
Natural horn
Main article: Natural horn
The natural horn is the ancestor of the modern horn. It is essentially descended from hunting horns, with its pitch controlled by air speed, aperture (opening of the lips through which the air passes) and the use of the right hand moving in and out of the bell. Today it is played as a period instrument. The natural horn can only play from a single harmonic series at a time because there is only one length of tubing available to the horn player. The player has a choice of key through changing the length of tubing with crooks.
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-flat, although many F horns have longer slides to tune them to E-flat, and almost all B-flat 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 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-flat 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-flat 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-flat alto descants are used in the performance of some baroque horn concertos and F, B-flat 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-flat instrument by Gebr. Alexander, now on display at the Royal Academy of Music in London.

Double horn
A display of double horns made by PaxmanDespite 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-flat. The use of the F versus the B-flat horn were a hotbed of debate between horn players of the late nineteenth century, until the German horn maker Ed. Kruspe 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-flat. By using a fourth valve (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-flat horn. 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.[1]
In the USA, the two most common styles ("wraps") of double horns are named Kruspe and Knopf, after the first instrument makers who developed and standardized them. The Kruspe wrap locates the B-flat change valve above the first valve, near the thumb. The Knopf wrap has the change valve behind the third valve, near the pinky 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 Knopf type. Typically, Kruspe models are constructed from nickel silver or German Silver, while Knopf type horns tend to be of yellow brass. Both models have their own strengths and weaknesses, and while the choice of instrument is very personal, an orchestral horn section is usually found to have either one or the other, owing to the differences in tone color, response, and projection of the two different styles.
In the UK and Europe the most popular horns are arguably those made by Gebr. Alexander, of Mainz (particularly the Alexander 103), and those made by Paxman in London. In Germany and the Benelux countries, the Alex. 103 is extremely popular. These horns do not fit strictly into the Kruspe or Knopf camps, but have features of both. Alexander prefers the traditional medium bell size, which they have produced for many years, whereas Paxman do offer their models in a range of bell throat sizes. In the United States, the Conn 8D, a mass produced instrument based on the Kruspe design, has been extremely popular in many areas (New York, Los Angeles, Cleveland, Philadelphia). Since roughly the early 1990s, however, for reasons ranging from changing tastes to a general dislike of Conn's newer 8Ds, orchestras have been moving away from the popular Conn 8D. Knopf model horns (by Geyer, Karl Hill, Keith Berg, Steve Lewis, Dan Rausch, and Ricco-Kuhn) are used in other areas (San Francisco, Chicago, Pittsburgh, Boston, Houston).

Vienna horn
Vienna hornMain article: Vienna horn
The Vienna horn is a special horn used primarily in Vienna, Austria. Instead of using rotary valves or piston valves, it uses the Pumpenvalve (or Vienna Valve), which is a double-piston operating inside of the valve slides, and usually situated on the opposite side of the corpus from the player's left hand, and operated by a long pushrod. Unlike the modern horn, which has grown considerably larger internally (for a bigger, broader, and louder tone), and considerably heavier (with the addition of valves and tubing in the case of the double horn) the Vienna horn very closely mimics the size and weight of the natural horn, (although the valves do add some weight, they are lighter than rotary valves) even using crooks in the front of the horn, between the mouthpiece and the instrument. Although instead of the full range of keys, Vienna horn players usually use an F crook for most music, switching to an A or B-flat crook for higher pitched music (Beethoven 7th symphony, Bach, various Mozart and Haydn, etc). Vienna horns are often used with funnel shaped mouthpieces similar to those used on the natural horn, with very little (if any) backbore and a very thin rim. The Viennese horn requires very specialized technique and can be quite challenging to play, even for accomplished players of modern horns.