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Every aspiring saxophonist has to master basic skills that are necessary for good musicianship.
Good Tone Production: This requires not only having a good reed, mouthpiece and ligature, but also a good daily regimen of "long tone" exercises. Long tones are practiced by playing individual tones for a comfortable length of time (6-8 seconds) without stress. For beginners I suggest playing long tones on a simple major scale. Advanced students should use a chromatic scale, octaves and intervals of the perfect fourths and fifths over the full range of the instrument.
Good Intonation: I suggest using a combination of the following tools: a well-tuned piano, an electronic tuner and a good ear-training course. If you haven't taken part in an ear training - NOW'S THE TIME! To be able to play in tune requires the ability to distinguish intervals and musical passages correctly and accurately. This is an invaluable skill for every good musician.
Good Technical Ability: This means practicing your scales, arpeggios and whatever other studies you have available regularly! "Repetition is the Mother of Skill". Not only regularly but also logically. Which means you must develop...
Good Practicing Skills: Often music students get into the habit of playing an exercise or study over and over again, first at a slow pace and eventually faster and that is called "practicing"! There is much more to practicing than that. You must learn to hear and sing the melodies that are being practiced. You must isolate "problem" (rhythmically or technically) passages. Above all, you must develop a regimen and method of practicing and become acutely sensitive to monitoring progress. This takes time and experimentation and perhaps a little bit of research.
Last but not least: before you even start playing or practicing you need a good warm-up. The warm-up starts out as basic as first relaxing your arms and shoulders, stretching the fingers, deep breathing to expand the lungs and make sure you have a standing or sitting posture that supports your breathing and does not disrupt it. On that note I'd like to say, "Have fun and practice with common sense".
