 of the connection between planetary motion and FM, see Benson, "Music: A Mathematical Offering".
Just for completeness, here's a derivation following Gray and Mathews, "A Treatise on Bessel Functions":
<img src="pix/fmeq59.png" alt="et again">
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<div class="greenish">simple FM examples</div>

<p>Here's a simple FM instrument:
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<pre class="indented">
(definstrument fm (beg dur freq amp mc-ratio index &amp;optional (index-