Basic Info

The saxophone in its many different forms is an essential instrument in the jazz genre and for almost any funk, blues or contemporary ensemble. In jazz big bands the saxophone sections provide the essential melodic and harmonic structures of almost any arrangement; their ability to harmonize and double up on lines to punch through the mix is one of the defining characteristic of jazz big band music. In smaller combos the saxophone is associated with some of the most famous jazz musicians ever, including John Coltrane, Charlie Parker, Sonny Rollins, Stan Getz, Cannonball Adderley, Wayne Shorter and countless others.
Types
Soprano Saxophone

Arguably the least common saxophone in most jazz and contemporary ensembles. The soprano saxophone is also a Bb instrument but is pitched one octave higher than the tenor sax (sounds a 2nd lower than written) and produces a higher pitched and much more piercing tone than the alto, tenor or baritone. Many famous saxophone players know for playing other variations have some compositions on the soprano, notably John Coltrane and Wayne Shorter.
Alto Saxophone

A staple of both big band and smaller jazz the alto saxophone is an Eb transposing instrument (sounds a 6th lower than written) pitched between the soprano and tenor. The alto produces a more piercing tone than the tenor saxophone but not quite as much as the soprano and can be used as both a melodic or harmonic instrument in an ensemble/section.
Tenor Saxophone

Common in almost every genre the tenor sax is a Bb transposing instrument pitched one octave lower than the soprano (sounds a 9th lower than written). While the tenor is (arguably) the instrument of choice in rock, blues and funk it is about as common as the alto in the jazz and fusion genres. An incredibly versatile instrument it produces a darker, lower tone than the alto saxophone.
Baritone Saxophone

Most common in jazz and funk big bands the baritone saxophone is an Eb transposing instrument (sounds a 13th lower than written) and is pitched one octave below the alto saxophone. Used to fill out the bottom end of the saxophone section.
Range
Soprano, Alto and Tenor Saxophone
Regular Range

With the exception of the baritone most saxophones have a similar regular and extended range. The safest range to write for a sax is from Bb below the treble clef to about a high F# above, keeping in mind that due to transpositions these notes will sound different on each version of the instrument.
Extended Range

Many skilled saxophone players can extend the standard rage of the saxophone up past the high F# up to about a D above that. Any higher than the standard F# should be used with caution and should be checked with the individual player.
Baritone Saxophone
Regular Range

The baritone sax has the same range as the other types of saxophones with one exception; many bari players also have access to an A3 below the treble clef. The higher range again safely extends up to about F# above the staff.
Extended Range

As with the other versions of the instrument many players can extend the range of the baritone sax higher than the safe high F#. As noted about this should be done with caution and if possible checked with the individual player to insure they have access to this higher range.
Articulations
Articulations
Staccato

Note(s) to be played short and separated. On the saxophone this means each note is articulated/tongued but played slightly shorter than its full value.
Tenuto

Best used in combination with staccato markings to indicate a note is to be played for its full value. Otherwise it means the note should receive some emphasis but what for that will take is context dependent.
Accent

Play the note accented for its full value. Very common when playing lines in a big band horn section.
Marcato

As with jazz arranging in general the marcato articulation usually results in an accented note with a shorter value (about 2/3) than a standard accent. Use for short, punchy lines that need some space and tightness to them.
Slur/Legato

Play smoothly without tonguing each note.
Effects
Special Effects
Glissando

A glissando (sometimes referred to as a slide) is a common brass and woodwind instrument articulation/effect that involves sliding up or down from one note to another. This can be accomplished either by playing chromatically between the two pitches or by bending in the direction of the gliss.
Vibrato

Slight oscillation of a note; used frequently in jazz by default but can be notated as well.
Trill/Shake

A trill on the saxophone is accomplished by playing two notes in rapid succession. Usually by default the trill will either be a whole step or the next logical note (next note in the key or altered note in the bar), accidentals can also be placed above the trill marking to specify which note is to be played.
Fall

A fall indicates a long or short fall-off from a note with no specific ending note; this is most frequently used in jazz and contemporary music. Long falls can be noted with a gliss downwards (first in the example) or with a quick fall marking (second in the example).
Rip

In contrast to a glissando that tends to emphasize a smooth transition between two notes a rip is a more aggressive and has a bit more style to it. Most commonly seen in big band, funk and other contemporary genres.
Doit

A doit is a quick upwards glissando away from a specified pitch with no real discernible ending. Like the rip it is most common in jazz, funk and contemporary music.
Scoop

A scoop is a short gliss to specified note.
Double/Triple Tonguing

Double and triple tonguing is a brass and woodwind instrument technique where notes are articulated rapidly using the tongue.