SAX 6^a.1 - When ?

This is of course entirely up to you.
Each student is different, some get into the high squeaks quickly, others battle for quite some time. But the essential requirement to succeed is regular Overtone practice. Without it nothing will happen.

Practise at least 20 minutes each day (5 days a week). At this rate you will get into the Head Register squeaks within one to six months. (In rare cases it can take longer, but don't give up.)

Once you are into the high squeaks the frustrating time is over as you now have something definite to work with.

I went through this process as a full time music student when I could afford one and a half to 2 hours Overtone practice per day. Through this effort I could play all possible Overtones within about 4 months. Their quality steadily improved during several years of sustained practice.
As my other playing skills developed the Overtone work gradually started to improve my normal playing tone.
Whenever I have time to practise these days I still start each session with 30 minutes of Overtones, followed by another 30 minutes of other tone exercises.

Here five more points regarding Overtone practice.

1. Blowing a handful of Overtones at the start of your practice is fine as a warmup, but it will not get you an inch closer to development of your Head Register. This requires a serious effort of sustained practice.

2. It appears to me that development of the Head Register requires a certain total amount of time of Overtone practice. This means that if you spend more time each session on Overtones you will get quicker results.
   If you spend less time each session, it is going to take a bit longer.

   

3. Do not worry about how you get the Overtones. Just get them, but try not to be too tense or 'intense' about it, this can be a main obstacle in the way of progress.
   As you gain more throat flexibility any excessive embouchure pressure will gradually return to normal.

   A relatively new or slightly harder reed sometimes also helps. Use this for Overtone practice only, and use your normal reed for all other playing.

4. After five days intensive Overtone practice you may find your throat somewhat rough. Always take the two remaining days of the week rest to let the throat muscles (and your neighbours ears) recover.
   In time you may find (like I did) that your speaking voice changes somewhat and also improves in clearness and projection.

5. Once you have broken into the Head Register and are able to move around in there, you may find that you are losing some control in your 'normal' playing. You get some unexpected break notes in your playing and also may have trouble with playing in tune.

   This can be disturbing until you realise what is actually happening to you. Your throat has suddenly developed much more flexibility, but you have not yet gained sufficient co-ordination to control this new freedom.

   Therefore, although it may seem that you are going backwards, you have actually made a huge leap forward. Just remain patient and your co-ordination control will catch up with your throat's flexibility.

SAX 6^a.2 - About singers and trumpet players

Well trained classical singers develop of course both their Chest Register and Head Register voice. I have anecdotal evidence that such trained singers can effortlessly play altissimo notes and Overtones on a saxophone.

Brass players too learn to manipulate Overtones with their oral tract from the first day they start practice. Recently an experienced trumpet player started with me as a beginner saxophone student. He could instantly play the full range of Overtones on the alto sax. He quickly changed over to a soprano (his preferred instrument). Within six months he developed a remarkably nice tone on this instrument, perfectly in tune, with a range up to altissimo C. He joined a Regional Concert Band and has been given all flute and clarinet solos besides his own because of his superior tone quality.