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Beginner Will a closed mouthpiece affect my embouchure development

I am not defying the laws of physics jbt - I can only suggest that you spend a few years playing blues harp - A blues harp player doesn't drop his jaw when bending the notes. In the beginning it's easy to do it on the "suck" notes but after a while you'll realize you can also use the same technique on the "blow" notes. It's all about manipulating the note in the oral cavity. I can only suggest you get back in the woodshed jbt and try to concentrate on how your tongue influences your sound and try to become aware of your ability to control it.

With all due respect Spike I have played saxophone for over 50 years. I know how to bend certain pitches using the shape of the oral cavity, back of the tongue, etc. I also know how to change the timbre of certain notes by how they are "voiced".

The blues harp and saxophone are entirely different instruments acoustically. The blues harp has many different reeds and a very small "box" which resonates and helps to amplify the sound. The saxophone has only one reed whose frequency is controlled by the resonance of the body tube. When one plays a low E that tube length resonance couples with the reed and causes it to vibrate at the frequency of E and its overtones.

Acoustic science tells us that in order for the "resonance" of the oral cavity to take over control of the reed's vibrations, the resonance of the body tube must be weak. This is how altissimo fingerings work. They set up a weak resonance in the body tube which allows the oral cavity resonance to take over and produce the desired altissimo note. In fact they have measured the oral cavity resonance of the player to be just slightly higher than the altissimo note they are playing.
 
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