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The language Benade uses is that the reed "collaborates" with the natural resonant frequency of the length of the vibrating air column.* As the length of the "tube" gets shorter and shorter, the natural resonant frequency weakens and has less control over the oscillation of the reed which then allows the player's oral cavity to take charge of the reed's vibrations. This is what makes playing in the altissimo range possible. This is also why an entire octave scale can be played on the mouthpiece alone and why players can play a palm D and lower the pitch as much as a step and a half or more just by changes in the oral cavity. On lower notes with a longer body tube this becomes much more difficult, if not impossible.

In a study entitled "Some Aspects of Tuning and Clean Intonation in Reed Instruments" J. P. Dalmont, B. Gazengel, and others found that the natural resonance frequency of a given note determined by the impedance is somewhat higher than the "played frequency" of the note. Their conclusion was that the mouthpiece combined with the player's embouchure produced a sort of "end correction".

* In my understanding of the term, this is not the same as "sympathetic vibrations" in which an object whose natural resonant frequency matches the frequency of soundwaves coming from another source and is thereby set into vibration. I used to demonstrate this effect to my class by pressing the sustain pedal on a piano and playing a note on a trumpet loudly into the open top. Once the trumpet stopped, one could hear the strings that matched the fundamental and harmonics of the played note sounding only those pitches.
Given this is true, which I believe it to be, what is the significance of blowing a particular pitch on a mouthpiece alone?
 
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