Playing long tones for several minutes everyday is important to developing your sound. During this time you can focus on tone, even sound throughout your range and consistancy of air support.
When I have my students play long tones starting from middle C down I have them do it in whole notes with the quartet at about 92. Then I have them listen to their sound as they are moving down diatonically keeping the tone very still with no vibration in the sound. I tell them not to move your embouchure as you change notes keeping the air consistent. After they finish I ask them if there are any notes that didn’t sound very good or was there vibrations or shaking in certain notes they were playing? Some students will have some vibration in the sound as they do long tones because their muscles in their embouchure is not developed enough yet, but continued work on long tones will eventually stabalize the tones.
Then I will have students play from middle C to High F#. If students are using enough air support and a set embouchure the sound will be consistent from bottom to top, but if not certain notes such as Middle D and the palm keys will jump out at you when played.
Long tones is the time you can focus on “your sound”. Always analyze your playing especially when you are doing long tones. If you don’t like the sound of a particular note on your sax ask yourself what can I do to make this sound better? I recommend about 20 minutes of long tones if possible or longer. Your sound is the first thing people hear and if you do not sound good you can have all the technquie possible and no one wants to listen to you.
There is another exercise I like to use with long tones. Same exercise as above, but I hold it for 8 counts starting on C. Start it niente crescendo to FF then move to the next note down and decrescendo to nothing. Then start on the note you ended with and repeat the same process. This exercise is great for developing amazing control and tone.