Four main saxophones are common in western music—soprano, alto, tenor and baritone. But there have been many others, some of which can be found manufactured new today and many that have become museum pieces. The saxophone family is much larger than these 4 common saxophones.
On the small side you will find the sopranino and soprillo saxophones. The sopranino sax is in the key of Eb, is smaller than a soprano sax, and plays an octave higher than an alto saxophone. Sopranino saxophones are not very common but the real toy is the soprillo saxophone; half the size of a soprano sax in the key of Bb and so small the octave key is built into the mouthpiece. I know a few players that own a sopranino but none that have a soprillo sax.
On the larger end of the family you will find the bass saxophone; the next larger sax after a baritone. The bass saxophone is in the key of Bb and sounds an octave lower than a Bb tenor sax. These saxophones get really large and very heavy.
And they get bigger…
The contra bass saxophone is twice the size of a baritone saxophone in the key of Eb. I actually know people that own bass and contra bass saxophones. I have also played both recently and can tell you they are large, heavy, and really cool!
As these saxophones get bigger, their design gets more interesting. Where a standard bass sax might just be an overgrown version of a baritone sax, the contra bass saxophones tend to have more bends and rows of tubing to create these ultra low notes while still allowing the instrument to clear the ceiling.
Large saxophones have been around since the beginning of the sax. The inventor of the saxophone, Adolph Sax, actually designed and manufactured a bass saxophone before developing other sizes. His original thought for making the saxophone was to create an instrument that could play more interesting and intricate low melodies for band and orchestra in a bass range. Many of the large instruments of that era did not cover melody very well.
Saxophones do get even bigger, but anything larger than a contra bass sax is very rare.
There were many experiments in various keys for the saxophone that never caught on. The most notable is the C melody saxophone. This sax was made to be able to play piano music in concert C without transcription. C melody saxophones look similar to a tenor sax on a diet and are also called a C tenor. Other oddities in the key center included a very rare C soprano sax and F alto. These are all primarily collector's pieces today.
You will also find shape variations that have had very little impact on the saxophone market like the straight alto, straight tenor, straight baritone, curved soprano and saxello which has a curved neck and tipped bell, or the very rare F Conn-O-Sax that has a neck straight body to a bowl with vents at the far end.
Another weird one was the Grafton plastic saxophone, made famous by Charlie Parker's brief time playing and recording on, what is now, a very sought for oddity.
Yes, every family has its unusual members. There are a few that take this list to an extreme though. The heckelphone was developed to sound similar to an English horn and the sarrusophone used a double reed similar to a bassoon or, a bari sax mouthpiece. Many of these are rare collector's pieces found in museums, a few college campuses, and locked away for the personal collector to enjoy.
As a professional musician, I am relieved that there are only 4 common saxophones in today's music. Can you imagine what it would cost to purchase a dozen or more saxophones to play in any ensemble or band?