Many flutists try to play from one register to the other by turning the flute in and out instead of changing only the embouchure. The right way is to modify the direction of the air-stream.
Changing registers by changing the direction of the air-stream
We have 3 registers on the flute
1. Low registers
2. Middle registers
3. High registers
You have to make your lower jaw project or recede to change the direction of the air-stream.
1. Low registers - make lower jaw more recede (more vertical air-stream)
2. Middle registers - make lower jaw not too recede nor too project
3. High registers - make lower jaw more project (more horizontal air-stream)
The following figure represents the cross-section of a head-joint and the approximate directions of the air-stream for those 3 registers.
Modification of the 'air pressure'
As the flute is a wind instrument, we have to play by tensing the diaphragm/stomach muscle. This will produce the air pressure. This system is called 'Support'!
The higher registers, the more air pressure!
1. Low registers - less air pressure
2. Middle registers - more air pressure
3. High registers - a lot of air pressure
Modification of the size of the aperture
The higher registers, the smaller aperture!
1. Low registers - small aperture
2. Middle registers - smaller aperture
3. High registers - very small aperture
Be careful! Many flutists play low notes with too big aperture which makes difficulties of tonguing and causes bad intonation (too flat). Furthermore, 'too big aperture' will block you to the virtuosity!
The size of the aperture for the low notes is just a little bigger then the middle!
Do not open your mouth to play low notes, but try to make your lower jaw backward!
The better and easier way is to start the very first lessons with middle or high registers instead of low registers to prevent a bad habit!
This is the method of the 'French Flute School'.
Philippe Bernold : La Technique d’Embouchure, 3° édition (La Stravagenza)
Henri Altès : Célèbre Méthode Complète de flûte (Leduc)