The fourth essential tip focusses upon getting a good control of the mouthpiece.
On a piano it isn't possible to manipulate the pitch of any notes, if you press down a key you always get the same sound. Whereas, on the saxophone you can actually get several different notes out of any one finger position. The way that you can do this is by manipulating your air flow into the mouthpiece by changing the shape of your mouth and throat. Through this you get a better control of your saxophone and therefore your sound, and you will be playing with more intention.
I demonstrate a couple of exercises to practise this, the first being to simply blow down the mouthpiece and see what sound comes out! Whatever pitch you do produce, try to sustain it for as long as you can and as evenly as you can. Before playing the note, go through the process practised in the Breath Control tip - i.e. put your mouthpiece in your mouth; take a long, even breath in; then blow out evenly.
It is useful to practise this exercise with a tuner to monitor the evenness of your airflow and sound. It is quite normal for the tuning to fluctuate dramatically at first, so don't be put off if this does happen. Over time you will gradually gain more control; the goal is to be able to sustain a pitch with very little fluctuation - but this is a goal, I am still to achieve a perfect evenness, so really don't worry if it's taking a while: this is an ongoing exercise to be practised regularly.
The second exercise in this essential tip practises changing the pitch. A warm up exercise for this is to try some whistling! Try whistling a range of pitches, some low and some high. As you do this, think about how it feels inside of your mouth and in your throat; this process is essentially the same when you play the mouthpiece. So, next try it with the mouthpiece. Play a note and then try to lower the sound as far down as you can and then bring it back up again - a bit like a siren. Again, it is quite normal to either find this difficult or to not achieve any movement straight away. Persevere! This too is an ongoing exercise to be practised regularly. The eventual goal with this is to be able to play specific pitches at will and to be able to play scales and arpeggios. But, to begin with any change in pitch is a victory! One warning is to keep your jaw still and to hold the mouthpiece roughly at the angle it would be on the saxophone, otherwise you're not doing the exercise properly.