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Yes I know it's airflow; but it's not just airflow, as the sax can also be blown without making an sound. The airflow makes the reed vibrate, and the reed makes the airflow vibrate???? Which comes first?
Is the answer that the airspeed through the narrow opening of the mouthpiece produces enough low pressure to bend the reed and start the vibration?

Exactly how does "supporting the breath", or breathing from the belly help to make the reed vibrate? Does it somehow increase airspeed?

Secondly how does lip pressure alter pitch? It doesn't shorten the conical tube, so why does the pitch go up so much?

I was just wondering if someone could give a simple technical answer please
Because I keep wondering.
 

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Adding pressure against the reed actually does two things to raise the pitch. It presses the reed up against the facing curve thereby making the reed shorter, and pressing the reed closer to the mouthpiece also decreases the "effective volume" inside the mouthpiece.

The vibrating or "beating" of the reed as it is called when it closes completely each cycle is a marvelously complex phenomenon that has been studied extensively by acoustic scientists. Simply put the reed acts like a "spring" which opens and closes depending on whether the pressure is greater inside or outside the mouthpiece. What is even more fascinating is that the standing wave inside the saxophone influences how fast the reed vibrates on any given note.
 
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