Another factor to consider is that alligators would be unable to form a pucker with their mouth and successfully play the trumpet.
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The intertwining of teeth throughout the top and bottom jaw, as well as the jaw bones themselves, would make it practically impossible to form the enclosed pucker formation of lips and force the needed condensed air in order for the instrument to function as designed.
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In addition to these setbacks, gators lack the required arm length to hold said instrument in the needed position to perform. Standing upright is also a required task of festive jazz playing which gators are unable to accomplish for any significant amount of time.
The lung capacity of gators is more like birds than humans, with one way airflow, which would make the entire process of playing the instrument quite impossible.
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This entire ride is going to be a lie.