Experiment with different positions of the oral cavity to see what works best for you and the type of music you are playing. It will take a while to figure out exactly what works best for you, but by listening, experimenting with embouchure formation, and positioning the oral cavity, you will get closer to that rich sound you’re looking for.
While other skills are certainly needed, a warm and full-bodied tone is what distinguishes a good performance from a great one. The sound of the music is what the audience notices first and what they will remember longest after the music has stopped. The embouchure and the breath support are the two most important things you can do to develop a good tone. Concentrate on these rather than the notes themselves. This is also why it is so important to work on your embouchure and breath support before you start playing the saxophone. Fast fingerings and complicated patterns are not as important as a good tone. Working on your embouchure and your breath support will allow you to produce a full, resonant, and rich sound that will improve the overall quality of your playing. The position and firmness of the embouchure and the strength and direction of the air stream are continually manipulated to produce a wide variety of tonal colors and dynamics.
My long tones each day help me learn what a good tone feels like, by playing long tones and focusing on the details of the tone. I begin in the middle of the range and work outwards, and notice that, for instance, the slightest movement of my tongue or the amount I open my jaw or the speed of the air stream changes the tone to sound sharp and bright, or mellow and warm. I record these practice sessions to check objectively on how my tone sounds. After months of this practice, I learn what it takes to create a good core tone, even when I am under pressure during a performance, or my embouchure gets tired. Nothing is ever 100% perfected, but this practice helps me have a consistently good tone day-to-day.
Mouthpiece and reed strength also influence the character of the sound, as some bring out certain harmonics at the expense of others. Using a relatively hard reed and an open mouthpiece can result in a bright sound with good carrying power for playing jazz solos, for example, while a softer combination will provide a warmer more mellow sound for playing ballads. Intelligent use of these variations rather than simply copying others will help a player to develop his or her own sound. Students are often warned against making too many changes once they have found a suitable setup, and instead to work with it to get as much as they can from it.
The third dimension is the vibrato. The vibrato gives the tone a sense of emotion by making the normally static pitches have a sense of pulsing life. To begin, the vibrato should be small and narrow, and should emanate from the diaphragm, not the jaw. The pitch of the note should always be the dominant characteristic of the sound, and the vibrato should add nuance to that pitch. Once the vibrato becomes more consistent and controllable, the pitch can be made to vibrate at various rates and widths depending on the musical situation. For instance, one may want a smaller, narrower vibrato for a more introspective section, or a more luxuriant and wide vibrato in a more exuberant section. The vibrato should be practiced in long tones and scales, so that eventually it becomes a natural part of the sound, rather than an addition to the sound, and it should be practiced alongside straight tones so that one can switch between the two effortlessly and expressively.
Lastly, having a great tone on the saxophone is an expression of the musician’s inner musical mind. Your technical ability and musicality are only as good as your tone allows them to be. It is through regular daily work on your tone that you will get a better sound and thus a bit more freedom to play the types of music you want to play. The fruits of your labor will be rewarded with more of those times when the saxophone feels like it’s playing itself and the music just comes out of the horn as if you were singing or speaking it. Your tone is the core of your sax playing, so focus on it and don’t leave it as an afterthought. This is the key to playing music that has character.