A Mathematical Method for Harmonizing the Vibrations of Compound Cymbals
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Abstract
Cymbal sounds are generally inharmonic. Using the property that their most energetic vibration modes are the same as those of thin circular plates, we develop a mathematical method to determine new configurations of compound cymbals made up of a centered disk and a ring around it that would vibrate with maximum harmonicity. We exemplify the method with plates made of aluminum and copper.
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