The Saxophone is a relatively new instrument, being invented in the 1840's by a man named Adolphe Sax. After looking at the the balance between woodwinds and brass instruments, he believed there was a "missing link" in the ensemble, one that could be a hybrid between Brass and Woodwind. Through a lot of developments, he invented the Saxophone putting the 'hybrid' idea together (brass body with a mouthpiece/reed set up similar to the clarinet). This combination led to an instrument that had the projection ability of a brass instrument and the agility of a Woodwind.
Once his patent expired, instrument manufactures started building their own Saxophones based on his inventions and improved upon them. Jazz, Vaudeville, and other popular music styles led itself very popular to the Saxophone, so brands like C.G. Conn made many to accommodate the demand. C.G. Conn and King (another instrument manufacturer) improved on the design in the 1930's-1940's with Selmer (instrument manufacturer) greatly improving on the design to develop what the modern Saxophone looks like today.
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On all reed instruments, the reed is arguably the most important part of the instrument. These reeds are made out of cane that is thinly cut and then filed to shape. Beginners on Saxophone should start at a 2.5 strength reed (or on some brands, labeled medium soft to medium) and after a while, move up to a 3 or 3.5 (or called medium hard). In a box of reeds, one should try out each reed and find the one or two that play/sound the best and use those as primary reeds. The rest should be used as back up. A good method for rotating reeds is to use your best one 3-4 days a week, second best 2-3 days a week, and a third once a week to make sure. As one breaks, chips, or wears out, move reeds up in the rotation and replace the third as needed. This ensures that one always has a back up reed ready to go at any given moment.
To put together, first put on the neck strap and start moistening the entire reed, not just the thin end. Pick up the body of the Saxophone and attach to the neck strap. Then attach the mouthpiece onto the neck (curvy part). Afterwards attach that to the body of the Saxophone. Make sure the screw at the top of the saxophone is loose, attach it to the top and make sure the extending pin goes inside the opening, and tighten to attach the Saxophone to it. To place the reed onto the mouthpiece, line it up so it is the same height as the mouthpiece, put on the ligature, and then tighten so that it is snug enough that it stays in place. Finally, adjust the neck position and mouthpiece angle to fit embouchure. More here.
The most common embouchure is called the Single Lip embouchure. To do this roll in the bottom lip so that the teeth are covered and then close your lips. Then place the mouthpiece in your mouth and form an airtight seal around it with your top lip and corners of your lips. Make sure you use your lips to form the seal and that you're not biting down to do so. More here.
To hold, first sit up straight and then bring the saxophone to you by tightening the neck strap. Many times, players adjust to the saxophone instead of adjusting it to them, which can lead to poor posture. The saxophone can either go between the legs or outside of the right leg. Check the picture for finger placements (left hand goes on top, red color keys are where fingers go). Make fingers are curled and have a C shape to them. More here.
John Coltrane was born in a small town in North Carolina. He is highly regarded as one of the most influential Jazz Saxophonists of all time. He performed with various groups and influential Jazz artists, most notably Miles Davis and collaborated with legendary pianist/composer, Thelonious Monk.
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