be simply called the "horn".
There is also a more specific use of "French horn" to describe a particular horn type, differentiated from the German horn and Vienna horn. In this sense, "French horn" refers to a narrow-bore instrument () with three Périnet (piston) valves. It retains the narrow bell-throat and mouthpipe crooks of the orchestral hand horn of the late 18th century, and most often has an "ascending" third valve. This is a whole-tone valve arranged so that with the valve in the "up" position the valve loop is engaged, but when the valve is pressed the loop is cut out, raising the pitch by a whole tone.
History.
As the name indicates, humans originally used to blow on the actual horns of animals before starting to emulate naturally occurring horns with metal ones. The use of animal horns survives with the shofar, a ram's horn, which plays an important role in Jewish religious rituals.
Early metal horns were less complex than modern horns, consisting of brass tubes, wound around a few times, with a slightly flared opening (the bell). These early "hunting" horns were originally played on a hunt, often while mounted, and the sound they produced was called a recheat). Change of pitch was controlled entirely by the lips (the horn not being equipped with valves until the 19th century. Without valves, only the notes within the harmonic series are available. By combining a long length with a narrow bore, the French horn's design allows the player to easily reach the higher overtones which differ by whole tones or less, thus making it capable of playing melodies before valves were invented.
Early horns were commonly pitched in B♭ alto, A, A♭, G, F, E, E♭, D, C, and B♭ basso. Since the only notes available were those on the harmonic series of one of those pitches, horn-players had no ability to play in different keys. The remedy for this limitation was the use of crooks, i.e., sections of tubing of differing length that, when inserted, altered the length of the instrument, and thus its pitch.
In the mid-18th century, horn players began to insert the right hand into the bell to change the length of the instrument, adjusting the tuning up to the distance between two adjacent harmonics depending on how much of the opening was covered.
In 1818 the German makers Heinrich Stölzel and Friedrich Blümel patented the first valved horn, using rotary valves. François Périnet introduced piston valves in France about 1839. The use of valves initially aimed to overcome problems associated with changing crooks during a performance. Valves' unreliability, musical taste, and players' distrust, among other reasons, slowed their adoption into the mainstream. Many traditional conservatories and players refused to use them at first, claiming that the valveless horn, or "natural horn", was a better instrument. Some musicians who specialize in period instruments use a natural horn to play in original performance styles, to try to recapture the sound of an older piece's original performances.
The use of valves, however, opened up a great deal more flexibility for playing in different keys; in effect, the horn became an entirely different instrument, fully chromatic for the first time. Valves were originally used primarily as a means to play in different keys without crooks, not for harmonic playing. That is reflected in compositions for horns, which only began to include chromatic passages in the late-19th century. There were many different versions of early valves, most being variants of the piston and rotary systems used in modern horns. Early valves by Blühmel are cited as possibly the first rotary valve, but the first confirmed rotary valve design was in 1832 by Joseph Riedl in Vienna. 
Types.
Horns may be classified into single horn, double horn, compensating double horn, and triple horn as well as having the option of detachable bells.
Single horn.
Single horns use a single set of tubes connected to the valves. This allows for simplicity of use and a much lighter weight. They are usually in the keys of F or B♭, although many F horns have longer slides to tune them to E♭, and almost all B♭ horns have a valve to put them in the key of A. The problem with single horns is the inevitable choice between accuracy or tone – while the F horn has the "typical" horn sound, above third-space C accuracy is a concern for the majority of players because, by its nature, one plays high in the horn's harmonic series where the overtones are closer together. This led to the development of the B♭ horn, which, although easier to play accurately, has a less desirable sound in the mid and especially the low register where it is not able to play all of the notes. The solution has been the development of the double horn, which combines the two into one horn with a single lead pipe and bell. Both main types of single horns are still used today as student models because they are cheaper and lighter than double horns. In addition, the single B♭ horns are sometimes used in solo and chamber performances and the single F survives orchestrally as the Vienna horn. Additionally, single F alto and B♭ alto descants are used in the performance of some baroque horn concertos and F, B♭ and F alto singles are occasionally used by jazz performers.
Dennis Brain's benchmark recordings of the Mozart Horn Concerti were made on a single B♭ instrument by Gebr. Alexander, now on display at the Royal Academy of Music in London.
Double horn.
Despite the introduction of valves, the single F horn proved difficult for use in the highest range, where the partials grew closer and closer, making accuracy a great challenge. An early solution was simply to use a horn of higher pitch—usually B♭. The use of the F versus the B♭ horn was extensively debated among horn players of the late 19th century, until the German horn maker Eduard Kruspe (namesake of his family's brass instrument firm) produced a prototype of the "double horn" in 1897.
The double horn also combines two instruments into a single frame: the original horn in F, and a second, higher horn keyed in B♭. By using a fourth valve (usually operated by the thumb), the horn player can quickly switch from the deep, warm tones of the F horn to the higher, brighter tones of the B♭ horn, or vice versa, as the horn player may choose to have the horn set into B♭ by default by making a simple adjustment to the valves. The two sets of tones are commonly called "sides" of the horn. Using the fourth valve not only changes the basic length (and thus the harmonic series and pitch) of the instrument, it also causes the three main valves to use proportionate slide lengths.
In the US, the two most common styles ("wraps") of double horns are named Kruspe and Geyer/Knopf, after the first instrument makers who developed and standardized them. The Kruspe wrap locates the B♭ change valve above the first valve, near the thumb. The Geyer wrap has the change valve behind the third valve, near the little finger (although the valve's trigger is still played with the thumb). In effect, the air flows in a completely different direction on the other model. Kruspe wrap horns tend to be larger in the bell throat than the Geyer wrap horns. Traditionally, Kruspe models are constructed from nickel silver (also called German silver, an alloy of copper, nickel and zinc, containing no actual silver) while Geyer horns tend to be of yellow brass; although these differences in finish aren't as prevalent today - horns of both finishes can be found in either wrap. Both models have their own strengths and weaknesses, and while the choice of instrument