History
The saxophone was created in the mid-1840s by Adolphe Sax, a Belgian-born instrument-maker and clarinetist working in Paris, and was first officially revealed to the public in the patent of 1846 (which was granted to him on May 17). Sax's amazing ability to offend rival instrument manufacturers, and unfortunate prejudice towards the man and his instruments led to it not being used in orchestral groups, and for a long time it was relegated to military bands - this despite his great friendship with the influential Parisian composer Berlioz.
The inspiration for the instrument is unknown, but there is good evidence that fitting a clarinet mouthpiece to an ophicleide is the most likely route (doing so results in a definitely saxophone-like sound). Sax worked in his father's workshop for many years, and both clarinets and ophicleides were manufactured there. Another speculative possibility is that he was trying to force a clarinet to overblow an octave, but this is perhaps unlikely as a man of his experience would have realised that many of the best harmonic properties of the clarinet stem from its cylindrical construction and inherent overblowing at the twelfth. It is likely; however, that Sax's intent was in fact to invent an entirely new instrument which suited his desires both tonally and technically and possessed a new level of flexibility. This would explain why he chose to name the instrument the "voice of Sax."
It is likely that the larger saxes were the first to be used, as Sax intended the saxophone to replace ophicleides in military bands. The smaller saxes, whilst now more common than their larger siblings came later, although all are listed in the patent.
The subsequent development is defined almost entirely in terms of Sax's patent, as for the duration of the patent (1846-1866) no one except the Sax factory in Rue St Georges, Paris could (legally) manufacture or modify the instruments. After 1866 a succession of modifications were introduced by a number of manufacturers, most notably Evette and Schaeffer, Lecomte, Fontaine-Besson and of course the Sax company, leading by the early 1900s to instruments very similar to those of today.
Technique
The first figure below shows a set of basic fingerings for the saxophone. The most important alternate fingerings are those involving Bb, as summarized in the second figure. The split Bb fingering is used in chromatic passages, and also makes a good default fingering because it keeps the hands in their normal positions. The left-hand fingering is often used in passages that have no B-naturals, while the bis fingering is useful for the A-Bb trill.
In the typical embouchure, the top teeth rest on the mouthpiece, while the lower lip is curled slightly so that it comes between the reed and the bottom teeth. Diaphragm and jaw vibrato are both used, with the latter being more typical.
The greatest intonation problems occur with C#, which is flat and can be compensated for with the use of the low C# fingering but with the addition of the octave key, and F#, which is sharp but not so egregiously out of tune as the open C#. This can be corrected by controlling the embouchure. The very highest notes in the normal range may also require correction, but this depends a great deal on the player and the setup. The instrument has faults in intonation, like any instrument, but each player should be held to the same standards as that of any other instrument as it is entirely possible to play the saxophone perfectly in tune.
See also: saxophonist